遗传算法求函数最小值matlab语言

以下是一个简单的 MATLAB 实现遗传算法求解函数最小值的例子：

% 设置遗传算法参数
popSize = 50; % 种群大小
numVars = 2; % 变量个数
numGenerations = 100; % 迭代次数
eliteCount = 2; % 精英数目
mutationRate = 0.01; % 变异率

% 初始化种群
population = rand(popSize, numVars);

% 开始迭代
for generation = 1:numGenerations
    
    % 计算适应度
    fitness = zeros(popSize, 1);
    for i = 1:popSize
        fitness(i) = myFitnessFunction(population(i, :));
    end
    
    % 选择精英
    [~, eliteIndices] = sort(fitness);
    elitePopulation = population(eliteIndices(1:eliteCount), :);
    
    % 选择交配伙伴
    parentIndices = randsample(popSize, popSize - eliteCount, true, fitness);
    parentPopulation = population(parentIndices, :);
    
    % 交叉
    crossoverPopulation = zeros(size(parentPopulation));
    for i = 1:2:popSize - eliteCount
        parent1 = parentPopulation(i, :);
        parent2 = parentPopulation(i + 1, :);
        crossoverPopulation(i:i+1, :) = myCrossoverFunction(parent1, parent2);
    end
    
    % 变异
    mutationPopulation = myMutationFunction(crossoverPopulation, mutationRate);
    
    % 合并种群
    population = [elitePopulation; mutationPopulation];
    
end

% 计算最终适应度并找到最优解
fitness = zeros(popSize, 1);
for i = 1:popSize
    fitness(i) = myFitnessFunction(population(i, :));
end
[~, index] = min(fitness);
bestSolution = population(index, :);
bestFitness = fitness(index);
disp(['最优解: ', num2str(bestSolution)]);
disp(['最优适应度: ', num2str(bestFitness)]);

% 自定义适应度函数
function fitness = myFitnessFunction(x)
    fitness = sin(x(1)) * cos(x(2)) - x(1) / (x(2) ^ 2 + 1);
end

% 自定义交叉函数
function offspring = myCrossoverFunction(parent1, parent2)
    crossoverPoint = randi(numel(parent1));
    offspring = [parent1(1:crossoverPoint), parent2(crossoverPoint+1:end)];
end

% 自定义变异函数
function offspring = myMutationFunction(parents, mutationRate)
    offspring = parents;
    numGenesToMutate = round(numel(parents) * mutationRate);
    for i = 1:numGenesToMutate
        index = randi(numel(parents));
        offspring(index) = rand();
    end
end

在这个例子中，我们使用遗传算法来求解一个二元函数的最小值。具体来说，我们将种群初始化为随机的二元向量，并且在每次迭代中计算每个个体的适应度，并根据适应度选择精英、交配伙伴、进行交叉和变异操作。最终，我们找到最优解和最优适应度。

需要注意的是，这只是遗传算法的一个简单实现，实际应用中需要根据问题的特点进行调整。