遗传算法matlab程序

以下是一个简单的遗传算法Matlab程序示例：

% 遗传算法示例程序
clc;
clear;

% 定义问题
fun = @(x) x.^2 + 2*x - 3;

% 定义参数
popSize = 50;  % 种群大小
numGen = 100;  % 迭代次数
pc = 0.8;      % 交叉概率
pm = 0.05;     % 变异概率
numVar = 1;    % 变量个数
lb = -10;      % 变量下限
ub = 10;       % 变量上限

% 初始化种群
pop = rand(popSize, numVar) * (ub - lb) + lb;

% 迭代
for i = 1:numGen
    % 评估适应度
    fit = fun(pop);
    % 选择
    parents = selection(pop, fit);
    % 交叉
    offspring = crossover(parents, pc);
    % 变异
    offspring = mutation(offspring, pm, lb, ub);
    % 合并种群
    pop = [pop; offspring];
    % 保留种群大小
    pop = pop(1:popSize, :);
end

% 输出结果
[minFit, minIdx] = min(fun(pop));
minX = pop(minIdx, :);
disp(['最小值：', num2str(minFit)]);
disp(['最小值对应的x：', num2str(minX)]);

% 选择函数
function parents = selection(pop, fit)
    % 锦标赛选择
    popSize = size(pop, 1);
    numParents = size(pop, 1);
    parents = zeros(numParents, size(pop, 2));
    for i = 1:numParents
        p1 = randi(popSize);
        p2 = randi(popSize);
        if fit(p1) < fit(p2)
            parents(i, :) = pop(p1, :);
        else
            parents(i, :) = pop(p2, :);
        end
    end
end

% 交叉函数
function offspring = crossover(parents, pc)
    % 单点交叉
    numParents = size(parents, 1);
    numVar = size(parents, 2);
    offspring = zeros(numParents, numVar);
    for i = 1:numParents/2
        if rand() < pc
            crossoverPoint = randi(numVar-1);
            offspring(2*i-1,:) = [parents(2*i-1, 1:crossoverPoint), parents(2*i, crossoverPoint+1:end)];
            offspring(2*i,:) = [parents(2*i, 1:crossoverPoint), parents(2*i-1, crossoverPoint+1:end)];
        else
            offspring(2*i-1,:) = parents(2*i-1, :);
            offspring(2*i,:) = parents(2*i, :);
        end
    end
end

% 变异函数
function offspring = mutation(offspring, pm, lb, ub)
    % 均匀变异
    numOffspring = size(offspring, 1);
    numVar = size(offspring, 2);
    offspring = reshape(offspring, [], 1);
    for i = 1:length(offspring)
        if rand() < pm
            offspring(i) = rand() * (ub - lb) + lb;
        end
    end
    offspring = reshape(offspring, numOffspring, numVar);
end

此程序实现了一个简单的遗传算法，用于求解函数 f(x) = x^2 + 2x - 3 在区间 [-10, 10] 上的最小值。程序采用了锦标赛选择、单点交叉和均匀变异三种标准的遗传算法操作。