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     : 3.0000000000016254
x         : [-5.2170832587254385e-8, -1.0000000634657706]
Iterations: 19
f(x) calls: 1047
----------------------------------- 
  0.006796 seconds (11.26 k allocations: 611.835 KiB)
OptimOutput
  num_iter: Int64 19
  num_call: Int64 1047
  x: Array{Float64}((2,)) [-5.2170832587254385e-8, -1.0000000634657706]
  feval: Float64 3.0000000000016254
  x_iters: Array{Float64}((2, 1000)) [0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0]
  feval_iters: Array{Float64}((19,)) [3.0000000009185137, 3.0000000009185137, 3.0000000009185137, 3.0000000009185137, 3.000000000229428, 3.0000000000328972, 3.0000000000032916, 3.0000000000032916, 3.0000000000021387, 3.000000000001862, 3.000000000001675, 3.000000000001675, 3.000000000001629, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254]
  x_calls: Array{Any}((19,))
  feval_calls: Array{Float64}((19,)) [3.0000000009185137, 3.0000000009185137, 3.0000000009185137, 3.0000000009185137, 3.000000000229428, 3.0000000000328972, 3.0000000000032916, 3.0000000000032916, 3.0000000000021387, 3.000000000001862, 3.000000000001675, 3.000000000001675, 3.000000000001629, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254, 3.0000000000016254]

Parameters

和 Python 版本相比，参数有调整：保留 update_eps，并新增 f_atol_inner 作为进入精细搜索的阈值。

• update_eps = true: 开启逐步精细化搜索，耗时更长，适合高精度优化
• update_eps = false: 降低精细化搜索强度，耗时更短，适合参数率定场景
• f_atol_inner: 用于换算内部精度阶数，n_eps = ceil(Int, -log10(f_atol_inner))

Table 1. SRS algorithm parameters

Name	Type	Default	Description
maxn	Int	1000	目标函数最大调用次数。
seed	Int	0	随机种子，用于结果可复现。
verbose	Bool	true	是否打印迭代日志。
p	Int	3	外层搜索保留的精英点数量。
po	Int	guess_po(p)	内层搜索使用的精英子集数量。
delta	Float64	0.01	边界收缩系数，用于局部收缩搜索区间。
f_atol	Float64	1e-5	全局收敛阈值（当前版本预留，暂未实际用于终止判断）。
f_atol_inner	Float64	1e-4	进入精细搜索的阈值；内部按 n_eps = ceil(Int, -log10(f_atol_inner)) 转换精度阶数。
update_eps	Bool	true	是否在精细搜索阶段动态提高内部精度阶数（n_eps）。
λ_short	Float64	0.02	短程洗牌强度（精度提高后使用）。
λ_long	Float64	0.2	长程洗牌强度（默认全局搜索阶段使用）。
init_min	Int	3	启动内层搜索前，外层最少迭代轮数。
loop_min_inner	Int	2	进入内层搜索后，触发条件检查的最小间隔轮数。

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.