遗传算法最短路径matlab代码

以下是一个基本的遗传算法最短路径Matlab代码示例：

function [best_path, shortest_distance] = ga_shortest_path(distance_matrix, population_size, generations, mutation_rate)

% 首先，我们需要随机生成一些个体作为种群
num_cities = size(distance_matrix, 1);
population = zeros(population_size, num_cities);
for i = 1:population_size
    population(i, :) = randperm(num_cities);
end

% 定义适应度函数，即计算每个个体的总路径长度
fitness_function = @(path) path_distance(path, distance_matrix);

% 开始迭代
for generation = 1:generations
    % 计算每个个体的适应度，即路径长度
    fitness_scores = zeros(population_size, 1);
    for i = 1:population_size
        fitness_scores(i) = fitness_function(population(i, :));
    end
    
    % 找到最短路径和对应的个体
    [shortest_distance, best_index] = min(fitness_scores);
    best_path = population(best_index, :);
    
    % 输出当前代数和最短路径长度
    fprintf('Generation %d: shortest distance = %f\n', generation, shortest_distance);
    
    % 选择新一代个体
    new_population = zeros(population_size, num_cities);
    for i = 1:population_size
        % 随机选择两个父代
        parent1 = population(randi(population_size), :);
        parent2 = population(randi(population_size), :);
        
        % 交叉操作
        child = crossover(parent1, parent2);
        
        % 变异操作
        if rand() < mutation_rate
            child = mutate(child);
        end
        
        % 添加到新一代种群中
        new_population(i, :) = child;
    end
    
    % 更新种群
    population = new_population;
end

end

% 计算路径长度的函数
function distance = path_distance(path, distance_matrix)
distance = 0;
for i = 1:length(path)-1
    distance = distance + distance_matrix(path(i), path(i+1));
end
distance = distance + distance_matrix(path(end), path(1)); % 回到起点
end

% 交叉操作的函数
function child = crossover(parent1, parent2)
num_cities = length(parent1);
child = zeros(1, num_cities);
start_index = randi(num_cities-1);
end_index = randi(start_index+1:num_cities);
child(start_index:end_index) = parent1(start_index:end_index);
remaining_cities = setdiff(parent2, child(start_index:end_index));
child(1:start_index-1) = remaining_cities(1:start_index-1);
child(end_index+1:end) = remaining_cities(start_index:end-1);
end

% 变异操作的函数
function child = mutate(parent)
num_cities = length(parent);
swap_index1 = randi(num_cities);
swap_index2 = randi(num_cities);
child = parent;
child([swap_index1 swap_index2]) = child([swap_index2 swap_index1]);
end

其中，`distance_matrix` 是一个二维矩阵，表示每两个城市之间的距离；`population_size` 是种群大小；`generations` 是迭代次数；`mutation_rate` 是变异率。函数返回最短路径和对应的距离。