StrategicRandomSearch.jl

The Strategic Random Search (SRS) —— A New Global Optimization Algorithm in Julia

Usage

using StrategicRandomSearch

function functn1(x::Vector{Float64})
  # This is the Goldstein - Price Function
  # Bound X1 = [-2, 2], X2 = [-2, 2]
  # Global Optimum:3.0, (0.0, -1.0)
  x1 = x[1]
  x2 = x[2]
  u1 = (x1 + x2 + 1.0)^2
  u2 = 19 .- 14 .* x1 + 3 .* x1^2 - 14 .* x2 + 6 .* x1 * x2 + 3 .* x2^2
  u3 = (2 .* x1 - 3 .* x2)^2
  u4 = 18 .- 32 .* x1 + 12 .* x1^2 + 48 .* x2 - 36 .* x1 * x2 + 27 .* x2^2
  u5 = u1 * u2
  u6 = u3 * u4
  (1 .+ u5) * (30 .+ u6)
end

lower = Float64.([-2, -2])
upper = Float64.([2, 2])
x0 = Float64.([1, 1])
@time r = SRS(functn1, lower, upper; seed=1)

----------------------------------- 
feval     : 3.0000000001097433
x         : [2.92590422779071e-7, -0.9999994691368533]
Iterations: 22
f(x) calls: 1002
----------------------------------- 
  0.038590 seconds (10.67 k allocations: 624.922 KiB)
OptimOutput
  num_iter: Int64 22
  num_call: Int64 1002
  x: Array{Float64}((2,)) [2.92590422779071e-7, -0.9999994691368533]
  feval: Float64 3.0000000001097433
  BY: Array{Float64}((22,)) [37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 26.841025563057322, 26.841025563057322, 21.605702566807324, 10.148481159630524, 5.8236442027222175, 3.0498664685729526  …  3.0000590042771944, 3.000032913496003, 3.000032913496003, 3.000001379924515, 3.0000004974780015, 3.000000289269808, 3.000000289269808, 3.000000022318343, 3.0000000001097433, 3.0000000001097433]
  EachPar: Array{Float64}((22, 2)) [-0.616285424931557 -0.4649638918252177; -0.616285424931557 -0.4649638918252177; … ; 2.92590422779071e-7 -0.9999994691368533; 2.92590422779071e-7 -0.9999994691368533]
  x_iters: Array{Float64}((27, 2)) [1.1122372527217e-311 1.112237252943e-311; 1.1122372531644e-311 1.1122372533857e-311; … ; 1.1122372637887e-311 1.11223726401e-311; 1.1122372642314e-311 1.112237264453e-311]
  feval_iters: Array{Float64}((972,)) [37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425, 37.96459778926425  …  3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433, 3.0000000001097433]

Parameters

和Python比有更新，加入update_eps参数，

• update_eps = true: 增加精细化搜索，耗时长，适合寻找精度要求高的测试函数最优解
• update_eps = false: 减小精细化搜索，耗时短，适合寻水文模型参数率定寻找最优解

Table 1. SRS algorithm parameters

Name	Type	Default	Description
p	int	3	p is the key parameter, and the value is generally 3-20, which needs to be given according to the specific situation
deps	float	12	(0, inf), key parameter for adjusting the precision, the larger the value, the higher the precision and the longer the time
delta	float	0.01	(0, 0.5), key parameter for adjusting the precision, the larger the value, the higher the precision and the longer the time
Vectorization	bool	false	Whether the objective function satisfies the vectorization condition
num	int	1000	if Vectorization=True: num=1000 else: num=10000 (defult).
		10000	The key parameter, representing the maximum number of times the target function is called. When testing, the accuracy can be improved by increasing num.
MAX	bool	true	Whether to find the maximum value of the objective function.
OptimalValue	float	None	The optimal value of the objective function.
ObjectiveLimit	float	None	When the optimal value is known, the algorithm terminates
			within ObjectiveLimit of the optimal value.
eps	Int	4	(0, +inf), it is not critical, and adjustment is not recommended.
update_eps	bool	true	Whether or not to update eps to do refined search parameters. Generally, it can be “false” for model parameter calibration.
ShortLambda	float	0.02	(0, 0.1), not critical, and adjustment is not recommended.
LongLambda	float	0.2	(0.1, 1), not critical, and adjustment is not recommended.
InitialLt	int	3	(0, 10), not critical, and adjustment is not recommended.
Lt	int	2	(0, 10), not critical, and adjustment is not recommended.

References

Please cite the following article:

1. Haoshan Wei, Yongqiang Zhang, Changming Liu, Qi Huang, Pengxin Jia, Zhenwu Xu, Yuhan Guo, The strategic random search (SRS) – A new global optimizer for calibrating hydrological models, Environmental Modelling & Software, 2024, https://doi.org/10.1016/j.envsoft.2023.105914.