matlab 遗传算法代码

遗传算法是一种模拟自然进化过程的优化算法，常用于解决复杂的优化问题。在MATLAB中，可以使用遗传算法工具箱来实现遗传算法。

以下是一个简单的MATLAB遗传算法代码示例：

% 定义适应度函数
fitnessFunc = @(x) x^2;

% 定义遗传算法参数
populationSize = 50; % 种群大小
geneLength = 10; % 基因长度
mutationRate = 0.01; % 变异率
crossoverRate = 0.8; % 交叉率
maxGenerations = 100; % 最大迭代次数

% 初始化种群
population = randi([0, 1], populationSize, geneLength);

% 迭代优化
for generation = 1:maxGenerations
    % 计算适应度值
    fitness = arrayfun(fitnessFunc, population);
    
    % 选择操作
    selectedPopulation = selection(population, fitness);
    
    % 交叉操作
    offspringPopulation = crossover(selectedPopulation, crossoverRate);
    
    % 变异操作
    mutatedPopulation = mutation(offspringPopulation, mutationRate);
    
    % 更新种群
    population = mutatedPopulation;
end

% 找到最优解
bestFitness = max(fitness);
bestIndividual = population(find(fitness == bestFitness, 1), :);

% 输出结果
disp(['最优解：', num2str(bestIndividual)]);
disp(['最优适应度：', num2str(bestFitness)]);

% 选择操作函数
function selectedPopulation = selection(population, fitness)
    % 使用轮盘赌选择算子
    totalFitness = sum(fitness);
    probabilities = fitness / totalFitness;
    cumulativeProbabilities = cumsum(probabilities);
    
    selectedPopulation = zeros(size(population));
    for i = 1:size(population, 1)
        r = rand();
        selectedIndividualIndex = find(cumulativeProbabilities >= r, 1);
        selectedPopulation(i, :) = population(selectedIndividualIndex, :);
    end
end

% 交叉操作函数
function offspringPopulation = crossover(selectedPopulation, crossoverRate)
    offspringPopulation = zeros(size(selectedPopulation));
    for i = 1:2:size(selectedPopulation, 1)
        if rand() < crossoverRate
            % 随机选择交叉点
            crossoverPoint = randi([1, size(selectedPopulation, 2) - 1]);
            
            % 进行交叉操作
            offspringPopulation(i, :) = [selectedPopulation(i, 1:crossoverPoint), selectedPopulation(i+1, crossoverPoint+1:end)];
            offspringPopulation(i+1, :) = [selectedPopulation(i+1, 1:crossoverPoint), selectedPopulation(i, crossoverPoint+1:end)];
        else
            % 不进行交叉操作，直接复制父代个体
            offspringPopulation(i, :) = selectedPopulation(i, :);
            offspringPopulation(i+1, :) = selectedPopulation(i+1, :);
        end
    end
end

% 变异操作函数
function mutatedPopulation = mutation(offspringPopulation, mutationRate)
    mutatedPopulation = offspringPopulation;
    for i = 1:size(mutatedPopulation, 1)
        for j = 1:size(mutatedPopulation, 2)
            if rand() < mutationRate
                % 变异操作，将基因取反
                mutatedPopulation(i, j) = ~mutatedPopulation(i, j);
            end
        end
    end
end

这段代码实现了一个简单的遗传算法，用于求解函数 f(x) = x^2 的最大值。其中，适应度函数为 f(x)，种群大小为 50，基因长度为 10，变异率为 0.01，交叉率为 0.8，最大迭代次数为 100。代码中的选择操作使用了轮盘赌选择算子，交叉操作使用了单点交叉，变异操作将基因取反。