diff --git a/README.rst b/README.rst
index 8728bcc2..7feb0258 100644
--- a/README.rst
+++ b/README.rst
@@ -66,7 +66,7 @@ Installation
 Supported Python Versions
 -------------------------
 
-The most recent version of GerryChain (as of February 2024) supports
+The most recent version of GerryChain (as of April 2024) supports
 
 - Python 3.9
 - Python 3.10
@@ -196,7 +196,7 @@ adjacencies or reading in shapefiles, then run
 This approach sometimes fails due to compatibility issues between our
 different Python GIS dependencies, like ``geopandas``, ``pyproj``,
 ``fiona``, and ``shapely``. If you run into this issue, try installing
-the dependencies using the `geo_settings.txt <https://github.com/mggg/GerryChain/raw/main/docs/geo_settings.txt>`_
+the dependencies using the `geo_settings.txt <https://github.com/mggg/GerryChain/tree/main/docs/geo_settings.txt>`_
 file. To do this, run ``pip install -r geo_settings.txt`` from the
 command line.
 
diff --git a/docs/_static/BG_05.json b/docs/_static/BG_05.json
new file mode 100644
index 00000000..c2018bb9
--- /dev/null
+++ b/docs/_static/BG_05.json
@@ -0,0 +1 @@
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\ No newline at end of file
diff --git a/docs/index.rst b/docs/index.rst
index 0a222281..0418c076 100644
--- a/docs/index.rst
+++ b/docs/index.rst
@@ -51,6 +51,7 @@ repository, where `bug reports and feature requests`_, as well as
     user/updaters
     user/data
     user/geometries
+    user/optimizers
 
 We also highly recommend the resources prepared by Daryl R. DeFord of
 MGGG for the 2019 MIT IAP course `Computational Approaches for Political Redistricting`_.
@@ -73,6 +74,7 @@ MGGG for the 2019 MIT IAP course `Computational Approaches for Political Redistr
     topics/reproducibility
     topics/tools
     topics/contributing
+    topics/reporting
 
 
 .. toctree::
diff --git a/docs/repeated_subsections/reproducible_envs.rst b/docs/repeated_subsections/reproducible_envs.rst
new file mode 100644
index 00000000..ed40cc40
--- /dev/null
+++ b/docs/repeated_subsections/reproducible_envs.rst
@@ -0,0 +1,243 @@
+Making an Environment Reproducible
+----------------------------------
+
+If you are working on a project wherein you would like to ensure
+particular runs are reproducible, it is necessary to invoke
+
+- **MacOS/Linux**: ``export PYTHONHASHSEED=0``
+- **Windows**: 
+
+  - PowerShell ``$env:PYTHONHASHSEED=0``
+  - Command Prompt ``set PYTHONHASHSEED=0``
+
+before running your code. This will ensure that the hash seed is deterministic
+which is important for the replication of spanning trees across your runs. If you
+would prefer to not have to do this every time, then you need to modify the
+activation script for the virtual environment. Again, this is different depending
+on your operating system:
+
+- **MacOS/Linux**: Open the file ``.venv/bin/activate`` located in your working
+  directory using your favorite text editor
+  and add the line ``export PYTHONHASHSEED=0`` after the ``export PATH`` command. 
+  So you should see something like:: 
+
+    _OLD_VIRTUAL_PATH="$PATH"
+    PATH="$VIRTUAL_ENV/Scripts:$PATH"
+    export PATH
+
+    export PYTHONHASHSEED=0
+  
+  Then, verify that the hash seed is set to 0 in your Python environment by
+  running ``python`` from the command line and typing 
+  ``import os; print(os.environ['PYTHONHASHSEED'])``.
+
+- **Windows**: To be safe, you will need to modify 3 files within your virtual
+  environment:
+
+  - ``.venv\Scripts\activate``: Add the line ``export PYTHONHASHSEED=0`` after
+    the ``export PATH`` command. So you should see something like:: 
+
+      _OLD_VIRTUAL_PATH="$PATH"
+      PATH="$VIRTUAL_ENV/Scripts:$PATH"
+      export PATH
+
+      export PYTHONHASHSEED=0
+
+  - ``.venv\Scripts\activate.bat``: Add the line ``set PYTHONHASHSEED=0`` to the
+    end of the file. So you should see something like::
+
+      if defined _OLD_VIRTUAL_PATH set PATH=%_OLD_VIRTUAL_PATH%
+      if not defined _OLD_VIRTUAL_PATH set _OLD_VIRTUAL_PATH=%PATH%
+
+      set PATH=%VIRTUAL_ENV%\Scripts;%PATH%
+      rem set VIRTUAL_ENV_PROMPT=(.venv) 
+      set PYTHONHASHSEED=0
+
+  - ``.venv\Scripts\Activate.ps1``: Add the line ``$env:PYTHONHASHSEED=0`` to the
+    end of the before the signature block. So you should see something like::
+
+      # Add the venv to the PATH
+      Copy-Item -Path Env:PATH -Destination Env:_OLD_VIRTUAL_PATH
+      $Env:PATH = "$VenvExecDir$([System.IO.Path]::PathSeparator)$Env:PATH"
+
+      $env:PYTHONHASHSEED=0
+
+      # SIG # Begin signature block
+
+After you have made these changes, verify that the hash seed is set to 0 in your
+Python environment by running ``python`` from the command line and typing 
+``import os; print(os.environ['PYTHONHASHSEED'])`` in the Python prompt.
+
+Reproducible Environments in VSCode and Jupyter Lab 
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In general, it is easier to use jupyter notebooks with bespoke virtual environments
+through a text editor like `VSCode <https://code.visualstudio.com/download>`_, but
+we will also show how to do this using the standard Jupyter Lab interface as well.
+
+Regardless of which method you prefer, you will need to make sure that you have
+installed the ``ipykernel`` package into the virtual environment that you will be
+working with:
+
+.. code:: console
+
+  pip install ipykernel
+
+
+VSCode
+~~~~~~
+
+First you will want to make sure that you have 
+`installed VSCode <https://code.visualstudio.com/download>`_.
+Then, you can click on "File" in the upper-left and select "Open Folder" to open the
+folder with your project and virtual environment in it. This should look something like
+this:
+
+.. image:: ../user/images/vscode_tutorial/open_the_folder.png
+  :align: center
+
+Notice that I have the folder ``.venv`` in my file explorer. This is just my virtual
+environment that I created for this project.
+
+
+To install the Python extension, open the extensions view by clicking on the square
+icon on the left side of the window. Then, search for "Python" and install the
+extension that is published by Microsoft. This will allow you to use the Python
+interpreter in your virtual environment and will give you some helpful things like
+code completion and debugging in the event that you would like it.
+
+.. image:: ../user/images/vscode_tutorial/python_extension_vscode.png
+  :align: center
+
+Likewise, we will want to install the "Jupyter" extension:
+
+.. image:: ../user/images/vscode_tutorial/jupyter_extension_vscode.png
+  :align: center
+
+Now let's make a new jupyter notebook. You can do this by right-clicking in the file
+explorer (or by using the File menu) and selecting "New File".
+
+.. image:: ../user/images/vscode_tutorial/Make_a_new_file.png
+  :align: center
+
+.. raw:: html
+
+   &nbsp;
+
+Then, you will want to save the file with the extension ``.ipynb`` since we are making
+a jupyter notebook. We can now open the file and select the Python interpreter
+that we would like to use:
+
+
+.. image:: ../user/images/vscode_tutorial/select_kernel_vscode.png
+  :align: center
+
+.. image:: ../user/images/vscode_tutorial/select_python_env.png
+  :align: center
+
+.. image:: ../user/images/vscode_tutorial/selecting_correct_venv.png
+  :align: center
+
+And now we are done! We can now use all of the packages in our ``.venv`` virtual environment
+inside of our jupyter notebook:
+
+.. image:: ../user/images/vscode_tutorial/show_gerrychain_import.png
+  :align: center
+
+Of course, if you would like to, you may also use a different name for your virtual environment,
+or you can even use the same process to allow for multiple virtual environments in the same
+project!
+
+
+Jupyter Lab / Notebook
+~~~~~~~~~~~~~~~~~~~~~~
+
+In order to use Jupyter Lab or Jupyter Notebook, we will need to make sure that it is installed
+for our virtual environment. This can be done by running the following command:
+
+.. code:: console
+
+  pip install jupyter
+
+Then, we will want to install the kernel for our virtual environment. This can be done by running
+the following command:
+
+.. code:: console
+
+  python -m ipykernel install --user --name=.venv
+
+
+Now, we can open Jupyter Lab by running the following command:
+
+.. code:: console
+
+  jupyter lab
+
+You will now see that the ``.venv`` is available in your list of kernels:
+
+.. image:: ../user/images/jupyter_tutorial/jupyter_lab.png
+  :align: center
+
+
+.. warning::
+
+  As opposed to VSCode, Jupyter Lab does not automatically use the virtual environment that
+  you have in your project, so you will need to make sure that you have the correct kernel
+  installed before opening the lab. You can see which kernel you are using by looking at the
+  output of the following command:
+
+  .. code:: console
+
+    jupyter kernelspec list
+
+  this will output something like
+
+  .. code:: console
+
+    Available kernels:
+      .venv      /Users/username/.local/share/jupyter/kernels/.venv
+      python3    /usr/local/share/jupyter/kernels/python3
+
+  You will then need to inspect the output of this command to see where the kernel is located.
+  In the above example, we can see that the kernel ``.venv`` is located at 
+  ``/Users/username/.local/share/jupyter/kernels/.venv`` which is the correct location for the
+  current working project. However, if we were to make a new project in 
+  ``/Users/username/Desktop/another_project`` and make a new virtual environment in this
+  location with the same name of ``.venv``, then, after running the command
+  ``python -m ipykernel install --user --name=.venv``,
+  the kernel will still look like it is located at 
+  ``/Users/username/.local/share/jupyter/kernels/.venv``, BUT this new kernel is actually
+  the one for for the second project and not the original! This is important to note because
+  if you are working on multiple projects and you have the same kernel name for each project,
+  things can get a little confusing, so it is best to always reinstall the appropriate kernel
+  before opening the project in Jupyter.
+
+  Of course, an easy fix for this is to just use a different name for the kernel in each project.
+  For example, I might make my kernel name for the project in 
+  ``/Users/username/Desktop/gerrychain_docs``
+  ``venv_gerrychain_docs`` via the command
+
+  .. code:: console
+
+    python -m ipykernel install --user --name=venv_gerrychain_docs
+
+  and the kernel name for the project in 
+  ``/Users/username/Desktop/another_project`` ``venv_another_project``.
+
+
+We can now make a new notebook and select the kernel that we would like to use: 
+
+.. image:: ../user/images/jupyter_tutorial/make_new_file.png
+  :align: center
+
+.. image:: ../user/images/jupyter_tutorial/select_kernel.png
+  :align: center
+
+.. raw:: html
+
+   &nbsp;
+
+Lastly, we can import GerryChain and use it in our notebook:
+
+.. image:: ../user/images/jupyter_tutorial/show_import_working.png
+  :align: center
\ No newline at end of file
diff --git a/docs/topics/reporting.rst b/docs/topics/reporting.rst
new file mode 100644
index 00000000..1d19478c
--- /dev/null
+++ b/docs/topics/reporting.rst
@@ -0,0 +1,12 @@
+================
+Reporting Issues
+================
+
+Sometimes, you may encounter a problem with GerryChain, and that is okay! We would
+love to hear about it so that we can fix it. If you can provide a minimal example that
+reproduces the issue, please feel free to report it on the `GitHub issue tracker
+<https://github.com/mggg/GerryChain/issues>`_.
+
+In the event that you would prefer not to post the issue publicly, you can also email
+us at "code[at]mggg[dot]org". We will do our best to respond to your issue in a timely
+manner. Thank you for your help in making GerryChain better! 
\ No newline at end of file
diff --git a/docs/topics/reproducibility.rst b/docs/topics/reproducibility.rst
index 669453f5..32f71385 100644
--- a/docs/topics/reproducibility.rst
+++ b/docs/topics/reproducibility.rst
@@ -63,127 +63,33 @@ running process and is compatible across future and past releases of GerryChain.
 Use the same versions of all of your dependencies
 -------------------------------------------------
 
+
 You will want to make sure that anyone who tries to repeat your analysis by
 running your code will have the exact same versions of all of the software and packages
 that you use, including the same version of Python.
 
-The easiest way to do this is to use `conda`_ to manage all of your dependencies.
-You can use conda to export an ``environment.yml`` file that anyone can use to replicate your
-environment by running the command ``conda env create -f environment.yml``. For instructions on
-how to do this, see `Sharing your environment`_ and `Creating an environment from an environment.yml file`_
-in the conda documentation.
-
-If you've published your code on GitHub, it is a good idea to include your ``environment.yml``
-file in the root folder of your code repository.
-
-.. _`conda`: https://conda.io/projects/conda/en/latest/index.html
-.. _`Sharing your environment`: https://conda.io/projects/conda/en/latest/user-guide/tasks/manage-environments.html#sharing-an-environment
-.. _`Creating an environment from an environment.yml file`: https://conda.io/projects/conda/en/latest/user-guide/tasks/manage-environments.html#creating-an-environment-from-an-environment-yml-file
-
-
-Making Your Environment Reproducible
-------------------------------------
-
-If you are working on a project wherein you would like to ensure
-particuluar runs are reproducible, it is necessary to invoke
-
-- **MacOS/Linux**: ``export PYTHONHASHSEED=0``
-- **Windows**: 
-
-  - PowerShell ``$env:PYTHONHASHSEED=0``
-  - Command Prompt ``set PYTHONHASHSEED=0``
-
-before running your code. This will ensure that the hash seed is deterministic
-which is important for the replication of spanning trees accross your runs. If you
-would prefer to not have to do this every time, then you need to modify the
-activation script for the virtual environment. Again, this is different depending
-on your operating system:
-
-- **MacOS/Linux**: Open the file ``.venv/bin/activate`` located in your working
-  directory using your favorite text editor
-  and add the line ``export PYTHONHASHSEED=0`` after the ``export PATH`` command. 
-  So you should see something like:: 
-
-    _OLD_VIRTUAL_PATH="$PATH"
-    PATH="$VIRTUAL_ENV/Scripts:$PATH"
-    export PATH
-
-    export PYTHONHASHSEED=0
-  
-  Then, verify that the hash seed is set to 0 in your Python environment by
-  running ``python`` from the command line and typing 
-  ``import os; print(os.environ['PYTHONHASHSEED'])``.
-
-- **Windows**: To be safe, you will need to modify 3 files within your virtual
-  environment:
-
-  - ``.venv\Scripts\activate``: Add the line ``export PYTHONHASHSEED=0`` after
-    the ``export PATH`` command. So you should see something like:: 
-
-      _OLD_VIRTUAL_PATH="$PATH"
-      PATH="$VIRTUAL_ENV/Scripts:$PATH"
-      export PATH
-
-      export PYTHONHASHSEED=0
-
-  - ``.venv\Scripts\activate.bat``: Add the line ``set PYTHONHASHSEED=0`` to the
-    end of the file. So you should see something like::
-
-      if defined _OLD_VIRTUAL_PATH set PATH=%_OLD_VIRTUAL_PATH%
-      if not defined _OLD_VIRTUAL_PATH set _OLD_VIRTUAL_PATH=%PATH%
-
-      set PATH=%VIRTUAL_ENV%\Scripts;%PATH%
-      rem set VIRTUAL_ENV_PROMPT=(.venv) 
-      set PYTHONHASHSEED=0
-
-  - ``.venv\Scripts\Activate.ps1``: Add the line ``$env:PYTHONHASHSEED=0`` to the
-    end of the before the signature bolck. So you should see something like::
-
-      # Add the venv to the PATH
-      Copy-Item -Path Env:PATH -Destination Env:_OLD_VIRTUAL_PATH
-      $Env:PATH = "$VenvExecDir$([System.IO.Path]::PathSeparator)$Env:PATH"
-
-      $env:PYTHONHASHSEED=0
-
-      # SIG # Begin signature block
-
-After you have made these changes, verify that the hash seed is set to 0 in your
-Python environment by running ``python`` from the command line and typing 
-``import os; print(os.environ['PYTHONHASHSEED'])`` in the Python prompt.
-
-.. admonition:: A Note on Jupyter
-  :class: note
-
-  If you are using a jupyter notebook, you will need to make sure that you have
-  installed the ``ipykernel`` package in your virtual environment as well as
-  either ``jupyternotebook`` or ``jupyterlab``. To install these packages, run
-  ``pip install <package-name>`` from the command line. Then, to use the virtual
-  python environment in your jupyter notebook, you need to invoke
-  
-  .. code-block:: console
-
-    jupyter notebook
+The best way to do this is to create a `virtual environment <../user/install.html#virtual-envs>`_ 
+and then save all of the dependencies to a file. This will allow anyone to recreate the
+exact same environment that you used to run your code. To save the packages that are in
+your current virtual environment, simply run
 
-  or
+.. code:: console 
 
-  .. code-block:: console
+  pip freeze > requirements.txt
 
-    jupyter lab
+and this will save the versions of all of your packages to a file called
+``requirements.txt``. You can then share this file with anyone who wants to run your code,
+and they can create the same virtual environment by running
 
-  from the command line of your working directory *while your virtual environment
-  is activated*. This will open a jupyter notebook in your default browser. You may
-  then check that the hash seed is set to 0 by running the following code in a cell
-  of your notebook:
+.. code:: console
 
-  .. code-block:: python
+  pip install -r requirements.txt
 
-    import os
-    print(os.environ['PYTHONHASHSEED'])
+Of course, you will both be responsible for making sure that your virtual environments
+have the same ``PYTHONHASHSEED`` set. How to do this is detailed in the next section.
 
 
-Of course, once this is all done, it would be a good idea to save the random seed
-that you used somewhere so that others may replicate your work in the future.
+.. include:: ../repeated_subsections/reproducible_envs.rst
 
-.. _`environment variable`: https://en.wikipedia.org/wiki/Environment_variable
 .. _`pcompress`: https://github.com/mggg/pcompress
 .. _`install Cargo`: https://doc.rust-lang.org/cargo/getting-started/installation.html
diff --git a/docs/user/data.rst b/docs/user/data.rst
index f6007874..6fd2dbb3 100644
--- a/docs/user/data.rst
+++ b/docs/user/data.rst
@@ -24,7 +24,7 @@ Writing Data to JSONL
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/docs/user/geometries.rst b/docs/user/geometries.rst
index f6c11875..7d80a7ba 100644
--- a/docs/user/geometries.rst
+++ b/docs/user/geometries.rst
@@ -35,7 +35,7 @@ Loading and Running a Plan
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/MN.zip" class="download-badge" download>Download MN File</a>
     </div>
     <br style="line-height: 5px;">
 
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diff --git a/docs/user/images/vscode_tutorial/selecting_correct_venv.png b/docs/user/images/vscode_tutorial/selecting_correct_venv.png
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diff --git a/docs/user/install.rst b/docs/user/install.rst
index 3c805a91..76bbcb75 100644
--- a/docs/user/install.rst
+++ b/docs/user/install.rst
@@ -4,7 +4,7 @@ Installation
 Supported Python Versions
 -------------------------
 
-The most recent version of GerryChain (as of January 2024) supports
+The most recent version of GerryChain (as of April 2024) supports
 
 - Python 3.9
 - Python 3.10
@@ -37,6 +37,8 @@ download the installer for one of these versions. [1]_
   and for the use of the Linux Subsystem for Windows).
 
 
+.. _virtual-envs:
+
 Setting Up a Virtual Environment
 --------------------------------
 
@@ -136,7 +138,7 @@ This approach sometimes fails due to compatibility issues between our
 different Python GIS dependencies, like ``geopandas``, ``pyproj``,
 ``fiona``, and ``shapely``. If you run into this issue, try installing
 the dependencies using the 
-`geo_settings.txt <https://github.com/mggg/GerryChain/raw/main/docs/geo_settings.txt>`_
+`geo_settings.txt <https://github.com/mggg/GerryChain/tree/main/docs/geo_settings.txt>`_
 file. To do this, run ``pip install -r geo_settings.txt`` from the
 command line.
 
@@ -154,101 +156,5 @@ command line.
   Python directly from the package manager if you find installing from source to be
   troublesome.
 
-Making an Environment Reproducible
-----------------------------------
-
-If you are working on a project wherein you would like to ensure
-particular runs are reproducible, it is necessary to invoke
-
-- **MacOS/Linux**: ``export PYTHONHASHSEED=0``
-- **Windows**: 
-
-  - PowerShell ``$env:PYTHONHASHSEED=0``
-  - Command Prompt ``set PYTHONHASHSEED=0``
-
-before running your code. This will ensure that the hash seed is deterministic
-which is important for the replication of spanning trees across your runs. If you
-would prefer to not have to do this every time, then you need to modify the
-activation script for the virtual environment. Again, this is different depending
-on your operating system:
-
-- **MacOS/Linux**: Open the file ``.venv/bin/activate`` located in your working
-  directory using your favorite text editor
-  and add the line ``export PYTHONHASHSEED=0`` after the ``export PATH`` command. 
-  So you should see something like:: 
-
-    _OLD_VIRTUAL_PATH="$PATH"
-    PATH="$VIRTUAL_ENV/Scripts:$PATH"
-    export PATH
-
-    export PYTHONHASHSEED=0
-  
-  Then, verify that the hash seed is set to 0 in your Python environment by
-  running ``python`` from the command line and typing 
-  ``import os; print(os.environ['PYTHONHASHSEED'])``.
-
-- **Windows**: To be safe, you will need to modify 3 files within your virtual
-  environment:
-
-  - ``.venv\Scripts\activate``: Add the line ``export PYTHONHASHSEED=0`` after
-    the ``export PATH`` command. So you should see something like:: 
-
-      _OLD_VIRTUAL_PATH="$PATH"
-      PATH="$VIRTUAL_ENV/Scripts:$PATH"
-      export PATH
-
-      export PYTHONHASHSEED=0
-
-  - ``.venv\Scripts\activate.bat``: Add the line ``set PYTHONHASHSEED=0`` to the
-    end of the file. So you should see something like::
-
-      if defined _OLD_VIRTUAL_PATH set PATH=%_OLD_VIRTUAL_PATH%
-      if not defined _OLD_VIRTUAL_PATH set _OLD_VIRTUAL_PATH=%PATH%
-
-      set PATH=%VIRTUAL_ENV%\Scripts;%PATH%
-      rem set VIRTUAL_ENV_PROMPT=(.venv) 
-      set PYTHONHASHSEED=0
-
-  - ``.venv\Scripts\Activate.ps1``: Add the line ``$env:PYTHONHASHSEED=0`` to the
-    end of the before the signature block. So you should see something like::
-
-      # Add the venv to the PATH
-      Copy-Item -Path Env:PATH -Destination Env:_OLD_VIRTUAL_PATH
-      $Env:PATH = "$VenvExecDir$([System.IO.Path]::PathSeparator)$Env:PATH"
-
-      $env:PYTHONHASHSEED=0
-
-      # SIG # Begin signature block
-
-After you have made these changes, verify that the hash seed is set to 0 in your
-Python environment by running ``python`` from the command line and typing 
-``import os; print(os.environ['PYTHONHASHSEED'])`` in the Python prompt.
-
-.. admonition:: A Note on Jupyter
-  :class: note
-
-  If you are using a jupyter notebook, you will need to make sure that you have
-  installed the ``ipykernel`` package in your virtual environment as well as
-  either ``jypyternotebook`` or ``jupyterlab``. To install these packages, run
-  ``pip install <package-name>`` from the command line. Then, to use the virtual
-  python environment in your jupyter notebook, you need to invoke
-  
-  .. code-block:: console
-
-    jupyter notebook
-
-  or
-
-  .. code-block:: console
-
-    jupyter lab
-
-  from the command line of your working directory *while your virtual environment
-  is activated*. This will open a jupyter notebook in your default browser. You may
-  then check that the hash seed is set to 0 by running the following code in a cell
-  of your notebook:
-
-  .. code-block:: python
 
-    import os
-    print(os.environ['PYTHONHASHSEED'])
\ No newline at end of file
+.. include:: ../repeated_subsections/reproducible_envs.rst
diff --git a/docs/user/optimizers.rst b/docs/user/optimizers.rst
new file mode 100644
index 00000000..3e8add69
--- /dev/null
+++ b/docs/user/optimizers.rst
@@ -0,0 +1,249 @@
+==================================
+Optimization Methods of GerryChain
+==================================
+
+In GerryChain, we provide a class known as the ``SingleMetricOptimizer`` as well as a
+``Gingelator`` subclass that allow us to perform optimization runs.
+
+
+Currently, there are 3 different optimization methods available in GerryChain:
+
+- **Short Bursts**: This method chains together a series of neutral explorers. The main
+  idea is to run the chain for a short period of time (short burst) and then continue
+  the chain from the partition that maximizes the objective function within the most
+  recent short burst. For more information, please refer to 
+  `this paper <https://arxiv.org/abs/2011.02288>`_.
+
+- **Simulated Annealing**: This method varies the probablity of accepting a worse plan
+  according to a temperature schedule which ranges from 0 to 1.
+
+- **Tilted Runs**: This method accepts a worse plan with a fixed probability :math:`p`,
+  and always accepts better plans.
+
+
+While sampling naively with GerryChain can give us an understanding of the neutral
+baseline for a state, there are often cases where we want to find plans with
+properties that are rare to encounter in a neutral run. Many states have
+laws/guidelines that state that plans should be as compact as feasibly possible, maximize
+preservation of political boundaries and/or communities of interest; some even look to
+minimize double bunking of incumbents or seek proportionality/competitiveness in
+contests. Heuristic optimization methods can be used to find example plans with these
+properties and to explore the trade-offs between them.
+
+
+.. raw:: html
+
+    <div class="center-container">
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/BG_05.json" class="download-badge" download>
+        Download Example File
+      </a>
+    </div>
+    <br style="line-height: 5px;">
+
+The first thing we should do is set up our import statements
+
+.. code:: python
+
+    from gerrychain import (GeographicPartition, Partition, Graph, MarkovChain,
+                            proposals, updaters, constraints, accept, Election)
+    from gerrychain.optimization import SingleMetricOptimizer, Gingleator
+    from gerrychain.tree import recursive_seed_part
+    from functools import partial
+    import pandas as pd
+    import json
+    from networkx.readwrite import json_graph
+    import matplotlib.pyplot as plt
+    from tqdm import tqdm
+    import numpy as np
+    import random
+
+    random.seed(2024)
+
+
+And now we load in our file and set up our initial chain.
+
+.. code:: python
+
+    graph = Graph.from_json("BG_05.json")
+
+    POPCOL = "TOTPOP"
+    SEN_DISTS = 35
+    EPS = 0.02
+    TOTPOP = sum(graph.nodes()[n][POPCOL] for n in graph.nodes())
+
+    chain_updaters = {
+    "population": updaters.Tally(POPCOL, alias="population"),
+    "VAP": updaters.Tally("VAP"),
+    "BVAP": updaters.Tally("BVAP")
+    }
+
+    initial_partition = Partition.from_random_assignment(
+        graph=graph,
+        n_parts=SEN_DISTS,
+        epsilon=EPS,
+        pop_col=POPCOL,
+        updaters=chain_updaters
+    )
+
+    proposal = partial(
+        proposals.recom,
+        pop_col=POPCOL,
+        pop_target=TOTPOP/SEN_DISTS,
+        epsilon=EPS,
+        node_repeats=1
+    )
+
+    constraints = constraints.within_percent_of_ideal_population(initial_partition, EPS)
+
+
+Using ``SingleMetricOptimizer``
+-------------------------------
+
+Now the ``SingleMetricOptimizer`` is set up as a wrapper around our basic ``MarkovChain``
+class, so interacting with it should be familiar. To set up our optimizer, we simply
+pass it a proposal function, some constraints, an initial state, and the objective function:
+
+.. code:: python
+
+    num_cut_edges = lambda p: len(p["cut_edges"])
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=constraints,
+        initial_state=initial_partition,
+        optimization_metric=num_cut_edges,
+        maximize=False
+    )
+
+And now we can run each of the optimization methods and collect some data!
+
+.. code:: python
+
+    total_steps = 10000
+    
+    # Short Bursts
+    min_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(optimizer.short_bursts(5, 2000, with_progress_bar=True)):
+        min_scores_sb[i] = optimizer.best_score
+    
+    # Simulated Annealing
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.jumpcycle_beta_function(200, 800),
+            beta_magnitude=1,
+            with_progress_bar=True
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    # Tilted Runs
+    min_scores_tilt = np.zeros(total_steps)
+    for i, part in enumerate(optimizer.tilted_run(total_steps, p=0.125, with_progress_bar=True)):
+        min_scores_tilt[i] = optimizer.best_score
+
+We can then plot the results to see how each method performed:
+
+.. code:: python
+
+    fig, ax = plt.subplots(figsize=(12,6))
+    plt.plot(min_scores_sb, label="Short Bursts")
+    plt.plot(min_scores_anneal, label="Simulated Annealing")
+    plt.plot(min_scores_tilt, label="Tilted Run")
+    plt.xlabel("Steps", fontsize=20)
+    plt.ylabel("Min #CutEdges Observered", fontsize=20)
+    plt.legend()
+    plt.show()
+
+
+This should give you something like:
+
+.. image:: ./images/single_metric_opt_comparison.png
+    :align: center
+    :alt: Single Metric Optimization Method Comparison Image
+
+
+Using ``Gingleator``
+--------------------
+
+Named for the Supreme Court case *Thornburg v. Gingles*, **Gingles' Districts** are
+districts that are 50% + 1 of a minority population subgroup (more colloquially called
+majority-minority districts).  It is common to seek plans with greater/maximal numbers
+of Gingles' districts to understand the landscape of the state space.
+
+The ``Gingleator`` class is a subclass of the ``SingleMetricOptimizer`` class, so much of
+the setup is the same:
+
+.. code:: python
+
+    gingles = Gingleator(
+        proposal, 
+        constraints, 
+        initial_partition,
+        minority_pop_col="BVAP",
+        total_pop_col="VAP",
+        score_function=Gingleator.reward_partial_dist
+    )
+
+Likewise, the methods are similar as well:
+
+.. code:: python
+
+    total_steps = 10000
+
+    # Short Bursts
+    max_scores_sb = np.zeros(total_steps)
+    scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(gingles.short_bursts(10, 1000, with_progress_bar=True)):
+        max_scores_sb[i] = gingles.best_score
+        scores_sb[i] = gingles.score(part)    
+
+    # Simulated Annealing
+    max_scores_anneal = np.zeros(total_steps)
+    scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        gingles.simulated_annealing(
+            total_steps,
+            gingles.jumpcycle_beta_function(1000, 4000),
+            beta_magnitude=500, 
+            with_progress_bar=True
+        )
+    ):
+        max_scores_anneal[i] = gingles.best_score
+        scores_anneal[i] = gingles.score(part)
+
+    # Tilted Runs
+    max_scores_tilt = np.zeros(total_steps)
+    scores_tilt = np.zeros(total_steps)
+    for i, part in enumerate(gingles.tilted_run(total_steps, 0.125, with_progress_bar=True)):
+        max_scores_tilt[i] = gingles.best_score
+        scores_tilt[i] = gingles.score(part)
+
+And we can plot the results again:
+
+.. code:: python
+
+    fig, ax = plt.subplots(figsize=(12,6))
+    plt.plot(max_scores_sb, label="Short Bursts")
+    plt.plot(max_scores_anneal, label="Simulated Annealing")
+    plt.plot(max_scores_tilt, label="Tilted Run")
+    plt.xlabel("Steps", fontsize=20)
+    plt.ylabel("Max Score Observered", fontsize=20)
+    plt.legend()
+    plt.show()
+
+This should give you something like:
+
+.. image:: ./images/gingleator_maxes.png
+    :align: center
+    :alt: Gingleator Optimization Method Comparison Image
+
+And we can see a little better how each method performs over the course of the run:
+
+.. image:: ./images/gingleator_all.png
+    :align: center
+    :alt: Gingleator Optimization Method Comparison All Steps Image
+
+From this we can observe that, throughout the entire run, the score function can dip all
+the way back down to 0 even relatively shortly after being at the maximum of 4.5.
\ No newline at end of file
diff --git a/docs/user/partitions.rst b/docs/user/partitions.rst
index 2bbe049b..ebdb1242 100644
--- a/docs/user/partitions.rst
+++ b/docs/user/partitions.rst
@@ -4,7 +4,7 @@ Working with Partitions
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
@@ -17,7 +17,7 @@ GerryChain ``Partition`` object.
     from gerrychain.updaters import cut_edges
 
 We'll use our 
-`Pennsylvania VTD json <https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json>`_ 
+`Pennsylvania VTD json <https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json>`_ 
 to create the graph we'll use in these examples.
 
 .. code-block:: python
@@ -27,7 +27,20 @@ to create the graph we'll use in these examples.
 Creating a partition
 --------------------
 
-Here is how you can create a Partition:
+There are a couple of ways in which we could make a partition. The first way is to
+just make a random assignment with a population balance of :math:`\varepsilon`
+
+.. code-block:: python
+
+    partition = Partition.from_random_assignment(
+        graph=graph,
+        n_parts=2,
+        epsilon=0.01,
+        pop_col="TOT_POP"
+    )
+
+However, in this example we will create a partition based on the "2011_PLA_1" plan
+that already exists in the file:
 
 .. code-block:: python
 
diff --git a/docs/user/quickstart.rst b/docs/user/quickstart.rst
index 5a6f4af9..ae6b6de4 100644
--- a/docs/user/quickstart.rst
+++ b/docs/user/quickstart.rst
@@ -13,7 +13,7 @@ What you'll need
 Before we can start running Markov chains, you'll need to:
 
 * Install ``gerrychain`` from PyPI. See the :doc:`installation guide <./install>` for instructions.
-* Download `this example json of Pennsylvania's VTDs <https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json>`_.
+* Download `this example json of Pennsylvania's VTDs <https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json>`_.
 * Open your preferred Python environment (e.g. JupyterLab, IPython, or a ``.py`` file
   in your favorite editor) in the directory containing the ``PA_VTDs.json`` file
   that you downloaded.
@@ -43,7 +43,7 @@ Creating the initial partition
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/docs/user/recom.rst b/docs/user/recom.rst
index a3c76e77..96de95b1 100644
--- a/docs/user/recom.rst
+++ b/docs/user/recom.rst
@@ -28,7 +28,7 @@ A Simple Recom Chain
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/gerrymandria.json" class="download-badge" download>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/gerrymandria.json" class="download-badge" download>
         Download GerryMandria File
       </a>
     </div>
@@ -155,7 +155,7 @@ bad idea to do this for a chain with a large number of steps).
 And this should generate a little widget that you can move through to see the chain
 in action! Here is a gif of what it should look like:
 
-.. image:: ./images/gerrymandria_ensamble.gif
+.. image:: ./images/gerrymandria_ensemble.gif
     :width: 400px
     :align: center
 
@@ -192,7 +192,7 @@ edges within the municipalities.
 
 And this will produce the following ensemble:
 
-.. image:: ./images/gerrymandria_region_ensamble.gif
+.. image:: ./images/gerrymandria_region_ensemble.gif
     :width: 400px
     :align: center
 
@@ -238,7 +238,7 @@ also increase the length of our chain to make sure that we have time to mix prop
 
 Then, we can run the chain and look at the last 40 assignments in the ensemble
 
-.. image:: ./images/gerrymandria_water_muni_ensamble.gif
+.. image:: ./images/gerrymandria_water_muni_ensemble.gif
     :width: 400px
     :align: center
 
@@ -372,7 +372,7 @@ district, then the chain will get stuck and throw an error. Here is the setup:
     from gerrychain.constraints import contiguous
     from functools import partial
     import random
-    random.seed(0)
+    random.seed(5)
 
     graph = Graph.from_json("./gerrymandria.json")
 
@@ -417,7 +417,7 @@ district, then the chain will get stuck and throw an error. Here is the setup:
 
     for i, item in enumerate(recom_chain):
         print(f"Finished step {i + 1}/{len(recom_chain)}", end="\r")
-        assignment_list.append(item.assignment))
+        assignment_list.append(item.assignment)
 
 This will output the following sequence of warnings and errors
 
@@ -429,10 +429,8 @@ This will output the following sequence of warnings and errors
     MarkovChain proposal method to allow the algorithm to select
     a different pair of nodes to try an recombine.
 
-    RuntimeError: Could not find a possible cut after 100000 attempts.
+    RuntimeError: Could not find a possible cut after 100 attempts.
 
-Note: if this error does not appear at step 8, then you probalby forgot
-to rerun the part of the script that sets the random seed to 42.
 Let's break down what is happening in each of these:
 
 .. raw:: html
@@ -471,29 +469,75 @@ node repeats:
 
 .. code-block:: python
 
+    random.seed(5)
+
+    graph = Graph.from_json("./gerrymandria.json")
+
+    my_updaters = {
+        "population": updaters.Tally("TOTPOP"),
+        "cut_edges": updaters.cut_edges
+    }
+
+    initial_partition = Partition(
+        graph,
+        assignment="district",
+        updaters=my_updaters
+    )
+
+    ideal_population = sum(initial_partition["population"].values()) / len(initial_partition)
+
     proposal = partial(
         recom,
         pop_col="TOTPOP",
         pop_target=ideal_population,
         epsilon=0.01,
-        node_repeats=100,
+        node_repeats=100,                # <-- This is the only change
         region_surcharge={
-            "muni": 1.0, 
-            "water_dist": 1.0
+            "muni": 2.0,
+            "water_dist": 2.0
         },
+        method = partial(
+            bipartition_tree,
+            max_attempts=100,
+        )
     )
 
+    recom_chain = MarkovChain(
+        proposal=proposal,
+        constraints=[contiguous],
+        accept=accept.always_accept,
+        initial_state=initial_partition,
+        total_steps=20,
+    )
+
+    assignment_list = []
+
+    for i, item in enumerate(recom_chain):
+        print(f"Finished step {i + 1}/{len(recom_chain)}", end="\r")
+        assignment_list.append(item.assignment)
+
 Running this code, we can see that we get stuck once again, so this was not the fix.
 Let's try to enable reselection instead:
 
 .. code-block:: python 
 
-    method = partial(
-        bipartition_tree,
-        max_attempts=100,
-        allow_pair_reselection=True
+    random.seed(5)
+
+    graph = Graph.from_json("./gerrymandria.json")
+
+    my_updaters = {
+        "population": updaters.Tally("TOTPOP"),
+        "cut_edges": updaters.cut_edges
+    }
+
+    initial_partition = Partition(
+        graph,
+        assignment="district",
+        updaters=my_updaters
     )
 
+    ideal_population = sum(initial_partition["population"].values()) / len(initial_partition)
+
     proposal = partial(
         recom,
         pop_col="TOTPOP",
@@ -501,12 +545,30 @@ Let's try to enable reselection instead:
         epsilon=0.01,
         node_repeats=1,
         region_surcharge={
-            "muni": 1.0,
-            "water_dist": 1.0
+            "muni": 2.0,
+            "water_dist": 2.0
         },
-        method=method
+        method = partial(
+            bipartition_tree,
+            max_attempts=100,
+            allow_pair_reselection=True  # <-- This is the only change
+        )
     )
 
+    recom_chain = MarkovChain(
+        proposal=proposal,
+        constraints=[contiguous],
+        accept=accept.always_accept,
+        initial_state=initial_partition,
+        total_steps=20,
+    )
+
+    assignment_list = []
+
+    for i, item in enumerate(recom_chain):
+        print(f"Finished step {i + 1}/{len(recom_chain)}", end="\r")
+        assignment_list.append(item.assignment)
+
 And this time it works! 
 
 
@@ -541,7 +603,7 @@ Setting up the initial districting plan
 .. raw:: html
 
     <div class="center-container">
-      <a href="https://github.com/mggg/GerryChain/raw/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
+      <a href="https://github.com/mggg/GerryChain/tree/main/docs/_static/PA_VTDs.json" class="download-badge" download>Download PA File</a>
     </div>
     <br style="line-height: 5px;">
 
diff --git a/gerrychain/chain.py b/gerrychain/chain.py
index bacef507..9b63f8a7 100644
--- a/gerrychain/chain.py
+++ b/gerrychain/chain.py
@@ -24,10 +24,9 @@
 Last Updated: 11 Jan 2024
 """
 
-from .constraints import Validator
 from typing import Union, Iterable, Callable, Optional
 
-from gerrychain.constraints import Bounds
+from gerrychain.constraints import Validator, Bounds
 from gerrychain.partition import Partition
 
 
@@ -54,7 +53,7 @@ def __init__(
         proposal: Callable,
         constraints: Union[Iterable[Callable], Validator, Iterable[Bounds], Callable],
         accept: Callable,
-        initial_state: Optional[Partition],
+        initial_state: Partition,
         total_steps: int,
     ) -> None:
         """
@@ -69,7 +68,7 @@ def __init__(
             Metropolis-Hastings acceptance rule, this is where you would implement it.
         :type accept: Callable
         :param initial_state: Initial :class:`gerrychain.partition.Partition` class.
-        :type initial_state: Optional[Partition]
+        :type initial_state: Partition
         :param total_steps: Number of steps to run.
         :type total_steps: int
 
diff --git a/gerrychain/constraints/contiguity.py b/gerrychain/constraints/contiguity.py
index 76abcb49..e1077e4a 100644
--- a/gerrychain/constraints/contiguity.py
+++ b/gerrychain/constraints/contiguity.py
@@ -155,6 +155,9 @@ def affected_parts(partition: Partition) -> Set[int]:
     if flips is None:
         return partition.parts
 
+    if parent is None:
+        return set(flips.values())
+
     affected = set()
     for node, part in flips.items():
         affected.add(part)
diff --git a/gerrychain/graph/graph.py b/gerrychain/graph/graph.py
index c85c5582..a587b58f 100644
--- a/gerrychain/graph/graph.py
+++ b/gerrychain/graph/graph.py
@@ -182,6 +182,7 @@ def from_geodataframe(
         cols_to_add: Optional[List[str]] = None,
         reproject: bool = False,
         ignore_errors: bool = False,
+        crs_override: Optional[str | int] = None,
     ) -> "Graph":
         """
         Creates the adjacency :class:`Graph` of geometries described by `dataframe`.
@@ -214,6 +215,9 @@ def from_geodataframe(
         :param ignore_errors: Whether to ignore all invalid geometries and
             attept to create the graph anyway. Default is ``False``.
         :type ignore_errors: bool, optional
+        :param crs_override: Value to override the CRS of the GeoDataFrame.
+            Default is None.
+        :type crs_override: Optional[str | int], optional
 
         :returns: The adjacency graph of the geometries from `dataframe`.
         :rtype: Graph
@@ -263,7 +267,21 @@ def from_geodataframe(
         networkx.set_node_attributes(graph, name="area", values=areas)
 
         graph.add_data(df, columns=cols_to_add)
-        graph.graph["crs"] = df.crs.to_json()
+
+        if crs_override is not None:
+            df.set_crs(crs_override, inplace=True)
+
+        if df.crs is None:
+            warnings.warn(
+                "GeoDataFrame has no CRS. Did you forget to set it? "
+                "If you're sure this is correct, you can ignore this warning. "
+                "Otherwise, please set the CRS using the `crs_override` parameter. "
+                "Attempting to proceed without a CRS."
+            )
+            graph.graph["crs"] = None
+        else:
+            graph.graph["crs"] = df.crs.to_json()
+
         return graph
 
     def lookup(self, node: Any, field: Any) -> Any:
diff --git a/gerrychain/optimization/__init__.py b/gerrychain/optimization/__init__.py
new file mode 100644
index 00000000..4192e674
--- /dev/null
+++ b/gerrychain/optimization/__init__.py
@@ -0,0 +1,4 @@
+from .optimization import SingleMetricOptimizer
+from .gingleator import Gingleator
+
+__all__ = ["SingleMetricOptimizer", "Gingleator"]
diff --git a/gerrychain/optimization/gingleator.py b/gerrychain/optimization/gingleator.py
new file mode 100755
index 00000000..37a0b05a
--- /dev/null
+++ b/gerrychain/optimization/gingleator.py
@@ -0,0 +1,233 @@
+from .optimization import SingleMetricOptimizer
+
+from functools import partial
+import numpy as np
+import warnings
+from typing import Callable, Iterable, Optional, Union
+from gerrychain.partition import Partition
+from gerrychain.constraints import Validator, Bounds
+
+
+class Gingleator(SingleMetricOptimizer):
+    """
+    `Gingleator` is a child class of `SingleMetricOptimizer` which can be used to search for plans
+    with increased numbers of Gingles' districts.
+
+    A gingles district (named for the Supreme Court case Thornburg v. Gingles) is a district that is
+    majority-minority.  aka 50% + 1 of some population subgroup.  Demonstrating additional Gingles
+    districts is one of the litmus tests used in bringing forth a VRA case.
+    """
+
+    def __init__(
+        self,
+        proposal: Callable,
+        constraints: Union[Iterable[Callable], Validator, Iterable[Bounds], Callable],
+        initial_state: Partition,
+        minority_perc_col: Optional[str] = None,
+        threshold: float = 0.5,
+        score_function: Optional[Callable] = None,
+        minority_pop_col: Optional[str] = None,
+        total_pop_col: str = "TOTPOP",
+        min_perc_column_name: str = "_gingleator_auxiliary_helper_updater_min_perc_col",
+    ):
+        """
+        :param proposal: Function proposing the next state from the current state.
+        :type proposal: Callable
+        :param constraints: A function with signature ``Partition -> bool`` determining whether
+            the proposed next state is valid (passes all binary constraints). Usually this is a
+            :class:`~gerrychain.constraints.Validator` class instance.
+        :type constraints: Union[Iterable[Callable], Validator, Iterable[Bounds], Callable]
+        :param initial_state: Initial :class:`gerrychain.partition.Partition` class.
+        :type initial_state: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. If no updater is 
+            specified, one is made according to the ``min_perc_column_name`` parameter.
+            Defaults to None.
+        :type minority_perc_col: Optional[str]
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district. Defaults to 0.5.
+        :type threshold: float, optional
+        :param score_function: The function to use during optimization.  Should have the
+            signature ``Partition * str (minority_perc_col) * float (threshold) ->
+            'a where 'a is Comparable``.  This class implements a few potential choices as class
+            methods. Defaults to None.
+        :type score_function: Optional[Callable]
+        :param minority_pop_col:  If minority_perc_col is not defined, the minority population 
+            column with which to compute percentage. Defaults to None.
+        :type minority_pop_col: Optional[str]
+        :param total_pop_col: If minority_perc_col is defined, the total population column with
+            which to compute percentage. Defaults to "TOTPOP".
+        :type total_pop_col: str, optional
+        :param min_perc_column_name: If minority_perc_col is not defined, the name to give the 
+            created percentage updater. Defaults to 
+            "_gingleator_auxiliary_helper_updater_min_perc_col".
+        :type min_perc_column_name: str, optional
+        """
+        if minority_perc_col is None and minority_pop_col is None:
+            raise ValueError(
+                "`minority_perc_col` and `minority_pop_col` cannot both be `None`. \
+                              Unclear how to compute gingles district."
+            )
+        elif minority_perc_col is not None and minority_pop_col is not None:
+            warnings.warn(
+                "`minority_perc_col` and `minority_pop_col` are both specified. By \
+                           default `minority_perc_col` will be used."
+            )
+        score_function = (
+            self.num_opportunity_dists if score_function is None else score_function
+        )
+
+        if minority_perc_col is None:
+            perc_up = {
+                min_perc_column_name: lambda part: {
+                    k: part[minority_pop_col][k] / part[total_pop_col][k]
+                    for k in part.parts.keys()
+                }
+            }
+            initial_state.updaters.update(perc_up)
+            minority_perc_col = min_perc_column_name
+
+        score = partial(
+            score_function, minority_perc_col=minority_perc_col, threshold=threshold
+        )
+
+        super().__init__(proposal, constraints, initial_state, score, maximize=True)
+
+    # ---------------------
+    #    Score functions
+    # ---------------------
+
+    @classmethod
+    def num_opportunity_dists(
+        cls, part: Partition, minority_perc_col: str, threshold: float
+    ) -> int:
+        """
+        Given a partition, returns the number of opportunity districts.
+
+        :param part: Partition to score.
+        :type part: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. 
+        :type minority_perc_col: str
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district.
+        :type threshold: float
+
+        :returns: Number of opportunity districts.
+        :rtype: int
+        """
+        dist_percs = part[minority_perc_col].values()
+        return sum(list(map(lambda v: v >= threshold, dist_percs)))
+
+    @classmethod
+    def reward_partial_dist(
+        cls, part: Partition, minority_perc_col: str, threshold: float
+    ) -> float:
+        """
+        Given a partition, returns the number of opportunity districts + the percentage of the next
+        highest district.
+
+        :param part: Partition to score.
+        :type part: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. 
+        :type minority_perc_col: str
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district.
+        :type threshold: float
+
+        :returns: Number of opportunity districts + the percentage of the next highest district.
+        :rtype: float
+        """
+        dist_percs = part[minority_perc_col].values()
+        num_opport_dists = sum(list(map(lambda v: v >= threshold, dist_percs)))
+        next_dist = max(i for i in dist_percs if i < threshold)
+        return num_opport_dists + next_dist
+
+    @classmethod
+    def reward_next_highest_close(
+        cls, part: Partition, minority_perc_col: str, threshold: float
+    ):
+        """
+        Given a partition, returns the number of opportunity districts, if no additional district
+        is within 10% of reaching the threshold. If one is, the distance that district is from the
+        threshold is scaled between 0 and 1 and added to the count of opportunity districts.
+
+        :param part: Partition to score.
+        :type part: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. 
+        :type minority_perc_col: str
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district.
+        :type threshold: float
+
+        :returns: Number of opportunity districts +
+            (next highest district - (threshold - 0.1)) * 10
+        :rtype: float
+        """
+        dist_percs = part[minority_perc_col].values()
+        num_opport_dists = sum(list(map(lambda v: v >= threshold, dist_percs)))
+        next_dist = max(i for i in dist_percs if i < threshold)
+
+        if next_dist < threshold - 0.1:
+            return num_opport_dists
+        else:
+            return num_opport_dists + (next_dist - threshold + 0.1) * 10
+
+    @classmethod
+    def penalize_maximum_over(
+        cls, part: Partition, minority_perc_col: str, threshold: float
+    ):
+        """
+        Given a partition, returns the number of opportunity districts + (1 - the maximum excess)
+        scaled to between 0 and 1.
+
+        :param part: Partition to score.
+        :type part: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. 
+        :type minority_perc_col: str
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district.
+        :type threshold: float
+
+        :returns: Number of opportunity districts + (1 - the maximum excess) / (1 - threshold)
+        :rtype: float
+        """
+        dist_percs = part[minority_perc_col].values()
+        num_opportunity_dists = sum(list(map(lambda v: v >= threshold, dist_percs)))
+        if num_opportunity_dists == 0:
+            return 0
+        else:
+            max_dist = max(dist_percs)
+            return num_opportunity_dists + (1 - max_dist) / (1 - threshold)
+
+    @classmethod
+    def penalize_avg_over(
+        cls, part: Partition, minority_perc_col: str, threshold: float
+    ):
+        """
+        Given a partition, returns the number of opportunity districts + (1 - the average excess)
+        scaled to between 0 and 1.
+
+        :param part: Partition to score.
+        :type part: Partition
+        :param minority_perc_col: The name of the updater mapping of district ids to the 
+            fraction of minority population within that district. 
+        :type minority_perc_col: str
+        :param threshold: Fraction beyond which to consider something a "Gingles"
+            (or opportunity) district.
+        :type threshold: float
+
+        :returns: Number of opportunity districts + (1 - the average excess)
+        :rtype: float
+        """
+        dist_percs = part[minority_perc_col].values()
+        opport_dists = list(filter(lambda v: v >= threshold, dist_percs))
+        if opport_dists == []:
+            return 0
+        else:
+            num_opportunity_dists = len(opport_dists)
+            avg_opportunity_dist = np.mean(opport_dists)
+            return num_opportunity_dists + (1 - avg_opportunity_dist) / (1 - threshold)
diff --git a/gerrychain/optimization/optimization.py b/gerrychain/optimization/optimization.py
new file mode 100644
index 00000000..0a3075a5
--- /dev/null
+++ b/gerrychain/optimization/optimization.py
@@ -0,0 +1,605 @@
+from ..chain import MarkovChain
+from ..partition import Partition
+from ..accept import always_accept
+import random
+from typing import Union, Callable, List, Any
+from tqdm import tqdm
+import math
+
+
+class SingleMetricOptimizer:
+    """
+    SingleMetricOptimizer represents the class of algorithms / chains that optimize plans with
+    respect to a single metric.  An instance of this class encapsulates the following state
+    information:
+        * the dual graph and updaters via the initial partition,
+        * the constraints new proposals are subject to,
+        * the metric over which to optimize,
+        * and whether or not to seek maximal or minimal values of the metric.
+
+    The SingleMetricOptimizer class implements the following common methods of optimization:
+        * Short Bursts
+        * Simulated Annealing
+        * Tilted Runs
+
+    Both during and after a optimization run, the class properties `best_part` and `best_score`
+    represent the optimal partition / corresponding score value observed.  Note that these
+    properties do NOT persist across multiple optimization runs, as they are reset each time an
+    optimization run is invoked.
+    """
+
+    def __init__(
+        self,
+        proposal: Callable[[Partition], Partition],
+        constraints: Union[
+            Callable[[Partition], bool], List[Callable[[Partition], bool]]
+        ],
+        initial_state: Partition,
+        optimization_metric: Callable[[Partition], Any],
+        maximize: bool = True,
+        step_indexer: str = "step",
+    ):
+        """
+
+        :param proposal: Function proposing the next state from the current state.
+        :type proposal: Callable
+        :param constraints: A function, or lists of functions, determining whether the proposed next
+            state is valid (passes all binary constraints). Usually this is a
+            :class:`~gerrychain.constraints.Validator` class instance.
+        :type constraints: Union[Callable[[Partition], bool], List[Callable[[Partition], bool]]]
+        :param initial_state: Initial state of the optimizer.
+        :type initial_state: Partition
+        :param optimization_metric: The score function with which to optimize over. This should have
+            the signature: ``Partition -> 'a`` where 'a is comparable.
+        :type optimization_metric: Callable[[Partition], Any]
+        :param maximize: Boolean indicating whether to maximize or minimize the function. Defaults to True for maximize.
+        :type maximize: bool, optional
+        :param step_indexer: Name of the updater tracking the partitions step in the chain. If not
+            implemented on the partition the constructor creates and adds it. Defaults to "step".
+        :type step_indexer: str, optional
+
+
+
+        :return: A SingleMetricOptimizer object
+        :rtype: SingleMetricOptimizer
+        """
+        self._initial_part = initial_state
+        self._proposal = proposal
+        self._constraints = constraints
+        self._score = optimization_metric
+        self._maximize = maximize
+        self._best_part = None
+        self._best_score = None
+        self._step_indexer = step_indexer
+
+        if self._step_indexer not in self._initial_part.updaters:
+            step_updater = lambda p: (
+                0 if p.parent is None else p.parent[self._step_indexer] + 1
+            )
+            self._initial_part.updaters[self._step_indexer] = step_updater
+
+    @property
+    def best_part(self) -> Partition:
+        """
+        Partition object corresponding to best scoring plan observed over the current (or most
+        recent) optimization run.
+
+        :return: Partition object with the best score.
+        :rtype: Partition
+        """
+        return self._best_part
+
+    @property
+    def best_score(self) -> Any:
+        """
+        Value of score metric corresponding to best scoring plan observed over the current (or most
+        recent) optimization run.
+
+        :return: Value of the best score.
+        :rtype: Any
+        """
+        return self._best_score
+
+    @property
+    def score(self) -> Callable[[Partition], Any]:
+        """
+        The score function which is being optimized over.
+
+        :return: The score function.
+        :rtype: Callable[[Partition], Any]
+        """
+        return self._score
+
+    def _is_improvement(self, new_score: float, old_score: float) -> bool:
+        """
+        Helper function defining improvement comparison between scores.  Scores can be any
+        comparable type.
+
+        :param new_score: Score of proposed partition.
+        :type new_score: float
+        :param old_score: Score of previous partition.
+        :type old_score: float
+
+        :return: Whether the new score is an improvement over the old score.
+        :rtype: bool
+        """
+        if self._maximize:
+            return new_score >= old_score
+        else:
+            return new_score <= old_score
+
+    def _tilted_acceptance_function(self, p: float) -> Callable[[Partition], bool]:
+        """
+        Function factory that binds and returns a tilted acceptance function.
+
+        :param p: The probability of accepting a worse score.
+        :type p: float
+
+        :return: An acceptance function for tilted chains.
+        :rtype: Callable[[Partition], bool]
+        """
+
+        def tilted_acceptance_function(part):
+            if part.parent is None:
+                return True
+
+            part_score = self.score(part)
+            prev_score = self.score(part.parent)
+
+            if self._is_improvement(part_score, prev_score):
+                return True
+            else:
+                return random.random() < p
+
+        return tilted_acceptance_function
+
+    def _simulated_annealing_acceptance_function(
+        self, beta_function: Callable[[int], float], beta_magnitude: float
+    ):
+        """
+        Function factory that binds and returns a simulated annealing acceptance function.
+
+        :param beta_function: Function (f: t -> beta, where beta is in [0,1]) defining temperature
+            over time.  f(t) = 0 the chain is hot and every proposal is accepted.  At f(t) = 1 the
+            chain is cold and worse proposal have a low probability of being accepted relative to
+            the magnitude of change in score.
+        :type beta_function: Callable[[int], float]
+        :param beta_magnitude: Scaling parameter for how much to weight changes in score.
+        :type beta_magnitude: float
+
+        :return: A acceptance function for simulated annealing runs.
+        :rtype: Callable[[Partition], bool]
+        """
+
+        def simulated_annealing_acceptance_function(part):
+            if part.parent is None:
+                return True
+            score_delta = self.score(part) - self.score(part.parent)
+            beta = beta_function(part[self._step_indexer])
+            if self._maximize:
+                score_delta *= -1
+            return random.random() < math.exp(-beta * beta_magnitude * score_delta)
+
+        return simulated_annealing_acceptance_function
+
+    @classmethod
+    def jumpcycle_beta_function(
+        cls, duration_hot: int, duration_cold: int
+    ) -> Callable[[int], float]:
+        """
+        Class method that binds and return simple hot-cold cycle beta temperature function, where
+        the chain runs hot for some given duration and then cold for some duration, and repeats that
+        cycle.
+
+        :param duration_hot: Number of steps to run chain hot.
+        :type duration_hot: int
+        :param duration_cold: Number of steps to run chain cold.
+        :type duration_cold: int
+
+        :return: Beta function defining hot-cold cycle.
+        :rtype: Callable[[int], float]
+        """
+        cycle_length = duration_hot + duration_cold
+
+        def beta_function(step: int):
+            time_in_cycle = step % cycle_length
+            return float(time_in_cycle >= duration_hot)
+
+        return beta_function
+
+    @classmethod
+    def linearcycle_beta_function(
+        cls, duration_hot: int, duration_cooldown: int, duration_cold: int
+    ) -> Callable[[int], float]:
+        """
+        Class method that binds and returns a simple linear hot-cool cycle beta temperature
+        function, where the chain runs hot for some given duration, cools down linearly for some
+        duration, and then runs cold for some duration before warming up again and repeating.
+
+        :param duration_hot: Number of steps to run chain hot.
+        :type duration_hot: int
+        :param duration_cooldown: Number of steps needed to transition from hot to cold or
+            vice-versa.
+        :type duration_cooldown: int
+        :param duration_cold: Number of steps to run chain cold.
+        :type duration_cold: int
+
+        :return: Beta function defining linear hot-cool cycle.
+        :rtype: Callable[[int], float]
+        """
+        cycle_length = duration_hot + 2 * duration_cooldown + duration_cold
+
+        def beta_function(step: int):
+            time_in_cycle = step % cycle_length
+            if time_in_cycle < duration_hot:
+                return 0
+            elif time_in_cycle < duration_hot + duration_cooldown:
+                return (time_in_cycle - duration_hot) / duration_cooldown
+            elif time_in_cycle < cycle_length - duration_cooldown:
+                return 1
+            else:
+                return (
+                    1
+                    - (time_in_cycle - cycle_length + duration_cooldown)
+                    / duration_cooldown
+                )
+
+        return beta_function
+
+    @classmethod
+    def linear_jumpcycle_beta_function(
+        cls, duration_hot: int, duration_cooldown, duration_cold: int
+    ):
+        """
+        Class method that binds and returns a simple linear hot-cool cycle beta temperature
+        function, where the chain runs hot for some given duration, cools down linearly for some
+        duration, and then runs cold for some duration before jumping back to hot and repeating.
+
+        :param duration_hot: Number of steps to run chain hot.
+        :type duration_hot: int
+        :param duration_cooldown: Number of steps needed to transition from hot to cold.
+        :type duration_cooldown: int
+        :param duration_cold: Number of steps to run chain cold.
+        :type duration_cold: int
+
+        :return: Beta function defining linear hot-cool cycle.
+        :rtype: Callable[[int], float]
+        """
+        cycle_length = duration_hot + duration_cooldown + duration_cold
+
+        def beta_function(step: int):
+            time_in_cycle = step % cycle_length
+            if time_in_cycle < duration_hot:
+                return 0
+            elif time_in_cycle < duration_hot + duration_cooldown:
+                return (time_in_cycle - duration_hot) / duration_cooldown
+            else:
+                return 1
+
+        return beta_function
+
+    @classmethod
+    def logitcycle_beta_function(
+        cls, duration_hot: int, duration_cooldown: int, duration_cold: int
+    ) -> Callable[[int], float]:
+        """
+        Class method that binds and returns a logit hot-cool cycle beta temperature function, where
+        the chain runs hot for some given duration, cools down according to the logit function
+
+        :math:`f(x) = (log(x/(1-x)) + 5)/10`
+
+        for some duration, and then runs cold for some duration before warming up again
+        using the :math:`1-f(x)` and repeating.
+
+        :param duration_hot: Number of steps to run chain hot.
+        :type duration_hot: int
+        :param duration_cooldown: Number of steps needed to transition from hot to cold or
+            vice-versa.
+        :type duration_cooldown: int
+        :param duration_cold: Number of steps to run chain cold.
+        :type duration_cold: int
+        """
+        cycle_length = duration_hot + 2 * duration_cooldown + duration_cold
+
+        # this will scale from 0 to 1 approximately
+        logit = lambda x: (math.log(x / (1 - x)) + 5) / 10
+
+        def beta_function(step: int):
+            time_in_cycle = step % cycle_length
+            if time_in_cycle <= duration_hot:
+                return 0
+            elif time_in_cycle < duration_hot + duration_cooldown:
+                value = logit((time_in_cycle - duration_hot) / duration_cooldown)
+                if value < 0:
+                    return 0
+                if value > 1:
+                    return 1
+                return value
+            elif time_in_cycle <= cycle_length - duration_cooldown:
+                return 1
+            else:
+                value = 1 - logit(
+                    (time_in_cycle - cycle_length + duration_cooldown)
+                    / duration_cooldown
+                )
+                if value < 0:
+                    return 0
+                if value > 1:
+                    return 1
+                return value
+
+        return beta_function
+
+    @classmethod
+    def logit_jumpcycle_beta_function(
+        cls, duration_hot: int, duration_cooldown: int, duration_cold: int
+    ) -> Callable[[int], float]:
+        """
+        Class method that binds and returns a logit hot-cool cycle beta temperature function, where
+        the chain runs hot for some given duration, cools down according to the logit function
+
+        :math:`f(x) = (log(x/(1-x)) + 5)/10`
+
+        for some duration, and then runs cold for some duration before jumping back to hot and
+        repeating.
+
+        :param duration_hot: Number of steps to run chain hot.
+        :type duration_hot: int
+        :param duration_cooldown: Number of steps needed to transition from hot to cold or
+            vice-versa.
+        :type duration_cooldown: int
+        :param duration_cold: Number of steps to run chain cold.
+        :type duration_cold: int
+        """
+        cycle_length = duration_hot + duration_cooldown + duration_cold
+
+        # this will scale from 0 to 1 approximately
+        logit = lambda x: (math.log(x / (1 - x)) + 5) / 10
+
+        def beta_function(step: int):
+            time_in_cycle = step % cycle_length
+            if time_in_cycle <= duration_hot:
+                return 0
+            elif time_in_cycle < duration_hot + duration_cooldown:
+                value = logit((time_in_cycle - duration_hot) / duration_cooldown)
+                if value < 0:
+                    return 0
+                if value > 1:
+                    return 1
+                return value
+            else:
+                return 1
+
+        return beta_function
+
+    def short_bursts(
+        self,
+        burst_length: int,
+        num_bursts: int,
+        accept: Callable[[Partition], bool] = always_accept,
+        with_progress_bar: bool = False,
+    ):
+        """
+        Performs a short burst run using the instance's score function. Each burst starts at the
+        best performing plan of the previous burst. If there's a tie, the later observed one is
+        selected.
+
+        :param burst_length: Number of steps to run within each burst.
+        :type burst_length: int
+        :param num_bursts: Number of bursts to perform.
+        :type num_bursts: int
+        :param accept: Function accepting or rejecting the proposed state. Defaults to
+            :func:`~gerrychain.accept.always_accept`.
+        :type accept: Callable[[Partition], bool], optional
+        :param with_progress_bar: Whether or not to draw tqdm progress bar. Defaults to False.
+        :type with_progress_bar: bool, optional
+
+        :return: Partition generator.
+        :rtype: Generator[Partition]
+        """
+        if with_progress_bar:
+            for part in tqdm(
+                self.short_bursts(
+                    burst_length, num_bursts, accept, with_progress_bar=False
+                ),
+                total=burst_length * num_bursts,
+            ):
+                yield part
+            return
+
+        self._best_part = self._initial_part
+        self._best_score = self.score(self._best_part)
+
+        for _ in range(num_bursts):
+            chain = MarkovChain(
+                self._proposal, self._constraints, accept, self._best_part, burst_length
+            )
+
+            for part in chain:
+                yield part
+                part_score = self.score(part)
+
+                if self._is_improvement(part_score, self._best_score):
+                    self._best_part = part
+                    self._best_score = part_score
+
+    def simulated_annealing(
+        self,
+        num_steps: int,
+        beta_function: Callable[[int], float],
+        beta_magnitude: float = 1,
+        with_progress_bar: bool = False,
+    ):
+        """
+        Performs simulated annealing with respect to the class instance's score function.
+
+        :param num_steps: Number of steps to run for.
+        :type num_steps: int
+        :param beta_function: Function (f: t -> beta, where beta is in [0,1]) defining temperature
+            over time.  f(t) = 0 the chain is hot and every proposal is accepted. At f(t) = 1 the
+            chain is cold and worse proposal have a low probability of being accepted relative to
+            the magnitude of change in score.
+        :type beta_function: Callable[[int], float]
+        :param beta_magnitude: Scaling parameter for how much to weight changes in score.
+            Defaults to 1.
+        :type beta_magnitude: float, optional
+        :param with_progress_bar: Whether or not to draw tqdm progress bar. Defaults to False.
+        :type with_progress_bar: bool, optional
+
+        :return: Partition generator.
+        :rtype: Generator[Partition]
+        """
+        chain = MarkovChain(
+            self._proposal,
+            self._constraints,
+            self._simulated_annealing_acceptance_function(
+                beta_function, beta_magnitude
+            ),
+            self._initial_part,
+            num_steps,
+        )
+
+        self._best_part = self._initial_part
+        self._best_score = self.score(self._best_part)
+
+        chain_generator = tqdm(chain) if with_progress_bar else chain
+
+        for part in chain_generator:
+            yield part
+            part_score = self.score(part)
+            if self._is_improvement(part_score, self._best_score):
+                self._best_part = part
+                self._best_score = part_score
+
+    def tilted_short_bursts(
+        self,
+        burst_length: int,
+        num_bursts: int,
+        p: float,
+        with_progress_bar: bool = False,
+    ):
+        """
+        Performs a short burst run using the instance's score function. Each burst starts at the
+        best performing plan of the previous burst. If there's a tie, the later observed one is
+        selected. Within each burst a tilted acceptance function is used where better scoring plans
+        are always accepted and worse scoring plans are accepted with probability `p`.
+
+        :param burst_length: Number of steps to run within each burst.
+        :type burst_length: int
+        :param num_bursts: Number of bursts to perform.
+        :type num_bursts: int
+        :param p: The probability of accepting a plan with a worse score.
+        :type p: float
+        :param with_progress_bar: Whether or not to draw tqdm progress bar. Defaults to False.
+        :type with_progress_bar: bool, optional
+
+
+        :return: Partition generator.
+        :rtype: Generator[Partition]
+        """
+        return self.short_bursts(
+            burst_length,
+            num_bursts,
+            accept=self._tilted_acceptance_function(p),
+            with_progress_bar=with_progress_bar,
+        )
+
+    # TODO: Maybe add a max_time variable so we don't run forever.
+    def variable_length_short_bursts(
+        self,
+        num_steps: int,
+        stuck_buffer: int,
+        accept: Callable[[Partition], bool] = always_accept,
+        with_progress_bar: bool = False,
+    ):
+        """
+        Performs a short burst where the burst length is allowed to increase as it gets harder to
+        find high scoring plans. The initial burst length is set to 2, and it is doubled each time
+        there is no improvement over the passed number (`stuck_buffer`) of runs.
+
+        :param num_steps: Number of steps to run for.
+        :type num_steps: int
+        :param stuck_buffer: How many bursts of a given length with no improvement to allow before
+            increasing the burst length.
+        :type stuck_buffer: int
+        :param accept: Function accepting or rejecting the proposed state. Defaults to :func:`~gerrychain.accept.always_accept`.
+        :type accept: Callable[[Partition], bool], optional
+        :param with_progress_bar: Whether or not to draw tqdm progress bar. Defaults to False.
+        :type with_progress_bar: bool, optional
+
+        :return: Partition generator.
+        :rtype: Generator[Partition]
+        """
+        if with_progress_bar:
+            for part in tqdm(
+                self.variable_length_short_bursts(
+                    num_steps, stuck_buffer, accept, with_progress_bar=False
+                ),
+                total=num_steps,
+            ):
+                yield part
+            return
+
+        self._best_part = self._initial_part
+        self._best_score = self.score(self._best_part)
+        time_stuck = 0
+        burst_length = 2
+        i = 0
+
+        while i < num_steps:
+            chain = MarkovChain(
+                self._proposal, self._constraints, accept, self._best_part, burst_length
+            )
+            for part in chain:
+                yield part
+                part_score = self.score(part)
+                if self._is_improvement(part_score, self._best_score):
+                    self._best_part = part
+                    self._best_score = part_score
+                    time_stuck = 0
+                else:
+                    time_stuck += 1
+
+                i += 1
+                if i >= num_steps:
+                    break
+
+            if time_stuck >= stuck_buffer * burst_length:
+                burst_length *= 2
+
+    def tilted_run(self, num_steps: int, p: float, with_progress_bar: bool = False):
+        """
+        Performs a tilted run. A chain where the acceptance function always accepts better plans
+        and accepts worse plans with some probability `p`.
+
+
+        :param num_steps: Number of steps to run for.
+        :type num_steps: int
+        :param p: The probability of accepting a plan with a worse score.
+        :type p: float
+        :param with_progress_bar: Whether or not to draw tqdm progress bar. Defaults to False.
+        :type with_progress_bar: bool, optional
+
+        :return: Partition generator.
+        :rtype: Generator[Partition]
+        """
+        chain = MarkovChain(
+            self._proposal,
+            self._constraints,
+            self._tilted_acceptance_function(p),
+            self._initial_part,
+            num_steps,
+        )
+
+        self._best_part = self._initial_part
+        self._best_score = self.score(self._best_part)
+
+        chain_generator = tqdm(chain) if with_progress_bar else chain
+
+        for part in chain_generator:
+            yield part
+            part_score = self.score(part)
+
+            if self._is_improvement(part_score, self._best_score):
+                self._best_part = part
+                self._best_score = part_score
diff --git a/gerrychain/partition/partition.py b/gerrychain/partition/partition.py
index a285e755..9f484f61 100644
--- a/gerrychain/partition/partition.py
+++ b/gerrychain/partition/partition.py
@@ -5,6 +5,7 @@
 from ..updaters import compute_edge_flows, flows_from_changes, cut_edges
 from .assignment import get_assignment
 from .subgraphs import SubgraphView
+from ..tree import recursive_tree_part
 from typing import Any, Callable, Dict, Optional, Tuple
 
 
@@ -63,6 +64,61 @@ def __init__(
         self._cache = dict()
         self.subgraphs = SubgraphView(self.graph, self.parts)
 
+    @classmethod
+    def from_random_assignment(
+        cls,
+        graph: Graph,
+        n_parts: int,
+        epsilon: float,
+        pop_col: str,
+        updaters: Optional[Dict[str, Callable]] = None,
+        use_default_updaters: bool = True,
+        flips: Optional[Dict] = None,
+        method: Callable = recursive_tree_part,
+    ) -> "Partition":
+        """
+        Create a Partition with a random assignment of nodes to districts.
+
+        :param graph: The graph to create the Partition from.
+        :type graph: :class:`~gerrychain.Graph`
+        :param n_parts: The number of districts to divide the nodes into.
+        :type n_parts: int
+        :param epsilon: The maximum relative population deviation from the ideal
+        :type epsilon: float
+            population. Should be in [0,1].
+        :param pop_col: The column of the graph's node data that holds the population data.
+        :type pop_col: str
+        :param updaters: Dictionary of updaters
+        :type updaters: Optional[Dict[str, Callable]], optional
+        :param use_default_updaters: If `False`, do not include default updaters.
+        :type use_default_updaters: bool, optional
+        :param flips: Dictionary assigning nodes of the graph to their new districts.
+        :type flips: Optional[Dict], optional
+        :param method: The function to use to partition the graph into ``n_parts``. Defaults to
+            :func:`~gerrychain.tree.recursive_tree_part`.
+        :type method: Callable, optional
+
+        :returns: The partition created with a random assignment
+        :rtype: Partition
+        """
+        total_pop = sum(graph.nodes[n][pop_col] for n in graph)
+        ideal_pop = total_pop / n_parts
+
+        assignment = method(
+            graph=graph,
+            parts=range(n_parts),
+            pop_target=ideal_pop,
+            pop_col=pop_col,
+            epsilon=epsilon,
+        )
+
+        return cls(
+            graph,
+            assignment,
+            updaters,
+            use_default_updaters=use_default_updaters,
+        )
+
     def _first_time(self, graph, assignment, updaters, use_default_updaters):
         if isinstance(graph, Graph):
             self.graph = FrozenGraph(graph)
diff --git a/gerrychain/proposals/tree_proposals.py b/gerrychain/proposals/tree_proposals.py
index f711026e..e66a718b 100644
--- a/gerrychain/proposals/tree_proposals.py
+++ b/gerrychain/proposals/tree_proposals.py
@@ -4,7 +4,7 @@
 
 from gerrychain.partition import Partition
 from ..tree import (
-    recursive_tree_part,
+    epsilon_tree_bipartition,
     bipartition_tree,
     bipartition_tree_random,
     _bipartition_tree_random_all,
@@ -119,7 +119,7 @@ def recom(
                 partition.parts[parts_to_merge[0]] | partition.parts[parts_to_merge[1]]
             )
 
-            flips = recursive_tree_part(
+            flips = epsilon_tree_bipartition(
                 subgraph.graph,
                 parts_to_merge,
                 pop_col=pop_col,
diff --git a/gerrychain/tree.py b/gerrychain/tree.py
index 0f61583f..06ce8433 100644
--- a/gerrychain/tree.py
+++ b/gerrychain/tree.py
@@ -23,7 +23,7 @@
 - random: Provides random number generation for probabilistic approaches.
 - typing: Used for type hints.
 
-Last Updated: 30 Jan 2024
+Last Updated: 25 April 2024
 """
 
 import networkx as nx
@@ -78,9 +78,11 @@ def random_spanning_tree(
     for edge in graph.edges():
         weight = random.random()
         for key, value in region_surcharge.items():
+            # We surcharge edges that cross regions and those that are not in any region
             if (
                 graph.nodes[edge[0]][key] != graph.nodes[edge[1]][key]
-                and graph.nodes[edge[0]][key] is not None
+                or graph.nodes[edge[0]][key] is None
+                or graph.nodes[edge[1]][key] is None
             ):
                 weight += value
 
@@ -186,9 +188,32 @@ def contract_node(self, node, parent) -> None:
         self.subsets[parent] |= self.subsets[node]
         self._degrees[parent] -= 1
 
-    def has_ideal_population(self, node) -> bool:
+    def has_ideal_population(self, node, one_sided_cut: bool = False) -> bool:
+        """
+        Checks if a node has an ideal population within the graph up to epsilon.
+
+        :param node: The node to check.
+        :type node: Any
+        :param one_sided_cut: Whether or not we are cutting off a single district. When
+            set to False, we check if the node we are cutting and the remaining graph
+            are both within epsilon of the ideal population. When set to True, we only
+            check if the node we are cutting is within epsilon of the ideal population.
+            Defaults to False.
+        :type one_sided_cut: bool, optional
+
+        :returns: True if the node has an ideal population within the graph up to epsilon.
+        :rtype: bool
+        """
+        if one_sided_cut:
+            return (
+                abs(self.population[node] - self.ideal_pop)
+                < self.epsilon * self.ideal_pop
+            )
+
         return (
-            abs(self.population[node] - self.ideal_pop) < self.epsilon * self.ideal_pop
+            abs(self.population[node] - self.ideal_pop) <= self.epsilon * self.ideal_pop
+            and abs((self.tot_pop - self.population[node]) - self.ideal_pop)
+            <= self.epsilon * self.ideal_pop
         )
 
     def __repr__(self) -> str:
@@ -210,17 +235,25 @@ def __repr__(self) -> str:
 Cut.__doc__ = "Represents a cut in a graph."
 Cut.edge.__doc__ = "The edge where the cut is made. Defaults to None."
 Cut.weight.__doc__ = "The weight assigned to the edge (if any). Defaults to None."
-Cut.subset.__doc__ = "The (frozen) subset of nodes on one side of the cut. Defaults to None."
+Cut.subset.__doc__ = (
+    "The (frozen) subset of nodes on one side of the cut. Defaults to None."
+)
 
 
 def find_balanced_edge_cuts_contraction(
-    h: PopulatedGraph, choice: Callable = random.choice
+    h: PopulatedGraph, one_sided_cut: bool = False, choice: Callable = random.choice
 ) -> List[Cut]:
     """
     Find balanced edge cuts using contraction.
 
     :param h: The populated graph.
     :type h: PopulatedGraph
+    :param one_sided_cut: Whether or not we are cutting off a single district. When
+        set to False, we check if the node we are cutting and the remaining graph
+        are both within epsilon of the ideal population. When set to True, we only
+        check if the node we are cutting is within epsilon of the ideal population.
+        Defaults to False.
+    :type one_sided_cut: bool, optional
     :param choice: The function used to make random choices.
     :type choice: Callable, optional
 
@@ -236,13 +269,13 @@ def find_balanced_edge_cuts_contraction(
     leaves = deque(x for x in h if h.degree(x) == 1)
     while len(leaves) > 0:
         leaf = leaves.popleft()
-        if h.has_ideal_population(leaf):
+        if h.has_ideal_population(leaf, one_sided_cut=one_sided_cut):
             e = (leaf, pred[leaf])
             cuts.append(
                 Cut(
                     edge=e,
                     weight=h.graph.edges[e].get("random_weight", random.random()),
-                    subset=frozenset(h.subsets[leaf].copy())
+                    subset=frozenset(h.subsets[leaf].copy()),
                 )
             )
         # Contract the leaf:
@@ -316,7 +349,7 @@ def _part_nodes(start, succ):
 
 
 def find_balanced_edge_cuts_memoization(
-    h: PopulatedGraph, choice: Callable = random.choice
+    h: PopulatedGraph, one_sided_cut: bool = False, choice: Callable = random.choice
 ) -> List[Cut]:
     """
     Find balanced edge cuts using memoization.
@@ -328,6 +361,12 @@ def find_balanced_edge_cuts_memoization(
 
     :param h: The PopulatedGraph object representing the graph.
     :type h: PopulatedGraph
+    :param one_sided_cut: Whether or not we are cutting off a single district. When
+        set to False, we check if the node we are cutting and the remaining graph
+        are both within epsilon of the ideal population. When set to True, we only
+        check if the node we are cutting is within epsilon of the ideal population.
+        Defaults to False.
+    :type one_sided_cut: bool, optional
     :param choice: The choice function used to select the root node.
     :type choice: Callable, optional
 
@@ -343,18 +382,36 @@ def find_balanced_edge_cuts_memoization(
     subtree_pops = _calc_pops(succ, root, h)
 
     cuts = []
-    for node, tree_pop in subtree_pops.items():
-        if abs(tree_pop - h.ideal_pop) <= h.ideal_pop * h.epsilon:
-            e = (node, pred[node])
-            wt = random.random()
-            cuts.append(
-                Cut(
-                    edge=e,
-                    weight=h.graph.edges[e].get("random_weight", wt),
-                    subset=frozenset(_part_nodes(node, succ))
+
+    if one_sided_cut:
+        for node, tree_pop in subtree_pops.items():
+            if abs(tree_pop - h.ideal_pop) <= h.ideal_pop * h.epsilon:
+                e = (node, pred[node])
+                wt = random.random()
+                cuts.append(
+                    Cut(
+                        edge=e,
+                        weight=h.graph.edges[e].get("random_weight", wt),
+                        subset=frozenset(_part_nodes(node, succ)),
+                    )
                 )
-            )
-        elif abs((total_pop - tree_pop) - h.ideal_pop) <= h.ideal_pop * h.epsilon:
+            elif abs((total_pop - tree_pop) - h.ideal_pop) <= h.ideal_pop * h.epsilon:
+                e = (node, pred[node])
+                wt = random.random()
+                cuts.append(
+                    Cut(
+                        edge=e,
+                        weight=h.graph.edges[e].get("random_weight", wt),
+                        subset=frozenset(set(h.graph.nodes) - _part_nodes(node, succ)),
+                    )
+                )
+
+        return cuts
+
+    for node, tree_pop in subtree_pops.items():
+        if (abs(tree_pop - h.ideal_pop) <= h.ideal_pop * h.epsilon) and (
+            abs((total_pop - tree_pop) - h.ideal_pop) <= h.ideal_pop * h.epsilon
+        ):
             e = (node, pred[node])
             wt = random.random()
             cuts.append(
@@ -386,9 +443,7 @@ class ReselectException(Exception):
     pass
 
 
-def _max_weight_choice(
-    cut_edge_list: List[Cut]
-) -> Cut:
+def _max_weight_choice(cut_edge_list: List[Cut]) -> Cut:
     """
     Each Cut object in the list is assigned a random weight.
     This random weight is either assigned during the call to
@@ -427,17 +482,13 @@ def _max_weight_choice(
 
 def _power_set_sorted_by_size_then_sum(d):
     power_set = [
-        s
-        for i in range(1, len(d) + 1)
-        for s in itertools.combinations(d.keys(), i)
+        s for i in range(1, len(d) + 1) for s in itertools.combinations(d.keys(), i)
     ]
 
     # Sort the subsets in descending order based on
     # the sum of their corresponding values in the dictionary
     sorted_power_set = sorted(
-        power_set,
-        key=lambda s: (len(s), sum(d[i] for i in s)),
-        reverse=True
+        power_set, key=lambda s: (len(s), sum(d[i] for i in s)), reverse=True
     )
 
     return sorted_power_set
@@ -448,9 +499,7 @@ def _power_set_sorted_by_size_then_sum(d):
 # are not modifying the object in the function, and the speed of
 # this randomized selection will not suffer for it.
 def _region_preferred_max_weight_choice(
-    populated_graph: PopulatedGraph,
-    region_surcharge: Dict,
-    cut_edge_list: List[Cut]
+    populated_graph: PopulatedGraph, region_surcharge: Dict, cut_edge_list: List[Cut]
 ) -> Cut:
     """
     This function is used in the case of a region-aware chain. It
@@ -502,8 +551,10 @@ def _region_preferred_max_weight_choice(
     # Prepare data for efficient access
     edge_region_info = {
         cut: {
-            key: (populated_graph.graph.nodes[cut.edge[0]].get(key),
-                  populated_graph.graph.nodes[cut.edge[1]].get(key))
+            key: (
+                populated_graph.graph.nodes[cut.edge[0]].get(key),
+                populated_graph.graph.nodes[cut.edge[1]].get(key),
+            )
             for key in region_surcharge
         }
         for cut in cut_edge_list
@@ -514,7 +565,8 @@ def _region_preferred_max_weight_choice(
     power_set = _power_set_sorted_by_size_then_sum(region_surcharge)
     for region_combination in power_set:
         suitable_cuts = [
-            cut for cut in cut_edge_list
+            cut
+            for cut in cut_edge_list
             if all(
                 edge_region_info[cut][key][0] != edge_region_info[cut][key][1]
                 for key in region_combination
@@ -536,11 +588,12 @@ def bipartition_tree(
     spanning_tree_fn: Callable = random_spanning_tree,
     region_surcharge: Optional[Dict] = None,
     balance_edge_fn: Callable = find_balanced_edge_cuts_memoization,
+    one_sided_cut: bool = False,
     choice: Callable = random.choice,
     max_attempts: Optional[int] = 100000,
     warn_attempts: int = 1000,
     allow_pair_reselection: bool = False,
-    cut_choice: Callable = _region_preferred_max_weight_choice
+    cut_choice: Callable = _region_preferred_max_weight_choice,
 ) -> Set:
     """
     This function finds a balanced 2 partition of a graph by drawing a
@@ -575,6 +628,13 @@ def bipartition_tree(
     :param balance_edge_fn: The function to find balanced edge cuts. Defaults to
         :func:`find_balanced_edge_cuts_memoization`.
     :type balance_edge_fn: Callable, optional
+    :param one_sided_cut: Passed to the ``balance_edge_fn``. Determines whether or not we are
+        cutting off a single district when partitioning the tree. When
+        set to False, we check if the node we are cutting and the remaining graph
+        are both within epsilon of the ideal population. When set to True, we only
+        check if the node we are cutting is within epsilon of the ideal population.
+        Defaults to False.
+    :type one_sided_cut: bool, optional
     :param choice: The function to make a random choice of root node for the population
         tree. Passed to ``balance_edge_fn``. Can be substituted for testing.
         Defaults to :func:`random.random()`.
@@ -604,6 +664,9 @@ def bipartition_tree(
     if "region_surcharge" in signature(spanning_tree_fn).parameters:
         spanning_tree_fn = partial(spanning_tree_fn, region_surcharge=region_surcharge)
 
+    if "one_sided_cut" in signature(balance_edge_fn).parameters:
+        balance_edge_fn = partial(balance_edge_fn, one_sided_cut=one_sided_cut)
+
     populations = {node: graph.nodes[node][pop_col] for node in graph.node_indices}
 
     possible_cuts: List[Cut] = []
@@ -742,6 +805,7 @@ def bipartition_tree_random(
     spanning_tree: Optional[nx.Graph] = None,
     spanning_tree_fn: Callable = random_spanning_tree,
     balance_edge_fn: Callable = find_balanced_edge_cuts_memoization,
+    one_sided_cut: bool = False,
     choice: Callable = random.choice,
     max_attempts: Optional[int] = 100000,
 ) -> Union[Set[Any], None]:
@@ -757,14 +821,14 @@ def bipartition_tree_random(
     Builds up a connected subgraph with a connected complement whose population
     is ``epsilon * pop_target`` away from ``pop_target``.
 
-    :param graph: The graph to partition
+    :param graph: The graph to partition.
     :type graph: nx.Graph
-    :param pop_col: The node attribute holding the population of each node
+    :param pop_col: The node attribute holding the population of each node.
     :type pop_col: str
-    :param pop_target: The target population for the returned subset of nodes
+    :param pop_target: The target population for the returned subset of nodes.
     :type pop_target: Union[int, float]
     :param epsilon: The allowable deviation from  ``pop_target`` (as a percentage of
-        ``pop_target``) for the subgraph's population
+        ``pop_target``) for the subgraph's population.
     :type epsilon: float
     :param node_repeats: A parameter for the algorithm: how many different choices
         of root to use before drawing a new spanning tree. Defaults to 1.
@@ -783,6 +847,13 @@ def bipartition_tree_random(
     :param balance_edge_fn: The algorithm used to find balanced cut edges. Defaults to
         :func:`find_balanced_edge_cuts_memoization`.
     :type balance_edge_fn: Callable, optional
+    :param one_sided_cut: Passed to the ``balance_edge_fn``. Determines whether or not we are
+        cutting off a single district when partitioning the tree. When
+        set to False, we check if the node we are cutting and the remaining graph
+        are both within epsilon of the ideal population. When set to True, we only
+        check if the node we are cutting is within epsilon of the ideal population.
+        Defaults to False.
+    :type one_sided_cut: bool, optional
     :param choice: The random choice function. Can be substituted for testing. Defaults
         to :func:`random.choice`.
     :type choice: Callable, optional
@@ -794,6 +865,9 @@ def bipartition_tree_random(
         valid spanning tree is not found.
     :rtype: Union[Set[Any], None]
     """
+    if "one_sided_cut" in signature(balance_edge_fn).parameters:
+        balance_edge_fn = partial(balance_edge_fn, one_sided_cut=True)
+
     possible_cuts = _bipartition_tree_random_all(
         graph=graph,
         pop_col=pop_col,
@@ -811,6 +885,89 @@ def bipartition_tree_random(
         return choice(possible_cuts).subset
 
 
+def epsilon_tree_bipartition(
+    graph: nx.Graph,
+    parts: Sequence,
+    pop_target: Union[float, int],
+    pop_col: str,
+    epsilon: float,
+    node_repeats: int = 1,
+    method: Callable = partial(bipartition_tree, max_attempts=10000),
+) -> Dict:
+    """
+    Uses :func:`~gerrychain.tree.bipartition_tree` to partition a tree into
+    two parts of population ``pop_target`` (within ``epsilon``).
+
+    :param graph: The graph to partition into two :math:`\varepsilon`-balanced parts.
+    :type graph: nx.Graph
+    :param parts: Iterable of part (district) labels (like ``[0,1,2]`` or ``range(4)``).
+    :type parts: Sequence
+    :param pop_target: Target population for each part of the partition.
+    :type pop_target: Union[float, int]
+    :param pop_col: Node attribute key holding population data.
+    :type pop_col: str
+    :param epsilon: How far (as a percentage of ``pop_target``) from ``pop_target`` the parts
+        of the partition can be.
+    :type epsilon: float
+    :param node_repeats: Parameter for :func:`~gerrychain.tree_methods.bipartition_tree` to use.
+        Defaults to 1.
+    :type node_repeats: int, optional
+    :param method: The partition method to use. Defaults to
+        `partial(bipartition_tree, max_attempts=10000)`.
+    :type method: Callable, optional
+
+    :returns: New assignments for the nodes of ``graph``.
+    :rtype: dict
+    """
+    if len(parts) != 2:
+        raise ValueError(
+            "This function only supports bipartitioning. Please ensure that there"
+            + " are exactly 2 parts in the parts list."
+        )
+
+    flips = {}
+    remaining_nodes = graph.node_indices
+
+    lb_pop = pop_target * (1 - epsilon)
+    ub_pop = pop_target * (1 + epsilon)
+    check_pop = lambda x: lb_pop <= x <= ub_pop
+
+    nodes = method(
+        graph.subgraph(remaining_nodes),
+        pop_col=pop_col,
+        pop_target=pop_target,
+        epsilon=epsilon,
+        node_repeats=node_repeats,
+        one_sided_cut=False,
+    )
+
+    if nodes is None:
+        raise BalanceError()
+
+    part_pop = 0
+    for node in nodes:
+        flips[node] = parts[-2]
+        part_pop += graph.nodes[node][pop_col]
+
+    if not check_pop(part_pop):
+        raise PopulationBalanceError()
+
+    remaining_nodes -= nodes
+
+    # All of the remaining nodes go in the last part
+    part_pop = 0
+    for node in remaining_nodes:
+        flips[node] = parts[-1]
+        part_pop += graph.nodes[node][pop_col]
+
+    if not check_pop(part_pop):
+        raise PopulationBalanceError()
+
+    return flips
+
+
+# TODO: Move these recursive partition functions to their own module. They are not
+# central to the operation of the recom function despite being tree methods.
 def recursive_tree_part(
     graph: nx.Graph,
     parts: Sequence,
@@ -825,16 +982,16 @@ def recursive_tree_part(
     ``len(parts)`` parts of population ``pop_target`` (within ``epsilon``). Can be used to
     generate initial seed plans or to implement ReCom-like "merge walk" proposals.
 
-    :param graph: The graph
+    :param graph: The graph to partition into ``len(parts)`` :math:`\varepsilon`-balanced parts.
     :type graph: nx.Graph
-    :param parts: Iterable of part labels (like ``[0,1,2]`` or ``range(4)``)
+    :param parts: Iterable of part (district) labels (like ``[0,1,2]`` or ``range(4)``).
     :type parts: Sequence
-    :param pop_target: Target population for each part of the partition
+    :param pop_target: Target population for each part of the partition.
     :type pop_target: Union[float, int]
-    :param pop_col: Node attribute key holding population data
+    :param pop_col: Node attribute key holding population data.
     :type pop_col: str
     :param epsilon: How far (as a percentage of ``pop_target``) from ``pop_target`` the parts
-        of the partition can be
+        of the partition can be.
     :type epsilon: float
     :param node_repeats: Parameter for :func:`~gerrychain.tree_methods.bipartition_tree` to use.
         Defaluts to 1.
@@ -857,7 +1014,11 @@ def recursive_tree_part(
     # 98% of the target population and the target population.
     debt: Union[int, float] = 0
 
-    for part in parts[:-1]:
+    lb_pop = pop_target * (1 - epsilon)
+    ub_pop = pop_target * (1 + epsilon)
+    check_pop = lambda x: lb_pop <= x <= ub_pop
+
+    for part in parts[:-2]:
         min_pop = max(pop_target * (1 - epsilon), pop_target * (1 - epsilon) - debt)
         max_pop = min(pop_target * (1 + epsilon), pop_target * (1 + epsilon) - debt)
         new_pop_target = (min_pop + max_pop) / 2
@@ -869,6 +1030,7 @@ def recursive_tree_part(
                 pop_target=new_pop_target,
                 epsilon=(max_pop - min_pop) / (2 * new_pop_target),
                 node_repeats=node_repeats,
+                one_sided_cut=True,
             )
         except Exception:
             raise
@@ -881,12 +1043,44 @@ def recursive_tree_part(
             flips[node] = part
             part_pop += graph.nodes[node][pop_col]
 
+        if not check_pop(part_pop):
+            raise PopulationBalanceError()
+
         debt += part_pop - pop_target
         remaining_nodes -= nodes
 
+    # After making n-2 districts, we need to make sure that the last
+    # two districts are both balanced.
+    nodes = method(
+        graph.subgraph(remaining_nodes),
+        pop_col=pop_col,
+        pop_target=pop_target,
+        epsilon=epsilon,
+        node_repeats=node_repeats,
+        one_sided_cut=False,
+    )
+
+    if nodes is None:
+        raise BalanceError()
+
+    part_pop = 0
+    for node in nodes:
+        flips[node] = parts[-2]
+        part_pop += graph.nodes[node][pop_col]
+
+    if not check_pop(part_pop):
+        raise PopulationBalanceError()
+
+    remaining_nodes -= nodes
+
     # All of the remaining nodes go in the last part
+    part_pop = 0
     for node in remaining_nodes:
         flips[node] = parts[-1]
+        part_pop += graph.nodes[node][pop_col]
+
+    if not check_pop(part_pop):
+        raise PopulationBalanceError()
 
     return flips
 
@@ -1003,7 +1197,7 @@ def get_seed_chunks(
 def get_max_prime_factor_less_than(n: int, ceil: int) -> Optional[int]:
     """
     Helper function for recursive_seed_part_inner. Returns the largest prime factor of ``n``
-        less than ``ceil``, or None if all are greater than ceil.
+    less than ``ceil``, or None if all are greater than ceil.
 
     :param n: The number to find the largest prime factor for.
     :type n: int
@@ -1095,7 +1289,7 @@ def recursive_seed_part_inner(
     :type ceil: Optional[int], optional
 
     :returns: New assignments for the nodes of ``graph``.
-    :rtype: List of lists, each list is a district
+    :rtype: List of sets, each set is a district
     """
 
     # Chooses num_chunks
@@ -1115,6 +1309,18 @@ def recursive_seed_part_inner(
     if num_dists == 1:
         return [set(graph.nodes)]
 
+    if num_dists == 2:
+        nodes = method(
+            graph,
+            pop_col=pop_col,
+            pop_target=pop_target,
+            epsilon=epsilon,
+            node_repeats=node_repeats,
+            one_sided_cut=False,
+        )
+
+        return [set(nodes), set(graph.nodes) - set(nodes)]
+
     # bite off a district and recurse into the remaining subgraph
     elif num_chunks is None or num_dists % num_chunks != 0:
         remaining_nodes = set(graph.nodes)
@@ -1124,6 +1330,7 @@ def recursive_seed_part_inner(
             pop_target=pop_target,
             epsilon=epsilon,
             node_repeats=node_repeats,
+            one_sided_cut=True,
         )
         remaining_nodes -= nodes
         assignment = [nodes] + recursive_seed_part_inner(
@@ -1140,7 +1347,13 @@ def recursive_seed_part_inner(
     # split graph into num_chunks chunks, and recurse into each chunk
     elif num_dists % num_chunks == 0:
         chunks = get_seed_chunks(
-            graph, num_chunks, num_dists, pop_target, pop_col, epsilon, method=method
+            graph,
+            num_chunks,
+            num_dists,
+            pop_target,
+            pop_col,
+            epsilon,
+            method=partial(method, one_sided_cut=True),
         )
 
         assignment = []
@@ -1227,3 +1440,7 @@ def recursive_seed_part(
 
 class BalanceError(Exception):
     """Raised when a balanced cut cannot be found."""
+
+
+class PopulationBalanceError(Exception):
+    """Raised when the population of a district is outside the acceptable epsilon range."""
diff --git a/tests/conftest.py b/tests/conftest.py
index da30c585..501906ab 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -3,7 +3,8 @@
 from gerrychain import Graph, Partition
 import random
 from gerrychain.updaters import cut_edges
-import networkx
+import networkx as nx
+
 random.seed(2018)
 
 
@@ -34,6 +35,83 @@ def three_by_three_grid():
     return graph
 
 
+@pytest.fixture
+def four_by_five_grid_for_opt():
+    #  1  2  2  2  2
+    #  1  2  1  1  2
+    #  1  2  2  1  2
+    #  1  1  1  1  2
+
+    # 15 16 17 18 19
+    # 10 11 12 13 14
+    #  5  6  7  8  9
+    #  0  1  2  3  4
+
+    graph = Graph()
+    graph.add_nodes_from(
+        [
+            (0, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (1, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (2, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (3, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (4, {"population": 10, "opt_value": 2, "MVAP": 2}),
+            (5, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (6, {"population": 10, "opt_value": 2, "MVAP": 2}),
+            (7, {"population": 10, "opt_value": 2, "MVAP": 2}),
+            (8, {"population": 10, "opt_value": 1, "MVAP": 2}),
+            (9, {"population": 10, "opt_value": 2, "MVAP": 2}),
+            (10, {"population": 10, "opt_value": 1, "MVAP": 6}),
+            (11, {"population": 10, "opt_value": 2, "MVAP": 6}),
+            (12, {"population": 10, "opt_value": 1, "MVAP": 6}),
+            (13, {"population": 10, "opt_value": 1, "MVAP": 4}),
+            (14, {"population": 10, "opt_value": 2, "MVAP": 4}),
+            (15, {"population": 10, "opt_value": 1, "MVAP": 6}),
+            (16, {"population": 10, "opt_value": 2, "MVAP": 6}),
+            (17, {"population": 10, "opt_value": 2, "MVAP": 6}),
+            (18, {"population": 10, "opt_value": 2, "MVAP": 4}),
+            (19, {"population": 10, "opt_value": 2, "MVAP": 4}),
+        ]
+    )
+
+    graph.add_edges_from(
+        [
+            (0, 1),
+            (0, 5),
+            (1, 2),
+            (1, 6),
+            (2, 3),
+            (2, 7),
+            (3, 4),
+            (3, 8),
+            (4, 9),
+            (5, 6),
+            (5, 10),
+            (6, 7),
+            (6, 11),
+            (7, 8),
+            (7, 12),
+            (8, 9),
+            (8, 13),
+            (9, 14),
+            (10, 11),
+            (10, 15),
+            (11, 12),
+            (11, 16),
+            (12, 13),
+            (12, 17),
+            (13, 14),
+            (13, 18),
+            (14, 19),
+            (15, 16),
+            (16, 17),
+            (17, 18),
+            (18, 19),
+        ]
+    )
+
+    return graph
+
+
 @pytest.fixture
 def graph_with_random_data_factory(three_by_three_grid):
     def factory(columns):
@@ -57,11 +135,12 @@ def graph(three_by_three_grid):
 
 @pytest.fixture
 def example_partition():
-    graph = Graph.from_networkx(networkx.complete_graph(3))
+    graph = Graph.from_networkx(nx.complete_graph(3))
     assignment = {0: 1, 1: 1, 2: 2}
     partition = Partition(graph, assignment, {"cut_edges": cut_edges})
     return partition
 
+
 # From the docs: https://docs.pytest.org/en/latest/example/simple.html#control-skipping-of-tests-according-to-command-line-option
 def pytest_addoption(parser):
     parser.addoption(
diff --git a/tests/optimization/test_gingleator.py b/tests/optimization/test_gingleator.py
new file mode 100644
index 00000000..b0d2c8e0
--- /dev/null
+++ b/tests/optimization/test_gingleator.py
@@ -0,0 +1,229 @@
+from gerrychain import Partition
+from gerrychain.optimization import Gingleator
+from gerrychain.constraints import contiguous
+from gerrychain.proposals import recom
+from gerrychain.updaters import Tally
+from functools import partial
+import pytest
+import numpy as np
+import random
+
+random.seed(2024)
+
+
+def simple_cut_edge_count(partition):
+    return len(partition["cut_edges"])
+
+
+def gingleator_test_partition(four_by_five_grid_for_opt):
+    return Partition(
+        graph=four_by_five_grid_for_opt,
+        assignment={
+            0: 0,
+            1: 0,
+            2: 0,
+            3: 0,
+            4: 0,
+            5: 1,
+            6: 1,
+            7: 1,
+            8: 1,
+            9: 1,
+            10: 2,
+            11: 2,
+            12: 2,
+            13: 2,
+            14: 2,
+            15: 3,
+            16: 3,
+            17: 3,
+            18: 3,
+            19: 3,
+        },
+        updaters={
+            "population": Tally("population", alias="population"),
+            "MVAP": Tally("MVAP", alias="MVAP"),
+            "m_perc": lambda p_dict: {
+                key: p_dict["MVAP"][key] / p_dict["population"][key]
+                for key in p_dict["MVAP"]
+            },
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+
+def test_ginglator_needs_min_perc_or_min_pop_col(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "MVAP": Tally("MVAP", alias="MVAP"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    with pytest.raises(ValueError) as gingle_err:
+        gingles = Gingleator(
+            proposal=proposal,
+            constraints=[contiguous],
+            initial_state=initial_partition,
+            total_pop_col="population",
+            score_function=Gingleator.num_opportunity_dists,
+        )
+
+    assert "`minority_perc_col` and `minority_pop_col` cannot both be `None`" in str(
+        gingle_err.value
+    )
+
+
+def test_ginglator_warns_if_min_perc_and_min_pop_col_set(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "MVAP": Tally("MVAP", alias="MVAP"),
+            "m_perc": lambda p_dict: {
+                key: p_dict["MVAP"][key] / p_dict["population"][key]
+                for key in p_dict["MVAP"]
+            },
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    with pytest.warns() as record:
+        gingles = Gingleator(
+            proposal=proposal,
+            constraints=[contiguous],
+            initial_state=initial_partition,
+            total_pop_col="population",
+            minority_pop_col="MVAP",
+            minority_perc_col="m_perc",
+            score_function=Gingleator.num_opportunity_dists,
+        )
+
+    assert "`minority_perc_col` and `minority_pop_col` are both specified" in str(
+        record.list[0].message
+    )
+
+
+def test_ginglator_finds_best_partition(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "MVAP": Tally("MVAP", alias="MVAP"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    gingles = Gingleator(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        minority_pop_col="MVAP",
+        total_pop_col="population",
+        score_function=Gingleator.num_opportunity_dists,
+    )
+
+    total_steps = 1000
+    burst_length = 10
+
+    max_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(
+        gingles.short_bursts(
+            burst_length=burst_length,
+            num_bursts=total_steps // burst_length,
+            with_progress_bar=True,
+        )
+    ):
+        max_scores_sb[i] = gingles.best_score
+
+    assert max_scores_sb[-1] == 2
+
+
+def test_count_num_opportunity_dists(four_by_five_grid_for_opt):
+    initial_partition = gingleator_test_partition(four_by_five_grid_for_opt)
+
+    assert Gingleator.num_opportunity_dists(initial_partition, "m_perc", 0.5) == 2
+    assert Gingleator.num_opportunity_dists(initial_partition, "m_perc", 0.6) == 0
+
+
+def test_reward_partial_dist(four_by_five_grid_for_opt):
+    initial_partition = gingleator_test_partition(four_by_five_grid_for_opt)
+
+    assert Gingleator.reward_partial_dist(initial_partition, "m_perc", 0.5) == 2 + 0.2
+    assert Gingleator.reward_partial_dist(initial_partition, "m_perc", 0.6) == 0.52
+
+
+def test_reward_next_highest_close(four_by_five_grid_for_opt):
+    initial_partition = gingleator_test_partition(four_by_five_grid_for_opt)
+
+    assert Gingleator.reward_next_highest_close(initial_partition, "m_perc", 0.5) == 2
+    # Rounding needed here because of floating point arithmetic
+    assert (
+        round(
+            Gingleator.reward_next_highest_close(initial_partition, "m_perc", 0.29), 5
+        )
+        == 2 + 0.1
+    )
+
+
+def test_penalize_maximum_over(four_by_five_grid_for_opt):
+    initial_partition = gingleator_test_partition(four_by_five_grid_for_opt)
+
+    assert (
+        Gingleator.penalize_maximum_over(initial_partition, "m_perc", 0.5)
+        == 2.0 + 0.48 / 0.50
+    )
+
+    assert Gingleator.penalize_maximum_over(initial_partition, "m_perc", 0.6) == 0
+
+
+def test_penalize_avg_over(four_by_five_grid_for_opt):
+    initial_partition = gingleator_test_partition(four_by_five_grid_for_opt)
+
+    assert (
+        Gingleator.penalize_avg_over(initial_partition, "m_perc", 0.5)
+        == 2.0 + 0.48 / 0.50
+    )
+
+    assert Gingleator.penalize_avg_over(initial_partition, "m_perc", 0.6) == 0
diff --git a/tests/optimization/test_single_metric.py b/tests/optimization/test_single_metric.py
new file mode 100644
index 00000000..0acbeb4a
--- /dev/null
+++ b/tests/optimization/test_single_metric.py
@@ -0,0 +1,583 @@
+from gerrychain import Partition
+from gerrychain.optimization import SingleMetricOptimizer
+from gerrychain.constraints import contiguous
+from gerrychain.proposals import recom
+from gerrychain.updaters import Tally
+from functools import partial
+import numpy as np
+import random
+
+random.seed(2024)
+
+
+def simple_cut_edge_count(partition):
+    return len(partition["cut_edges"])
+
+
+# ================
+#   SHORT BURSTS
+# ================
+
+
+def test_single_metric_sb_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+    burst_length = 5
+
+    min_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.short_bursts(
+            burst_length=burst_length,
+            num_bursts=total_steps // burst_length,
+            with_progress_bar=True,
+        )
+    ):
+        min_scores_sb[i] = optimizer.best_score
+
+    assert min_scores_sb[-1] == 11
+
+
+def test_single_metric_tilted_sb_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+    burst_length = 5
+
+    min_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.tilted_short_bursts(
+            burst_length=burst_length,
+            num_bursts=total_steps // burst_length,
+            p=0.2,
+            with_progress_bar=True,
+        )
+    ):
+        min_scores_sb[i] = optimizer.best_score
+
+    assert min_scores_sb[-1] == 11
+
+
+def test_single_metric_variable_len_sb_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.variable_length_short_bursts(
+            num_steps=total_steps,
+            stuck_buffer=2,
+            with_progress_bar=True,
+        )
+    ):
+        min_scores_sb[i] = optimizer.best_score
+
+    assert min_scores_sb[-1] == 11
+
+
+# ========================
+#   SIMULATED ANNEALING
+# ========================
+
+
+def test_single_metric_sa_jumpcycle_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.jumpcycle_beta_function(10, 10),
+            beta_magnitude=1,
+            with_progress_bar=True,
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    assert min_scores_anneal[-1] == 11
+
+
+def test_single_metric_sa_lincycle_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.linearcycle_beta_function(10, 10, 10),
+            beta_magnitude=1,
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    assert min_scores_anneal[-1] == 11
+
+
+def test_single_metric_sa_linear_jumpcycle_attains_min_quickly(
+    four_by_five_grid_for_opt,
+):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.linear_jumpcycle_beta_function(10, 10, 10),
+            beta_magnitude=1,
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    assert min_scores_anneal[-1] == 11
+
+
+def test_single_metric_sa_logitcycle_attains_min_quickly(four_by_five_grid_for_opt):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.logitcycle_beta_function(10, 10, 10),
+            beta_magnitude=1,
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    assert min_scores_anneal[-1] == 11
+
+
+def test_single_metric_sa_logit_jumpcycle_attains_min_quickly(
+    four_by_five_grid_for_opt,
+):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 200
+
+    min_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.logit_jumpcycle_beta_function(10, 10, 10),
+            beta_magnitude=1,
+        )
+    ):
+        min_scores_anneal[i] = optimizer.best_score
+
+    assert min_scores_anneal[-1] == 11
+
+
+# ===============
+#   TILTED RUNS
+# ===============
+
+
+def test_single_metric_tilted_runs_attains_min_quickly_with_p_eq_0p1(
+    four_by_five_grid_for_opt,
+):
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={
+            "population": Tally("population", alias="population"),
+            "my_cut_edges": simple_cut_edge_count,
+        },
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=simple_cut_edge_count,
+        maximize=False,
+    )
+
+    total_steps = 1000
+
+    min_scores_tilt = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.tilted_run(num_steps=total_steps, p=0.1, with_progress_bar=True)
+    ):
+        min_scores_tilt[i] = optimizer.best_score
+
+    assert min_scores_tilt[-1] == 11
+
+
+# ==========================
+#   SOME HARDER TEST CASES
+# ==========================
+
+
+def test_single_metric_sb_finds_hard_max(four_by_five_grid_for_opt):
+    def opt_fn(partition):
+        mx = 10
+        count = sum(1 for x in partition["opt_value_sum"].values() if x == mx)
+        return count
+
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={"opt_value_sum": Tally("opt_value", alias="opt_value_sum")},
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=opt_fn,
+        maximize=True,
+    )
+
+    total_steps = 10000
+    burst_length = 100
+
+    max_scores_sb = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.short_bursts(
+            burst_length=burst_length,
+            num_bursts=total_steps // burst_length,
+            with_progress_bar=True,
+        )
+    ):
+        max_scores_sb[i] = optimizer.best_score
+
+    assert np.max(max_scores_sb) == 2
+
+
+def test_single_metric_sa_finds_hard_max(four_by_five_grid_for_opt):
+    def opt_fn(partition):
+        mx = 10
+        count = sum(1 for x in partition["opt_value_sum"].values() if x == mx)
+        return count
+
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={"opt_value_sum": Tally("opt_value", alias="opt_value_sum")},
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=opt_fn,
+        maximize=True,
+    )
+
+    total_steps = 10000
+
+    max_scores_anneal = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.simulated_annealing(
+            total_steps,
+            optimizer.linear_jumpcycle_beta_function(10, 10, 10),
+            beta_magnitude=1,
+        )
+    ):
+        max_scores_anneal[i] = optimizer.best_score
+
+    assert np.max(max_scores_anneal) == 2
+
+
+def test_single_metric_tilted_runs_finds_hard_max(four_by_five_grid_for_opt):
+    def opt_fn(partition):
+        mx = 10
+        count = sum(1 for x in partition["opt_value_sum"].values() if x == mx)
+        return count
+
+    initial_partition = Partition.from_random_assignment(
+        graph=four_by_five_grid_for_opt,
+        n_parts=4,
+        epsilon=0.0,
+        pop_col="population",
+        updaters={"opt_value_sum": Tally("opt_value", alias="opt_value_sum")},
+    )
+
+    ideal_pop = sum(initial_partition["population"].values()) / 4
+
+    proposal = partial(
+        recom,
+        pop_col="population",
+        pop_target=ideal_pop,
+        epsilon=0.0,
+        node_repeats=1,
+    )
+
+    optimizer = SingleMetricOptimizer(
+        proposal=proposal,
+        constraints=[contiguous],
+        initial_state=initial_partition,
+        optimization_metric=opt_fn,
+        maximize=True,
+    )
+
+    total_steps = 5000
+
+    min_scores_tilt = np.zeros(total_steps)
+    for i, part in enumerate(
+        optimizer.tilted_run(num_steps=total_steps, p=0.1, with_progress_bar=True)
+    ):
+        min_scores_tilt[i] = optimizer.best_score
+
+    assert np.max(min_scores_tilt) == 2
diff --git a/tests/test_reproducibility.py b/tests/test_reproducibility.py
index 755d499b..9c0ffd94 100644
--- a/tests/test_reproducibility.py
+++ b/tests/test_reproducibility.py
@@ -1,10 +1,10 @@
 import os
-
 import pytest
-
 import random
+
 random.seed(2018)
 
+
 @pytest.mark.skipif(
     True or os.environ.get("PYTHONHASHSEED", 1) != "0",
     reason="Need to fix the PYTHONHASHSEED for reproducibility. The expected flips "
@@ -61,7 +61,8 @@ def test_repeatable(three_by_three_grid):
     print(flips)
     assert flips == expected_flips
 
-@pytest.mark.slow
+
+# @pytest.mark.slow
 def test_pa_freeze():
     from gerrychain import (
         GeographicPartition,
@@ -75,6 +76,7 @@ def test_pa_freeze():
     import hashlib
     from gerrychain.proposals import recom
     from functools import partial
+
     random.seed(2018)
 
     graph = Graph.from_json("docs/_static/PA_VTDs.json")
@@ -91,10 +93,16 @@ def test_pa_freeze():
     # We use functools.partial to bind the extra parameters (pop_col, pop_target, epsilon, node_repeats)
     # of the recom proposal.
     proposal = partial(
-        recom, pop_col="TOT_POP", pop_target=ideal_population, epsilon=0.02, node_repeats=2
+        recom,
+        pop_col="TOT_POP",
+        pop_target=ideal_population,
+        epsilon=0.02,
+        node_repeats=2,
     )
 
-    pop_constraint = constraints.within_percent_of_ideal_population(initial_partition, 0.02)
+    pop_constraint = constraints.within_percent_of_ideal_population(
+        initial_partition, 0.02
+    )
 
     chain = MarkovChain(
         proposal=proposal,
@@ -109,8 +117,10 @@ def test_pa_freeze():
         result += str(list(sorted(partition.population.values())))
         result += str(len(partition.cut_edges))
         result += str(count) + "\n"
-    
+
     # This needs to be changed every time we change the
     # tests around
-    assert hashlib.sha256(result.encode()).hexdigest() == "7f355cd0f7c235f4d285db1c7593ba0d4a5558c404b70521c9837125df418384"
-    
\ No newline at end of file
+    assert (
+        hashlib.sha256(result.encode()).hexdigest()
+        == "aa7a5f7116c7b10b7857aeb3555fd88d8dfc5d810dc0b706f8772efba3c78607"
+    )
diff --git a/tests/test_tree.py b/tests/test_tree.py
index e419a3ca..1805b8ca 100644
--- a/tests/test_tree.py
+++ b/tests/test_tree.py
@@ -12,15 +12,18 @@
     bipartition_tree,
     random_spanning_tree,
     find_balanced_edge_cuts_contraction,
+    find_balanced_edge_cuts_memoization,
     recursive_tree_part,
     recursive_seed_part,
     PopulatedGraph,
     uniform_spanning_tree,
     get_max_prime_factor_less_than,
-    bipartition_tree_random
+    bipartition_tree_random,
 )
 from gerrychain.updaters import Tally, cut_edges
+from functools import partial
 import random
+
 random.seed(2018)
 
 
@@ -66,35 +69,132 @@ def test_bipartition_tree_returns_within_epsilon_of_target_pop(graph_with_pop):
     assert abs(part_pop - ideal_pop) / ideal_pop < epsilon
 
 
-def test_recursive_tree_part_returns_within_epsilon_of_target_pop(twelve_by_twelve_with_pop):
+def test_recursive_tree_part_returns_within_epsilon_of_target_pop(
+    twelve_by_twelve_with_pop,
+):
+    n_districts = 7  # 144/7 ≈ 20.5 nodes/subgraph (1 person/node)
+    ideal_pop = (
+        sum(
+            twelve_by_twelve_with_pop.nodes[node]["pop"]
+            for node in twelve_by_twelve_with_pop
+        )
+    ) / n_districts
+    epsilon = 0.05
+    result = recursive_tree_part(
+        twelve_by_twelve_with_pop,
+        range(n_districts),
+        ideal_pop,
+        "pop",
+        epsilon,
+    )
+    partition = Partition(
+        twelve_by_twelve_with_pop, result, updaters={"pop": Tally("pop")}
+    )
+    return all(
+        abs(part_pop - ideal_pop) / ideal_pop < epsilon
+        for part_pop in partition["pop"].values()
+    )
+
+
+def test_recursive_tree_part_returns_within_epsilon_of_target_pop_using_contraction(
+    twelve_by_twelve_with_pop,
+):
     n_districts = 7  # 144/7 ≈ 20.5 nodes/subgraph (1 person/node)
-    ideal_pop = (sum(twelve_by_twelve_with_pop.nodes[node]["pop"]
-                     for node in twelve_by_twelve_with_pop)) / n_districts
+    ideal_pop = (
+        sum(
+            twelve_by_twelve_with_pop.nodes[node]["pop"]
+            for node in twelve_by_twelve_with_pop
+        )
+    ) / n_districts
     epsilon = 0.05
-    result = recursive_tree_part(twelve_by_twelve_with_pop, range(n_districts),
-                                 ideal_pop, "pop", epsilon)
-    partition = Partition(twelve_by_twelve_with_pop, result,
-                          updaters={"pop": Tally("pop")})
-    return all(abs(part_pop - ideal_pop) / ideal_pop < epsilon
-               for part_pop in partition['pop'].values())
-
-def test_recursive_seed_part_returns_within_epsilon_of_target_pop(twelve_by_twelve_with_pop):
+    result = recursive_tree_part(
+        twelve_by_twelve_with_pop,
+        range(n_districts),
+        ideal_pop,
+        "pop",
+        epsilon,
+        method=partial(
+            bipartition_tree,
+            max_attempts=10000,
+            balance_edge_fn=find_balanced_edge_cuts_contraction,
+        ),
+    )
+    partition = Partition(
+        twelve_by_twelve_with_pop, result, updaters={"pop": Tally("pop")}
+    )
+    return all(
+        abs(part_pop - ideal_pop) / ideal_pop < epsilon
+        for part_pop in partition["pop"].values()
+    )
+
+
+def test_recursive_seed_part_returns_within_epsilon_of_target_pop(
+    twelve_by_twelve_with_pop,
+):
     n_districts = 7  # 144/7 ≈ 20.5 nodes/subgraph (1 person/node)
-    ideal_pop = (sum(twelve_by_twelve_with_pop.nodes[node]["pop"]
-                     for node in twelve_by_twelve_with_pop)) / n_districts
+    ideal_pop = (
+        sum(
+            twelve_by_twelve_with_pop.nodes[node]["pop"]
+            for node in twelve_by_twelve_with_pop
+        )
+    ) / n_districts
     epsilon = 0.1
-    result = recursive_seed_part(twelve_by_twelve_with_pop, range(n_districts),
-                                 ideal_pop, "pop", epsilon, n=5, ceil=None)
-    partition = Partition(twelve_by_twelve_with_pop, result,
-                          updaters={"pop": Tally("pop")})
-    return all(abs(part_pop - ideal_pop) / ideal_pop < epsilon
-               for part_pop in partition['pop'].values())
+    result = recursive_seed_part(
+        twelve_by_twelve_with_pop,
+        range(n_districts),
+        ideal_pop,
+        "pop",
+        epsilon,
+        n=5,
+        ceil=None,
+    )
+    partition = Partition(
+        twelve_by_twelve_with_pop, result, updaters={"pop": Tally("pop")}
+    )
+    return all(
+        abs(part_pop - ideal_pop) / ideal_pop < epsilon
+        for part_pop in partition["pop"].values()
+    )
+
+
+def test_recursive_seed_part_returns_within_epsilon_of_target_pop_using_contraction(
+    twelve_by_twelve_with_pop,
+):
+    n_districts = 7  # 144/7 ≈ 20.5 nodes/subgraph (1 person/node)
+    ideal_pop = (
+        sum(
+            twelve_by_twelve_with_pop.nodes[node]["pop"]
+            for node in twelve_by_twelve_with_pop
+        )
+    ) / n_districts
+    epsilon = 0.1
+    result = recursive_seed_part(
+        twelve_by_twelve_with_pop,
+        range(n_districts),
+        ideal_pop,
+        "pop",
+        epsilon,
+        n=5,
+        ceil=None,
+        method=partial(
+            bipartition_tree,
+            max_attempts=10000,
+            balance_edge_fn=find_balanced_edge_cuts_contraction,
+        ),
+    )
+    partition = Partition(
+        twelve_by_twelve_with_pop, result, updaters={"pop": Tally("pop")}
+    )
+    return all(
+        abs(part_pop - ideal_pop) / ideal_pop < epsilon
+        for part_pop in partition["pop"].values()
+    )
 
 
 def test_recursive_seed_part_uses_method(twelve_by_twelve_with_pop):
     calls = 0
 
-    def dummy_method(graph, pop_col, pop_target, epsilon, node_repeats):
+    def dummy_method(graph, pop_col, pop_target, epsilon, node_repeats, one_sided_cut):
         nonlocal calls
         calls += 1
         return bipartition_tree(
@@ -104,6 +204,7 @@ def dummy_method(graph, pop_col, pop_target, epsilon, node_repeats):
             epsilon=epsilon,
             node_repeats=node_repeats,
             max_attempts=10000,
+            one_sided_cut=one_sided_cut,
         )
 
     n_districts = 7  # 144/7 ≈ 20.5 nodes/subgraph (1 person/node)
@@ -130,8 +231,11 @@ def dummy_method(graph, pop_col, pop_target, epsilon, node_repeats):
     # implementation detail)
     assert calls >= n_districts - 1
 
-def test_recursive_seed_part_with_n_unspecified_within_epsilon(twelve_by_twelve_with_pop):
-    n_districts = 6 # This should set n=3
+
+def test_recursive_seed_part_with_n_unspecified_within_epsilon(
+    twelve_by_twelve_with_pop,
+):
+    n_districts = 6  # This should set n=3
     ideal_pop = (
         sum(
             twelve_by_twelve_with_pop.nodes[node]["pop"]
@@ -147,10 +251,14 @@ def test_recursive_seed_part_with_n_unspecified_within_epsilon(twelve_by_twelve_
         epsilon,
         ceil=None,
     )
-    partition = Partition(twelve_by_twelve_with_pop, result,
-                          updaters={"pop": Tally("pop")})
-    return all(abs(part_pop - ideal_pop) / ideal_pop < epsilon
-               for part_pop in partition['pop'].values())
+    partition = Partition(
+        twelve_by_twelve_with_pop, result, updaters={"pop": Tally("pop")}
+    )
+    return all(
+        abs(part_pop - ideal_pop) / ideal_pop < epsilon
+        for part_pop in partition["pop"].values()
+    )
+
 
 def test_random_spanning_tree_returns_tree_with_pop_attribute(graph_with_pop):
     tree = random_spanning_tree(graph_with_pop)
@@ -164,9 +272,9 @@ def test_uniform_spanning_tree_returns_tree_with_pop_attribute(graph_with_pop):
 
 def test_bipartition_tree_returns_a_tree(graph_with_pop):
     ideal_pop = sum(graph_with_pop.nodes[node]["pop"] for node in graph_with_pop) / 2
-    tree = Graph.from_networkx(networkx.Graph(
-        [(0, 1), (1, 2), (1, 4), (3, 4), (4, 5), (3, 6), (6, 7), (6, 8)]
-    ))
+    tree = Graph.from_networkx(
+        networkx.Graph([(0, 1), (1, 2), (1, 4), (3, 4), (4, 5), (3, 6), (6, 7), (6, 8)])
+    )
     for node in tree:
         tree.nodes[node]["pop"] = graph_with_pop.nodes[node]["pop"]
 
@@ -186,13 +294,14 @@ def test_recom_works_as_a_proposal(partition_with_pop):
     proposal = functools.partial(
         recom, pop_col="pop", pop_target=ideal_pop, epsilon=0.25, node_repeats=5
     )
-    constraints = [within_percent_of_ideal_population(partition_with_pop, 0.25, "pop")]
+    constraints = [contiguous]
 
     chain = MarkovChain(proposal, constraints, lambda x: True, partition_with_pop, 100)
 
     for state in chain:
         assert contiguous(state)
 
+
 def test_reversible_recom_works_as_a_proposal(partition_with_pop):
     random.seed(2018)
     graph = partition_with_pop.graph
@@ -208,11 +317,10 @@ def test_reversible_recom_works_as_a_proposal(partition_with_pop):
         assert contiguous(state)
 
 
-
 def test_find_balanced_cuts_contraction():
-    tree = Graph.from_networkx(networkx.Graph(
-        [(0, 1), (1, 2), (1, 4), (3, 4), (4, 5), (3, 6), (6, 7), (6, 8)]
-    ))
+    tree = Graph.from_networkx(
+        networkx.Graph([(0, 1), (1, 2), (1, 4), (3, 4), (4, 5), (3, 6), (6, 7), (6, 8)])
+    )
 
     # 0 - 1 - 2
     #   ||
@@ -230,13 +338,62 @@ def test_find_balanced_cuts_contraction():
     assert edges == {(1, 4), (3, 4), (3, 6)}
 
 
+def test_no_balanced_cuts_contraction_when_one_side_okay():
+    tree = Graph.from_networkx(networkx.Graph([(0, 1), (1, 2), (2, 3), (3, 4)]))
+
+    populations = {0: 4, 1: 4, 2: 3, 3: 3, 4: 3}
+
+    populated_tree = PopulatedGraph(
+        graph=tree, populations=populations, ideal_pop=10, epsilon=0.1
+    )
+
+    cuts = find_balanced_edge_cuts_contraction(populated_tree, one_sided_cut=False)
+    assert cuts == []
+
+
+def test_find_balanced_cuts_memo():
+    tree = Graph.from_networkx(
+        networkx.Graph([(0, 1), (1, 2), (1, 4), (3, 4), (4, 5), (3, 6), (6, 7), (6, 8)])
+    )
+
+    # 0 - 1 - 2
+    #   ||
+    # 3= 4 - 5
+    # ||
+    # 6- 7
+    # |
+    # 8
+
+    populated_tree = PopulatedGraph(
+        tree, {node: 1 for node in tree}, len(tree) / 2, 0.5
+    )
+    cuts = find_balanced_edge_cuts_memoization(populated_tree)
+    edges = set(tuple(sorted(cut.edge)) for cut in cuts)
+    assert edges == {(1, 4), (3, 4), (3, 6)}
+
+
+def test_no_balanced_cuts_memo_when_one_side_okay():
+    tree = Graph.from_networkx(networkx.Graph([(0, 1), (1, 2), (2, 3), (3, 4)]))
+
+    populations = {0: 4, 1: 4, 2: 3, 3: 3, 4: 3}
+
+    populated_tree = PopulatedGraph(
+        graph=tree, populations=populations, ideal_pop=10, epsilon=0.1
+    )
+
+    cuts = find_balanced_edge_cuts_memoization(populated_tree)
+    assert cuts == []
+
+
 def test_prime_bound():
-    assert get_max_prime_factor_less_than(2024, 20) == 11 \
-        and get_max_prime_factor_less_than(2024, 1) == None \
-        and get_max_prime_factor_less_than(2024, 2000) == 23 \
+    assert (
+        get_max_prime_factor_less_than(2024, 20) == 11
+        and get_max_prime_factor_less_than(2024, 1) == None
+        and get_max_prime_factor_less_than(2024, 2000) == 23
         and get_max_prime_factor_less_than(2024, -1) == None
-      
-  
+    )
+
+
 def test_bipartition_tree_random_returns_a_subset_of_nodes(graph_with_pop):
     ideal_pop = sum(graph_with_pop.nodes[node]["pop"] for node in graph_with_pop) / 2
     result = bipartition_tree_random(graph_with_pop, "pop", ideal_pop, 0.25, 10)
@@ -250,4 +407,4 @@ def test_bipartition_tree_random_returns_within_epsilon_of_target_pop(graph_with
     result = bipartition_tree_random(graph_with_pop, "pop", ideal_pop, epsilon, 10)
 
     part_pop = sum(graph_with_pop.nodes[node]["pop"] for node in result)
-    assert abs(part_pop - ideal_pop) / ideal_pop < epsilon
\ No newline at end of file
+    assert abs(part_pop - ideal_pop) / ideal_pop < epsilon
diff --git a/tests/updaters/test_cut_edges.py b/tests/updaters/test_cut_edges.py
index f43c97ba..bca561c8 100644
--- a/tests/updaters/test_cut_edges.py
+++ b/tests/updaters/test_cut_edges.py
@@ -4,10 +4,12 @@
 
 from gerrychain import MarkovChain, Partition, proposals
 from gerrychain.accept import always_accept
-from gerrychain.constraints import (no_vanishing_districts,
-                                    single_flip_contiguous)
+from gerrychain.constraints import no_vanishing_districts, contiguous
 from gerrychain.grid import Grid
 from gerrychain.updaters import cut_edges, cut_edges_by_part
+import random
+
+random.seed(2018)
 
 # This is copied and pasted, but should be done with some proper
 # pytest configuration instead:
@@ -27,7 +29,7 @@ def invalid_cut_edges(partition):
 
 
 def test_cut_edges_doesnt_duplicate_edges_with_different_order_of_nodes(
-    three_by_three_grid
+    three_by_three_grid,
 ):
     graph = three_by_three_grid
     assignment = {0: 1, 1: 1, 2: 2, 3: 1, 4: 1, 5: 2, 6: 2, 7: 2, 8: 2}
@@ -65,7 +67,7 @@ def test_cut_edges_can_handle_multiple_flips(three_by_three_grid):
 
 
 def test_cut_edges_by_part_doesnt_duplicate_edges_with_opposite_order_of_nodes(
-    three_by_three_grid
+    three_by_three_grid,
 ):
     graph = three_by_three_grid
     assignment = {0: 1, 1: 1, 2: 2, 3: 1, 4: 1, 5: 2, 6: 2, 7: 2, 8: 2}
@@ -144,7 +146,7 @@ def test_cut_edges_matches_naive_cut_edges_at_every_step(proposal, number_of_ste
 
     chain = MarkovChain(
         proposal,
-        [single_flip_contiguous, no_vanishing_districts],
+        [contiguous, no_vanishing_districts],
         always_accept,
         partition,
         number_of_steps,