写出遗传算法求 delta_h 最优值的程序

好的，下面是使用遗传算法求解 `delta_h` 的最优值的 MATLAB 程序示例：

function [best_delta_h, best_fitness] = geneticAlgorithm()
    % 遗传算法参数设置
    populationSize = 50;
    numGenerations = 100;
    crossoverRate = 0.8;
    mutationRate = 0.1;
    
    % 问题参数设置
    R_1 = 10;
    R_s = 20;
    h_m = 5;
    w_t = 1;
    w_s = 0.5;
    delta_sm = 0.2;
    alpha = 0.1;
    p = 2;

    % 初始化种群
    population = initializePopulation(populationSize, R_1);

    % 迭代进化
    for generation = 1:numGenerations
        disp(['Generation: ' num2str(generation)]);

        % 计算适应度
        fitness = calculateFitness(population, R_1, R_s, h_m, w_t, w_s, delta_sm);

        % 选择操作
        selectedParents = selection(population, fitness, populationSize);

        % 交叉操作
        offspringCrossover = crossover(selectedParents, crossoverRate);

        % 变异操作
        offspringMutation = mutation(offspringCrossover, mutationRate);

        % 合并新种群
        population = [selectedParents; offspringMutation];
    end

    % 计算最佳解
    fitness = calculateFitness(population, R_1, R_s, h_m, w_t, w_s, delta_sm);
    [best_fitness, best_index] = min(fitness);
    best_delta_h = population(best_index);

    % 打印结果
    disp(['Best delta_h: ' num2str(best_delta_h)]);
    disp(['Best fitness: ' num2str(best_fitness)]);
end

% 初始化种群
function population = initializePopulation(populationSize, R_1)
    delta_h_min = 0;
    delta_h_max = R_1;
    
    population = rand(populationSize, 1) * (delta_h_max - delta_h_min) + delta_h_min;
end

% 计算适应度
function fitness = calculateFitness(population, R_1, R_s, h_m, w_t, w_s, delta_sm)
    fitness = zeros(size(population));
    
    for i = 1:length(population)
        delta_h = population(i);
        
        % 计算公式中的各个变量
        theta = linspace(-pi * alpha / (2 * p), pi * alpha / (2 * p), 100);
        K_delta = (w_t / (w_t - delta_sm * w_s)) * ((sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) + delta_h - R_1 * cosd(theta)) ./ (sqrt(R_s^2 - (R_1 * sind(theta)).^2) - sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) - R_1 * cosd(theta)) + 1) - (sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) + delta_h - R_1 * cosd(theta)) ./ (sqrt(R_s^2 - (R_1 * sind(theta)).^2) - sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) - R_1 * cosd(theta));
        h_p = sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) + delta_h - R_1 * cosd(theta);
        l_g = sqrt(R_s^2 - (R_1 * sind(theta)).^2) - sqrt((h_m + R_1 - delta_h)^2 - (R_1 * sind(theta)).^2) - R_1 * cosd(theta);

        % 计算 B_g
        B_r = 1; % 这里假设 B_r 的值为 1
        sigma = 0; % 这里假设 sigma 的值为 0
        B_g = B_r ./ (sigma + K_delta .* h_p ./ l_g);
        
        % 计算适应度
        fitness(i) = mean(B_g);
    end
end

% 选择操作
function selectedParents = selection(population, fitness, populationSize)
    [~, sortedIndex] = sort(fitness, 'descend');
    selectedParents = population(sortedIndex(1:populationSize), :);
end

% 交叉操作
function offspringCrossover = crossover(selectedParents, crossoverRate)
    numParents = size(selectedParents, 1);
    offspringCrossover = zeros(size(selectedParents));
    
    for i = 1:numParents
        parent1 = selectedParents(i, :);
        
        if rand <= crossoverRate && i+1 <= numParents
            parent2 = selectedParents(i+1, :);
            crossoverPoint = randi([1, numel(parent1)]);
            
            offspringCrossover(i, :) = [parent1(1:crossoverPoint), parent2(crossoverPoint+1:end)];
            offspringCrossover(i+1, :) = [parent2(1:crossoverPoint), parent1(crossoverPoint+1:end)];
        else
            offspringCrossover(i, :) = parent1;
        end
    end
end

% 变异操作
function offspringMutation = mutation(offspringCrossover, mutationRate)
    numOffspring = size(offspringCrossover, 1);
    offspringMutation = zeros(size(offspringCrossover));
    
    for i = 1:numOffspring
        offspring = offspringCrossover(i, :);
        
        if rand <= mutationRate
            mutatedGene = rand * range(offspring);
            offspringMutation(i, :) = offspring + mutatedGene;
        else
            offspringMutation(i, :) = offspring;
        end
    end
end

你可以通过调用 `geneticAlgorithm` 函数来运行遗传算法。它将返回最优的 `delta_h` 值以及对应的适应度。

请注意，在计算适应度时，为了获得更准确的结果，我在 `theta` 上生成了 100 个离散点进行计算。你可以根据实际情况进行调整。

希望这可以满足你的需求！如果你有任何其他问题，请随时提问。