From e9c3306135ac60f37638052f947f17b450d0b1d8 Mon Sep 17 00:00:00 2001 From: Matt Helm <30706758+mthelm85@users.noreply.github.com> Date: Tue, 5 Mar 2024 06:24:42 -0800 Subject: [PATCH] Add Optimal Meatballs and The Traveling Salesman Game (#53) --- src/plot/Optimal Meatballs.jl | 1249 ++++++++++++++++++ src/puzzles-games/Traveling Salesman Game.jl | 486 +++++++ 2 files changed, 1735 insertions(+) create mode 100644 src/plot/Optimal Meatballs.jl create mode 100644 src/puzzles-games/Traveling Salesman Game.jl diff --git a/src/plot/Optimal Meatballs.jl b/src/plot/Optimal Meatballs.jl new file mode 100644 index 0000000..4c92805 --- /dev/null +++ b/src/plot/Optimal Meatballs.jl @@ -0,0 +1,1249 @@ +### A Pluto.jl notebook ### +# v0.19.36 + +#> [frontmatter] +#> license_url = "https://unlicense.org/" +#> image = "https://upload.wikimedia.org/wikipedia/commons/thumb/3/37/9975Poblacion%2C_Baliuag%2C_Bulacan_06.jpg/640px-9975Poblacion%2C_Baliuag%2C_Bulacan_06.jpg" +#> title = "Optimal Meatballs" +#> date = "2024-02-08" +#> tags = ["circle-packing", "Plots.jl", "PlutoUI.jl"] +#> description = "Learn about circle packing by optimizing the size of meatballs! 🍝" +#> license = "Unlicense" +#> +#> [[frontmatter.author]] +#> name = "Matt Helm" +#> url = "https://avatars.githubusercontent.com/u/30706758?v=4" + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═║ fc7f9b9c-e5b8-4188-b14a-cf8905de4e86 +begin + using Plots + using PlutoUI +end + +# ╔═║ fc6cfa1f-2d92-4677-8dbc-0dd7ef20aa1b +md""" +## Optimal Meatballs + +### Background + +I was recently preparing a meal of spaghetti and meatballs and, after forming all of my meatballs, was disappointed to learn that they would not all fit in my sautΓ© pan. This meant that I would have to brown my meatballs in two batches, taking more time. I wondered: **Can I fit more of the meatball mix in the pan by forming a large number of small meatballs, or is it better to make a smaller number of large meatballs?** + +As I like to let my browned meatballs simmer in my tomato sauce for a while, I had some time on my hands and I knew I could answer this question with Julia and a Pluto notebook. + +### The Process + +I needed to first determine the most efficient way to organize the meatballs in the sautΓ© pan. It turns out, per [this Wikipedia article](https://en.wikipedia.org/wiki/Circle_packing), that the most efficient way to organize circles in a two-dimensional plane is with a hexagonal packing arrangement. The article states: + +> In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, like a honeycomb), and each circle is surrounded by six other circles. + +Armed with this knowledge, I set up a plot with a large grey circle, representing my pan, and a number of smaller brown circles inside, representing the meatballs, arranged in a hexagonal lattice. I decided that I didn't want meatballs with a diameter less than 1 inch, nor did I want my meatballs to be larger than 3 inches. I was also constrained by the size of my sautΓ© pan, 10 inches in diameter. Using these bounds, I created the following plot, which allowed me to visualize different meatball sizes in my pan, along with the number of resulting meatballs, and the total weight of the meatball mixture: +""" + +# ╔═║ 8839c735-a990-4b49-b3e8-1384cf5dc2bc +radius_min = 0.5 # minimum meatball radius + +# ╔═║ b7a76ab8-3533-4b76-8971-c27ff631860f +radius_max = 1.5 # maximum meatball radius + +# ╔═║ 004a0be9-4f8f-441d-8f46-bea893a7a62e +pan_radius = 5 + +# ╔═║ d9268e61-13b3-467b-b52a-254fda9a6e04 +md""" +Meatball radius slider: +""" + +# ╔═║ 3766ebc2-96d6-4339-aee2-bc05d22f7cca +@bind r Slider(radius_min:0.1:radius_max; show_value=true) + +# ╔═║ d8258617-81e5-48a3-b935-49e6f80f2170 +md""" +### The Solution + +It turns out, given my parameters (pan size, max/min meatball size), the optimal solution is to prepare seven, 2.8 inch (diameter) meatballs! So, while I won't be measuring my meatballs in the future, I know now that I should generally opt for fewer, but larger meatballs and I may be able to cook them all at once. + +Bon AppΓ©tit 🍝 +""" + +# ╔═║ 94d37278-0aad-4979-aa41-0eddb3fffaf1 +TableOfContents() + +# ╔═║ 9185ac2d-6ef3-45d9-a474-b4b104968532 +function circle_shape(h, k, r) + ΞΈ = LinRange(0, 2 * Ο€, 500) + h .+ r * sin.(ΞΈ), k .+ r * cos.(ΞΈ) +end; + +# ╔═║ 71294855-6d31-4539-b396-2177cd86254e +begin + R = pan_radius + D = sqrt(3) * r # hexagon diameter + + grid = [ + (iseven(i) ? x + r : x, y) for x in -R:2*r:R, # offset for hexagonal lattice + (i, y) in enumerate(-R:D:R) + ] + + in_pan(pair) = sqrt(pair[1]^2 + pair[2]^2) + r ≀ R # check to see if the meatball is contained in the pan + num_meatballs = count(pair -> in_pan(pair), grid) + total_volume(N, r) = (4/3 * Ο€ * r^3) * N + V = total_volume(num_meatballs, r) + total_weight(V) = (V * 16.387) / 453.592 + # total weight formula assumes density of 1 gram per cubic centimeter. 1 cubic inch β‰ˆ 16.387cmΒ³. Also, there are approximately 453.592 grams per pound + + p = plot( + circle_shape(0,0,R), + seriestype=:shape, + aspect_ratio=1, + legend=false, + color=:silver, + framestyle=:none, + title="Size = $(r*2) in Total Meatballs = $(num_meatballs) Weight = $(round(total_weight(V), digits=1)) lbs" + ) + + for pair in grid + if in_pan(pair) + plot!( + circle_shape(pair[1], pair[2], r), + aspect_ratio=1, + color=:brown, + seriestype=:shape, + ) + end + end + + p +end + +# ╔═║ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" + +[compat] +Plots = "~1.39.0" +PlutoUI = "~0.7.55" +""" + +# ╔═║ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.0" +manifest_format = "2.0" +project_hash = "ba273c428884691a260691f03ec51300a3d7ca2b" + 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tags = ["optimization", "game", "traveling-salesman"] +#> license = "Unlicense" +#> description = "A fun game to learn about the traveling salesman problem and the simulated annealing algorithm." +#> date = "2024-02-16" +#> +#> [[frontmatter.author]] +#> name = "Matt Helm" +#> url = "https://avatars.githubusercontent.com/u/30706758?v=4" + +using Markdown +using InteractiveUtils + +# ╔═║ 5bf31410-c914-11ee-33f0-c5c134d6b4d8 +begin + using Distances + using HypertextLiteral + using Random + using Statistics +end + +# ╔═║ 2ee01ff1-a85f-4ff9-8d25-6af053b2d8aa +md""" +## The Traveling Salesman Game + +The Traveling Salesman Problem (TSP) is a classic optimization problem in the fields of computer science and operations research. It involves finding the shortest possible route that visits a set of given cities once, and then returns to the original city. The challenge is to determine the optimal ordering of the cities to minimize the total distance traveled by the salesman. + +In this notebook, you get a chance to try to solve the problem while competing against the computer, which solves it using an algorithm known as *Simulated Annealing*, an optimization algorithm inspired by the annealing process in metallurgy. It is used to solve combinatorial optimization problems like the TSP. + +#### How to Play + +In the cell below, set `N` to the number of cities (or houses in our case) that you would like to start with. These will be generated randomly. Then, set `your_solution` to the path that you believe is the shortest. There is no need to add the starting point to the end of the vector; there is code below that handles that for you. Once you have entered your solution, push the `Go!` button and see if you beat the computer! + +To play another round, or to generate new points, re-run the cell that defines `N`. +""" + +# ╔═║ 243063ab-0556-4fcb-950a-f7533a2f88fa +N = 5 + +# ╔═║ 069a3cdc-6f8e-4470-a6a8-8312eb6b5df5 +your_solution = [1,2,3,4,5] + +# ╔═║ d25e7bed-3aae-43a1-aa5c-ef44cca55242 +begin + truck_url = "https://raw.githubusercontent.com/mthelm85/travelling-salesman-game/main/assets/car2.png" + truck2_url = "https://raw.githubusercontent.com/mthelm85/travelling-salesman-game/main/assets/car5.png" + house_url = "https://raw.githubusercontent.com/mthelm85/travelling-salesman-game/main/assets/house1.png" + map_url = "https://raw.githubusercontent.com/mthelm85/travelling-salesman-game/main/assets/grass.png" +end; + +# ╔═║ d9ca9f51-d5dd-4321-bae8-fec16a53d250 +begin + struct Bounds + x::Int + y::Int + width::Int + height::Int + end + + struct Point + x::Int + y::Int + end +end + +# ╔═║ c5a0d444-770d-4dc8-8267-963d9f2be545 +function random_point(bounds, points) + x = rand(bounds.x:bounds.x + bounds.width - 1) + y = rand(bounds.y:bounds.y + bounds.height - 1) + + # make sure points aren't too close together + threshold = 20 + + for point in points + if abs(point.x - x) < threshold || abs(point.y - y) < threshold + return random_point(bounds, points) + end + end + + return Point(x, y) +end; + +# ╔═║ 739b8137-f6b6-4516-b28d-acdb79828be6 +function create_points(b, N) + points = [] + for i in 1:N + push!(points, random_point(b, points)) + end + return points +end; + +# ╔═║ fdfdbb5c-2204-434c-8249-bc9ad3e72531 +begin + get_points_xs(points) = [point.x for point in points] + get_points_ys(points) = [point.y for point in points] +end; + +# ╔═║ 7c0f26a0-a478-4887-91c8-e5a747b97c19 +function total_distance(points, tour) + total_distance = 0.0 + n = length(points) + + for i in 1:n-1 + p1 = points[tour[i]] + p2 = points[tour[i+1]] + total_distance += evaluate(Euclidean(), [p1.x, p1.y], [p2.x, p2.y]) + end + + p_last = points[tour[end]] + p_first = points[tour[1]] + # Return to the starting point + total_distance += evaluate(Euclidean(), [p_last.x, p_last.y], [p_first.x, p_first.y]) + return total_distance +end; + +# ╔═║ 39556336-9d1c-417a-b3d7-4e424710902d +function simulated_annealing_tsp(points, max_iter, initial_temperature, cooling_rate) + n = length(points) + current_tour = randperm(n) # Initialize with a random tour + best_tour = copy(current_tour) # Keep track of the best tour found + current_distance = total_distance(points, current_tour) + best_distance = current_distance + temperature = initial_temperature + + for iter in 1:max_iter + next_tour = copy(current_tour) # Make a copy of the current tour to modify + i, j = rand(1:n, 2) # Select two random indices + next_tour[i], next_tour[j] = next_tour[j], next_tour[i] # Swap the cities at these indices + next_distance = total_distance(points, next_tour) + delta = next_distance - current_distance + + # If the new tour is shorter, or if it is longer but accepted by the annealing probability + if delta < 0 || exp(-delta / temperature) > rand() + current_tour = copy(next_tour) + current_distance = next_distance + # If the new tour is the best found so far, update the best tour and distance + if current_distance < best_distance + best_tour = copy(current_tour) + best_distance = current_distance + end + end + + temperature *= cooling_rate # Cool down the temperature + end + + return best_tour +end; + +# ╔═║ bb9d1888-9214-43d2-b002-b31ded8715a9 +begin + b = Bounds(100, 100, 450, 280) + points = create_points(b, N) +end; + +# ╔═║ 624c3dc0-2186-4185-9fba-87e522d4a163 +begin + points_xs = get_points_xs(points) + points_ys = get_points_ys(points) + distances = pairwise(Euclidean(), [points_xs points_ys], dims=1) + max_iter = 1000 + initial_temperature = mean(distances) + 3 * std(distances) + cooling_rate = 0.99 + solution_player = vcat(your_solution, your_solution[1]) + player_xs = get_points_xs(points[solution_player]) + player_ys = get_points_ys(points[solution_player]) + solution_computer = simulated_annealing_tsp(points, max_iter, initial_temperature, cooling_rate) + push!(solution_computer, solution_computer[1]) # return to start + computer_xs = get_points_xs(points[solution_computer]) + computer_ys = get_points_ys(points[solution_computer]) + player_distance = total_distance([Point(z[1], z[2]) for z in zip(player_xs, player_ys)], 1:size(player_xs, 1)) + computer_distance = total_distance([Point(z[1], z[2]) for z in zip(computer_xs, computer_ys)], 1:size(computer_xs, 1)) +end; + +# ╔═║ f3bf1b25-cb37-4594-b92b-fcd3f44429e9 +if length(your_solution) == N + @htl(""" + +
+ + + """) +else + @htl(""" +
Make sure  
length(your_solution) == length(N)
+ """) +end + +# ╔═║ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7" +HypertextLiteral = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2" +Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" +Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" + +[compat] +Distances = "~0.10.11" +HypertextLiteral = "~0.9.5" +""" + +# ╔═║ 00000000-0000-0000-0000-000000000002 +PLUTO_MANIFEST_TOML_CONTENTS = """ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.10.1" +manifest_format = "2.0" +project_hash = "1adaeaec1fd57885bb7f86606f24f3c905de5e8d" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" + +[[deps.CompilerSupportLibraries_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae" +version = "1.1.0+0" + +[[deps.Distances]] +deps = ["LinearAlgebra", "Statistics", "StatsAPI"] +git-tree-sha1 = "66c4c81f259586e8f002eacebc177e1fb06363b0" +uuid = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7" +version = "0.10.11" + + [deps.Distances.extensions] + DistancesChainRulesCoreExt = "ChainRulesCore" + DistancesSparseArraysExt = "SparseArrays" + + [deps.Distances.weakdeps] + ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" + SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" + +[[deps.HypertextLiteral]] +deps = ["Tricks"] +git-tree-sha1 = "7134810b1afce04bbc1045ca1985fbe81ce17653" +uuid = "ac1192a8-f4b3-4bfe-ba22-af5b92cd3ab2" +version = "0.9.5" + +[[deps.Libdl]] +uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb" + +[[deps.LinearAlgebra]] +deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"] +uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" + +[[deps.OpenBLAS_jll]] +deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"] +uuid = "4536629a-c528-5b80-bd46-f80d51c5b363" +version = "0.3.23+4" + +[[deps.Random]] +deps = ["SHA"] +uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" + +[[deps.SHA]] +uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce" +version = "0.7.0" + +[[deps.Serialization]] +uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b" + +[[deps.SparseArrays]] +deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"] +uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf" +version = "1.10.0" + +[[deps.Statistics]] +deps = ["LinearAlgebra", "SparseArrays"] +uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" +version = "1.10.0" + +[[deps.StatsAPI]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "1ff449ad350c9c4cbc756624d6f8a8c3ef56d3ed" +uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0" +version = "1.7.0" + +[[deps.SuiteSparse_jll]] +deps = ["Artifacts", "Libdl", "libblastrampoline_jll"] +uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c" +version = "7.2.1+1" + +[[deps.Tricks]] +git-tree-sha1 = "eae1bb484cd63b36999ee58be2de6c178105112f" +uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775" +version = "0.1.8" + +[[deps.libblastrampoline_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" +version = "5.8.0+1" +""" + +# ╔═║ Cell order: +# β•Ÿβ”€2ee01ff1-a85f-4ff9-8d25-6af053b2d8aa +# ╠═243063ab-0556-4fcb-950a-f7533a2f88fa +# ╠═069a3cdc-6f8e-4470-a6a8-8312eb6b5df5 +# β•Ÿβ”€f3bf1b25-cb37-4594-b92b-fcd3f44429e9 +# ╠═5bf31410-c914-11ee-33f0-c5c134d6b4d8 +# ╠═d25e7bed-3aae-43a1-aa5c-ef44cca55242 +# ╠═d9ca9f51-d5dd-4321-bae8-fec16a53d250 +# ╠═c5a0d444-770d-4dc8-8267-963d9f2be545 +# ╠═739b8137-f6b6-4516-b28d-acdb79828be6 +# ╠═fdfdbb5c-2204-434c-8249-bc9ad3e72531 +# ╠═7c0f26a0-a478-4887-91c8-e5a747b97c19 +# ╠═39556336-9d1c-417a-b3d7-4e424710902d +# ╠═bb9d1888-9214-43d2-b002-b31ded8715a9 +# ╠═624c3dc0-2186-4185-9fba-87e522d4a163 +# β•Ÿβ”€00000000-0000-0000-0000-000000000001 +# β•Ÿβ”€00000000-0000-0000-0000-000000000002