求函数f(x,y)=-((x^2+y-1)+(x+y^2-7)^2)/200+10的最大值，x和y取值区间[-100,100]；经过下面的优化过程，得到结果：x=-2，y=-3，最大值为10。
原理
源码
%%%%%%%%%%%%% 离散差分进化算法求函数极值 %%%%%%%%%%%%%
%%%%%%%%%%%%% 初始化 %%%%%%%%%%%%%
clear;clc;
NP = 20; % 种群数量
D = 2; % 变量维度
G = 200; % 最大进化代数
F = 0.5; % 初始编译算子
CR = 0.1; % 交叉算子
Xs = 100; % 上限
Xx = -100; % 下限
%%%%%%%%%%%%% 赋初值 %%%%%%%%%%%%%
Ob = zeros(NP, 1);
Ob1 = zeros(NP, 1);
trace = zeros(G + 1, 1);
v = zeros(D, NP); % 变异种群
u = zeros(D, NP); % 选择种群
x = randi([Xx, Xs], D, NP);
%%%%%%%%%%%%% 计算目标函数 %%%%%%%%%%%%%
for m = 1:NP
Ob(m) = func3(x(:, m));
end
trace(1) = min(Ob);
%%%%%%%%%%%%% 差分进化循环 %%%%%%%%%%%%%
for gen = 1:G
%%%%%%%%%%%%% 变异操作 %%%%%%%%%%%%%
%%%%%%%%%% r1、r2、r3和m互不相同 %%%%%%%%%%
for m = 1:NP
r1 = randi([1, NP], 1);
while r1 == m
r1 = randi([1, NP], 1);
end
r2 = randi([1, NP], 1);
while r2 == m || r2 == r1
r2 = randi([1, NP], 1);
end
r3 = randi([1, NP], 1);
while r3 == m || r3 == r2 || r3 == r1
r3 = randi([1, NP], 1);
end
v(:, m) = floor(x(:, r1) + F*(x(:, r2) - x(:, r3)));
end
%%%%%%%%%%%%% 交叉操作 %%%%%%%%%%%%%
r = randi([1, D], 1);
for n = 1:D
cr = rand;
if cr <= CR || n == r
u(n, :) = v(n, :);
else
u(n, :) = x(n, :);
end
end
%%%%%%%%%%%%% 边界条件的处理 %%%%%%%%%%%%%
%%%%%%%%%%%%% 边界吸收 %%%%%%%%%%%%%
for n = 1:D
for m = 1:NP
if u(n, m) < Xx
u(n, m) = Xx;
end
if u(n, m) > Xs
u(n, m) = Xs;
end
end
end
%%%%%%%%%%%%% 选择操作 %%%%%%%%%%%%%
for m = 1:NP
Ob1(m) = func3(u(:, m));
end
for m = 1:NP
if Ob1(m) > Ob(m)
x(:, m) = u(:, m);
end
end
for m = 1:NP
Ob(m) = func3(x(:, m));
end
trace(gen + 1) = min(Ob);
end
[SortOb, Index] = sort(Ob);
x = x(:, Index);
X = x(:, 1); % 最优变量
Y = min(Ob); % 最优值
disp(['最优x：' num2str(X')]);
disp(['最优y：' num2str(Y)]);
plot(trace);
xlabel('迭代次数');
ylabel('目标函数值');
title('DE目标函数曲线');
%%%%%%%%%%%%% 适应度函数 %%%%%%%%%%%%%
function result = func3(x)
result = -((x(1).^2 + x(2) - 1).^2 + (x(1) + x(2).^2 - 7).^2)/200 + 10;
