多目标优化遗传算法完整代码

多目标优化遗传算法（MOGA）是一种用于解决多目标优化问题的进化算法。下面是一个简单的MOGA的完整代码示例：

% 设置参数
popSize = 100; % 种群大小
maxGen = 100; % 最大迭代次数
numObj = 2; % 目标函数数量

% 初始化种群
pop = rand(popSize, numObj); % 随机生成种群

% 迭代进化
for gen = 1:maxGen
    % 计算适应度
    fitness = calculateFitness(pop);
    
    % 选择操作
    selectedPop = selection(pop, fitness);
    
    % 交叉操作
    crossedPop = crossover(selectedPop);
    
    % 变异操作
    mutatedPop = mutation(crossedPop);
    
    % 合并新种群和原种群
    combinedPop = [pop; mutatedPop];
    
    % 非支配排序
    [fronts, ranks] = nonDominatedSort(combinedPop);
    
    % 拥挤度计算
    crowdingDistances = crowdingDistance(combinedPop, fronts);
    
    % 选择下一代种群
    pop = nextGeneration(combinedPop, fronts, ranks, crowdingDistances, popSize);
end

% 输出最终结果
paretoFront = pop(ranks == 1, :); % 获取帕累托前沿解集合
disp(paretoFront);

% 计算适应度函数（根据具体问题进行定义）
function fitness = calculateFitness(population)
    % 这里假设有两个目标函数，可以根据具体问题进行修改
    fitness(:, 1) = population(:, 1).^2 + population(:, 2).^2;
    fitness(:, 2) = (population(:, 1)-1).^2 + population(:, 2).^2;
end

% 选择操作（这里使用锦标赛选择）
function selectedPop = selection(population, fitness)
    tournamentSize = 2; % 锦标赛大小
    popSize = size(population, 1);
    selectedPop = zeros(size(population));
    
    for i = 1:popSize
        % 随机选择锦标赛参与者
        participants = randperm(popSize, tournamentSize);
        
        % 选择最优个体
        [~, winnerIndex] = min(fitness(participants, :));
        selectedPop(i, :) = population(participants(winnerIndex), :);
    end
end

% 交叉操作（这里使用单点交叉）
function crossedPop = crossover(selectedPop)
    crossoverRate = 0.8; % 交叉概率
    popSize = size(selectedPop, 1);
    numObj = size(selectedPop, 2);
    crossedPop = zeros(size(selectedPop));
    
    for i = 1:2:popSize
        % 随机选择两个个体进行交叉
        if rand < crossoverRate
            crossoverPoint = randi(numObj-1);
            crossedPop(i, :) = [selectedPop(i, 1:crossoverPoint), selectedPop(i+1, crossoverPoint+1:end)];
            crossedPop(i+1, :) = [selectedPop(i+1, 1:crossoverPoint), selectedPop(i, crossoverPoint+1:end)];
        else
            crossedPop(i, :) = selectedPop(i, :);
            crossedPop(i+1, :) = selectedPop(i+1, :);
        end
    end
end

% 变异操作（这里使用高斯变异）
function mutatedPop = mutation(crossedPop)
    mutationRate = 0.1; % 变异概率
    popSize = size(crossedPop, 1);
    numObj = size(crossedPop, 2);
    mutatedPop = crossedPop;
    
    for i = 1:popSize
        % 对每个个体的每个基因进行变异
        for j = 1:numObj
            if rand < mutationRate
                mutatedPop(i, j) = crossedPop(i, j) + randn;
            end
        end
    end
end

% 非支配排序
function [fronts, ranks] = nonDominatedSort(population)
    popSize = size(population, 1);
    numObj = size(population, 2);
    fronts = cell(popSize, 1);
    ranks = zeros(popSize, 1);
    dominatedCount = zeros(popSize, 1);
    dominatedSet = cell(popSize, 1);
    
    for i = 1:popSize
        fronts{i} = [];
        dominatedSet{i} = [];
        
        for j = 1:popSize
            if i == j
                continue;
            end
            
            if all(population(j,:) <= population(i,:)) && any(population(j,:) < population(i,:))
                fronts{i} = [fronts{i}, j];
            elseif all(population(i,:) <= population(j,:)) && any(population(i,:) < population(j,:))
                dominatedCount(i) = dominatedCount(i) + 1;
                dominatedSet{i} = [dominatedSet{i}, j];
            end
        end
        
        if dominatedCount(i) == 0
            ranks(i) = 1;
        end
    end
    
    frontIndex = 1;
    
    while ~isempty(fronts{frontIndex})
        nextFront = [];
        
        for i = fronts{frontIndex}
            for j = dominatedSet{i}
                dominatedCount(j) = dominatedCount(j) - 1;
                
                if dominatedCount(j) == 0
                    ranks(j) = frontIndex + 1;
                    nextFront = [nextFront, j];
                end
            end
        end
        
        frontIndex = frontIndex + 1;
        fronts{frontIndex} = nextFront;
    end
end

% 拥挤度计算
function crowdingDistances = crowdingDistance(population, fronts)
    popSize = size(population, 1);
    numObj = size(population, 2);
    crowdingDistances = zeros(popSize, 1);
    
    for i = 1:length(fronts)
        front = fronts{i};
        
        for j = 1:numObj
            [~, sortedIndices] = sort(population(front, j));
            crowdingDistances(front(sortedIndices(1))) = inf;
            crowdingDistances(front(sortedIndices(end))) = inf;
            
            for k = 2:length(front)-1
                crowdingDistances(front(sortedIndices(k))) = crowdingDistances(front(sortedIndices(k))) + ...
                    (population(front(sortedIndices(k+1)), j) -1)), j)) / ...
                    (max(population(front, j)) - min(population(front, j)));
            end
        end
    end
end

% 选择下一代种群
function nextGenPop = nextGeneration(population, fronts, ranks, crowdingDistances, popSize)
    popSize = size(population, 1);
    numObj = size(population, 2);
    nextGenPop = zeros(popSize, numObj);
    nextGenIndex = 1;
    frontIndex = 1;
    
    while nextGenIndex <= popSize
        front = fronts{frontIndex};
        
        if nextGenIndex + length(front) <= popSize
            nextGenPop(nextGenIndex:nextGenIndex+length(front)-1, :) = population(front, :);
            nextGenIndex = nextGenIndex + length(front);
        else
            [~, sortedIndices] = sort(crowdingDistances(front), 'descend');
            nextGenPop(nextGenIndex:popSize, :) = population(front(sortedIndices(1:popSize-nextGenIndex+1)), :);
            break;
        end
        
        frontIndex = frontIndex + 1;
    end
end

这段代码实现了一个简单的MOGA，其中包括初始化种群、迭代进化、适应度计算、选择操作、交叉操作、变异操作、非支配排序、拥挤度计算和选择下一代种群等步骤。你可以根据具体问题进行适当的修改和扩展。

希望对你有帮助！如果你有任何问题，请随时提问。