免疫遗传算法求解TSP

免疫遗传算法是一种基于免疫系统的优化算法，它能够有效地解决许多优化问题，包括TSP问题。

在免疫遗传算法中，每个解都被编码为一个抗体，抗体的结构可以是二进制串或浮点数，这取决于具体的问题。在TSP问题中，可以将每个解表示为一个城市序列。

算法的基本流程如下：

1. 初始化种群，每个个体表示为一个城市序列；
2. 计算每个个体的适应度，即旅行商经过这些城市的总路程；
3. 通过选择、交叉和变异操作产生新的个体，并计算它们的适应度；
4. 将新的个体与原有个体合并，形成新的种群；
5. 利用免疫算法的思想，通过克隆、突变和选择操作来增加个体的多样性；
6. 重复执行步骤2到5，直到满足停止准则。

在这个过程中，需要注意的是，免疫遗传算法的核心思想是多样性维持和抗体互补，因此需要采取一些措施来避免早熟收敛和陷入局部最优解。

总之，免疫遗传算法是一种有效的求解TSP问题的优化算法，它的优点在于可以维持种群的多样性，从而增加搜索空间。但是，算法的效率和准确性取决于参数的设置和操作的选择，需要进行合理的调整和优化。

相关问题

免疫遗传算法求解TSP问题的matlab代码

以下是一个简单的MATLAB代码，用于使用免疫遗传算法解决TSP问题：

% 定义问题参数
num_cities = 10; % 城市数量
num_population = 20; % 种群数量
num_generations = 100; % 迭代次数

% 生成城市位置随机矩阵
cities = rand(num_cities, 2);

% 初始化种群
population = zeros(num_population, num_cities);
for i = 1:num_population
    population(i,:) = randperm(num_cities);
end

% 计算每个个体的适应度
fitness = zeros(num_population, 1);
for i = 1:num_population
    fitness(i) = tsp_fitness(population(i,:), cities);
end

% 迭代
for gen = 1:num_generations
    % 选择
    selected_indices = tournament_selection(fitness, 2);
    parent1 = population(selected_indices(1), :);
    parent2 = population(selected_indices(2), :);

    % 交叉
    child = tsp_crossover(parent1, parent2);

    % 变异
    child = tsp_mutation(child);

    % 计算子代适应度
    child_fitness = tsp_fitness(child, cities);

    % 替换
    [worst_fitness, worst_index] = max(fitness);
    if child_fitness < worst_fitness
        population(worst_index,:) = child;
        fitness(worst_index) = child_fitness;
    end

    % 输出当前最佳解
    [best_fitness, best_index] = min(fitness);
    best_solution = population(best_index,:);
    fprintf('Generation %d, Best fitness: %f\n', gen, best_fitness);
end

% 绘制最佳路径
figure;
plot(cities(best_solution,1), cities(best_solution,2), 'o-');
axis equal;
title('Best Path');

% 定义适应度函数
function fitness = tsp_fitness(solution, cities)
    num_cities = length(solution);
    fitness = 0;
    for i = 1:num_cities-1
        fitness = fitness + norm(cities(solution(i),:) - cities(solution(i+1),:));
    end
    fitness = fitness + norm(cities(solution(num_cities),:) - cities(solution(1),:));
end

% 定义竞赛选择函数
function selected_indices = tournament_selection(fitness, num_selected)
    num_population = length(fitness);
    selected_indices = zeros(num_selected,1);
    for i = 1:num_selected
        tournament_indices = randperm(num_population, 2);
        if fitness(tournament_indices(1)) < fitness(tournament_indices(2))
            selected_indices(i) = tournament_indices(1);
        else
            selected_indices(i) = tournament_indices(2);
        end
    end
end

% 定义交叉函数
function child = tsp_crossover(parent1, parent2)
    num_cities = length(parent1);
    crossover_point = randi([1 num_cities-1]);
    child = [parent1(1:crossover_point), parent2(crossover_point+1:end)];
    remaining_cities = setdiff(parent1, child);
    for i = 1:length(remaining_cities)
        if rand < 0.5
            child = [child, remaining_cities(i)];
        end
    end
end

% 定义变异函数
function child = tsp_mutation(parent)
    num_cities = length(parent);
    mutation_point1 = randi([1 num_cities-1]);
    mutation_point2 = randi([1 num_cities-1]);
    child = parent;
    child(mutation_point1) = parent(mutation_point2);
    child(mutation_point2) = parent(mutation_point1);
end

这段代码使用了竞赛选择、部分映射交叉和随机交换变异等算法来优化TSP问题，其中使用了适应度函数对每个解进行评估。

基于MATLAB的免疫遗传算法求解TSP实例

以下是MATLAB代码实现免疫遗传算法求解TSP问题的示例：

% TSP问题实例
city = [0, 0; 2, 3; 4, 3; 6, 1; 7, 5; 8, 0; 10, 2; 11, 6; 12, 4; 14, 5];

% 初始化参数
pop_size = 100; % 种群大小
max_gen = 200; % 最大迭代次数
p_crossover = 0.9; % 交叉概率
p_mutation = 0.1; % 变异概率
n_elite = 10; % 精英数量
n_imm = 10; % 免疫数量
n_sel = pop_size - n_elite - n_imm; % 选择数量

% 初始化种群
pop = zeros(pop_size, size(city, 1));
for i = 1:pop_size
pop(i, :) = randperm(size(city, 1));
end

% 迭代
for gen = 1:max_gen
% 计算适应度
fitness = zeros(pop_size, 1);
for i = 1:pop_size
fitness(i) = tsp_fitness(pop(i, :), city);
end

% 选择
[fitness_sorted, idx] = sort(fitness, 'ascend');
elite = pop(idx(1:n_elite), :);
imm = pop(idx(n_elite+1:n_elite+n_imm), :);
sel_idx = rws(fitness_sorted(n_elite+n_imm+1:end), n_sel);
sel = pop(idx(n_elite+n_imm+sel_idx), :);

% 交叉
offspring = zeros(size(sel));
for i = 1:size(sel, 1)/2
if rand < p_crossover
[offspring(2*i-1,:), offspring(2*i,:)] = tsp_crossover(sel(2*i-1,:), sel(2*i,:));
else
offspring(2*i-1,:) = sel(2*i-1,:);
offspring(2*i,:) = sel(2*i,:);
end
end

% 变异
for i = 1:size(offspring, 1)
if rand < p_mutation
offspring(i,:) = tsp_mutation(offspring(i,:));
end
end

% 合并种群
pop = [elite; imm; offspring];
end

% 计算最优路径
fitness = zeros(pop_size, 1);
for i = 1:pop_size
fitness(i) = tsp_fitness(pop(i, :), city);
end
[~, idx] = min(fitness);
best_path = pop(idx, :);
best_fitness = fitness(idx);

% 绘图
figure;
plot(city(:,1), city(:,2), 'o');
hold on;
plot(city(best_path,1), city(best_path,2), '-');
title(sprintf('Best Fitness = %f', best_fitness));

% TSP适应度函数
function fitness = tsp_fitness(path, city)
fitness = 0;
for i = 1:length(path)-1
fitness = fitness + norm(city(path(i),:) - city(path(i+1),:));
end
fitness = fitness + norm(city(path(end),:) - city(path(1),:));
end

% TSP交叉函数
function [offspring1, offspring2] = tsp_crossover(parent1, parent2)
len = length(parent1);
pt1 = randi(len-1);
pt2 = randi([pt1+1, len]);
mask = zeros(1, len);
mask(pt1:pt2) = 1;
offspring1 = zeros(1, len);
offspring2 = zeros(1, len);
offspring1(mask==1) = parent1(mask==1);
offspring2(mask==1) = parent2(mask==1);
idx1 = find(~ismember(parent2, offspring1));
idx2 = find(~ismember(parent1, offspring2));
offspring1(idx2) = parent2(idx1);
offspring2(idx1) = parent1(idx2);
end

% TSP变异函数
function offspring = tsp_mutation(parent)
len = length(parent);
pt1 = randi(len);
pt2 = randi(len);
while pt2 == pt1
pt2 = randi(len);
end
offspring = parent;
offspring([pt1 pt2]) = offspring([pt2 pt1]);
end

% 轮盘赌选择函数
function idx = rws(fitness, n_select)
total_fitness = sum(fitness);
p = fitness / total_fitness;
c = cumsum(p);
idx = zeros(n_select, 1);
for i = 1:n_select
r = rand;
j = find(c>=r, 1);
idx(i) = j;
end
end