Matlab 遗传算法求解分段函数最值

下面是一个使用 Matlab 实现遗传算法求解分段函数最值的代码示例：

% 定义问题的适应度函数
function fitness = fitness_function(solution)
    % 计算适应度值，即分段函数的最值
    x = solution(1);
    if x < 0
        fitness = -x;
    elseif x >= 0 && x <= 10
        fitness = x^2;
    else
        fitness = 100 - x;
    end
end

% 定义交叉操作
function offspring = crossover(parent1, parent2)
    % 交叉操作，例如单点交叉或多点交叉
    crossover_point = randi([1, numel(parent1)]);
    offspring = [parent1(1:crossover_point), parent2(crossover_point+1:end)];
end

% 定义变异操作
function mutated_solution = mutate(solution)
    % 变异操作，例如随机改变一个基因值
    mutate_point = randi([1, numel(solution)]);
    solution(mutate_point) = randi([-100, 100]);
    mutated_solution = solution;
end

% 定义遗传算法主体
function best_solution = genetic_algorithm(population_size, fitness_function, crossover_rate, mutation_rate, generations)
    % 初始化种群
    population = zeros(population_size, 1);
    for i = 1:population_size
        solution = randi([-100, 100]);
        population(i) = solution;
    end

    for gen = 1:generations
        % 计算种群中每个个体的适应度值
        fitness_values = arrayfun(@(x) fitness_function(x), population);

        % 选择操作，根据适应度值进行选择
        selected_population = [];
        for i = 1:population_size
            % 根据适应度值选择个体
            parent1 = randsample(population, 1, true, fitness_values);
            parent2 = randsample(population, 1, true, fitness_values);
            selected_population = [selected_population; parent1, parent2];
        end

        % 交叉操作
        offspring_population = [];
        for i = 1:population_size
            if rand() < crossover_rate
                offspring = crossover(selected_population(i, 1), selected_population(i, 2));
            else
                offspring = selected_population(i, 1);
            end
            offspring_population = [offspring_population; offspring];
        end

        % 变异操作
        mutated_population = arrayfun(@(x) mutate(x), offspring_population);

        % 更新种群
        population = mutated_population;
    end

    % 找到最优解
    fitness_values = arrayfun(@(x) fitness_function(x), population);
    [~, best_index] = max(fitness_values);
    best_solution = population(best_index);
end

% 使用遗传算法求解分段函数最值
population_size = 100;
crossover_rate = 0.8;
mutation_rate = 0.1;
generations = 100;

best_solution = genetic_algorithm(population_size, @fitness_function, crossover_rate, mutation_rate, generations);

disp('最优解：');
disp(best_solution);
disp('最优值：');
disp(fitness_function(best_solution));

请注意，这只是一个基本的示例代码，实际使用时需要根据具体问题进行适当的修改和调整。