微分進化(Difference Evolution,DE)算法是一種優化算法,據稱其比GA(遺傳算法)等更為優秀。
借鑒網上實現的DE算法,用Matlab實現了對若干函數優化問題的解法,代碼如下:
function [] = de_test
clear all;
分數階微分方程matlab代碼,close all;
clc;
%解:X = [0, 0, ...]
%nVar = 30
%dims: [-30, 30]
matlab中dsolve函數。function fitness = sphere(vals)
prod = vals .* vals;
fitness = sum(prod, 2);
end
%f(x) = 1/4000 * sum^n_1(x_i)^2 - prod^n_1 * cos(x_i/sqrt(i)) + 1
matlab解一階微分方程組、%f* = 0, x* = [0, 0, ...];
%nVar = 30
%dims: [-600, 600]
function fitness = griewank(vals)
[h w] = size(vals);
polyval函數matlab。p1 = vals.^2;
p1 = 1/4000 .* sum(p1, 2);
t = sqrt([1:w]);
p2 = vals ./ repmat(t, h, 1);
p2 = cos(p2);
matlab微分器。p2 = prod(p2, 2);
fitness = p1 - p2 + 1;
end
%解: X = [1, 1, 1, ...]
function fitness = RosenBroek(vals)
matlab函數求導?[k n] = size(vals);
vals1 = vals(:, 1:n-1);
vals2 = vals(:, 2:n);
tmp = vals2 - vals1 .* vals1;
tmp = 100 * tmp .* tmp;
matlab求全微分?tmp1 = (vals1 - 1).^2;
fitness = sum(tmp, 2) + sum(tmp1, 2);
end
%許多局部最小值,最優解:X = [0, 0], 固定2個變量
function fitness = Rastrigin (X)
matlab積分函數,v = X.^2 - 10 .* cos(2 * pi .* X) + 10;
fitness = sum(v, 2);
%fitness = 20 + X(:, 1).^2 + X(:, 2).^2 - 10 .* (cos(2 * pi * X(:, 1)) + cos(2 * pi * X(:, 2)));
end
%參數
matlab函數大全。popSize = 100; % 群規模
F = 0.5; ? ? ? ? ? ? ? ? ? ?% 突變因子
C = 0.9; ? ? ? ? ? ? ? ? ? ?% 交叉率
iterTimes = 300; % 迭代次數
Run = 4; ? ? ? ?% 測試輪次
matlab求一個函數的微分,id = [1:popSize];
%結果
bestFit = 1e5; ?%設取最小值
bestGene = [];
for r = 1:Run ?%輪次
matlab數據歸一化函數?Func = r; ? ? % 測試適應度函數
switch Func
case 1
Func = @sphere;
Xmin = -100;
Xmax = 100;
nVar = 30;
case 2
Func = @griewank;
Xmin = -600;
Xmax = 600;
nVar = 2;
case 3
nVar = 2;
Func = @RosenBroek;
Xmin = -100;
Xmax = 100;
case 4
nVar = 2;
Func = @Rastrigin
Xmin = -5.12;
Xmax = 5.12;
end;
Func
tic;
%1.初始化種群
X = Xmin + rand(popSize, nVar) * Xmax;
%2.每輪迭代
for i = 1:iterTimes
X0 = X;
% ? ? ? ? ? ? F = 2 * (1 - (i-1)/iterTimes);
%個體突變得到V
for j = 1:popSize
ids = id;
ids(j) = [];
rids = randperm(popSize - 1, 3);
rids = ids(rids);
V = X(rids(1), :) + F * (X(rids(2), :) - X(rids(3), :));
%對V(j, :)值域檢查
ids = find(V < Xmin);
if length(ids) > 0
V(ids) = Xmin;
end;
ids = find(V > Xmax);
if length(ids) > 0
V(ids) = Xmax;
end;
%對每個X和V的配對,進行交叉操作,結果存在U中
jrand = floor(rand() * nVar + 1); ?%必交叉項,保證至少一個交叉
for n = 1:nVar
R1 = rand();
if (R1 < C || n == jrand)
U = V; ? ?%保留子代基因
else
U = X(j, :); ? ?%保留父代基因
end
end
%在子代和父代間做選擇運算
if Func(U) < Func(X(j, :))
Tr = U;
else
Tr=X(j, :);
end
% 更新種群基因
X(j,:) = Tr;
%計算新的適應度
fitness = Func(X(j,:));
%記錄全局最優解
if fitness < bestFit
bestFit = fitness;
bestGene = X(j, :);
end;
end ?%結束個體更新
end
bestGene
bestFit
toc
end
end運行結果如下:
Func =
@de_test/sphere
bestGene =
Columns 1 through 15
-7.5570 ?-11.9099 ? ?9.9957 ?-37.8403 ?-17.9445 ? -7.1438 ?-21.4304 ?-33.6260 ?-22.1812 ?-66.1438 ? ?0.9014 ?-39.6724 ? -0.3175 ?-56.4815 ? 26.5422
Columns 16 through 30
6.5446 ?-31.9653 ? -9.3640 ?-37.1629 ?-23.7325 ? ?2.7271 ? -6.3413 ?-21.3204 ?-13.1450 ? 28.7402 ?-28.8170 ?-22.6226 ? 10.9031 ?-16.6128 ?-14.7637
bestFit =
2.0583e+04 ?(從此結果看,算法效果不佳)
時間已過 2.285354 秒。
Func =
@de_test/griewank
bestGene =
1.0e-08 *
0.1702 ? ?0.1424
bestFit =
0
時間已過 3.337347 秒。
Func =
@de_test/RosenBroek
bestGene =
1.0e-08 *
0.1702 ? ?0.1424
bestFit =
0
時間已過 1.747765 秒。
Func =
@de_test/Rastrigin
Func =
@de_test/Rastrigin
bestGene =
1.0e-08 *
0.1702 ? ?0.1424
bestFit =
0
時間已過 1.403871 秒。
版权声明:本站所有资料均为网友推荐收集整理而来,仅供学习和研究交流使用。
工作时间:8:00-18:00
客服电话
电子邮件
admin@qq.com
扫码二维码
获取最新动态