遗传算法求解20个城市tsp问题 matlab代码
时间: 2023-10-10 15:04:42 浏览: 44
下面是一个简单的遗传算法求解20个城市的TSP问题的Matlab代码:
```matlab
% 遗传算法求解TSP问题
% 城市坐标
city_x = [41 37 54 25 7 2 68 71 54 83 64 18 22 83 91 25 24 58 71 74];
city_y = [94 84 67 62 64 99 58 44 62 69 60 54 60 46 38 42 60 35 32 22];
% 城市数量
num_city = length(city_x);
% 计算城市之间的距离矩阵
dist_mat = zeros(num_city, num_city);
for i = 1:num_city
for j = 1:num_city
dist_mat(i,j) = sqrt((city_x(i)-city_x(j))^2 + (city_y(i)-city_y(j))^2);
end
end
% 遗传算法参数
pop_size = 50; % 种群大小
num_gen = 200; % 迭代次数
elite_rate = 0.1; % 精英率
cross_rate = 0.8; % 交叉率
mutate_rate = 0.1; % 变异率
% 初始化种群
pop = zeros(pop_size, num_city);
for i = 1:pop_size
pop(i,:) = randperm(num_city);
end
% 迭代遗传算法
best_dist = inf;
for gen = 1:num_gen
% 计算种群中每个个体的适应度
dist = zeros(1, pop_size);
for i = 1:pop_size
d = 0;
for j = 1:num_city-1
d = d + dist_mat(pop(i,j),pop(i,j+1));
end
d = d + dist_mat(pop(i,num_city),pop(i,1));
dist(i) = d;
end
% 找到当前最优解
[min_dist, min_idx] = min(dist);
if min_dist < best_dist
best_dist = min_dist;
best_path = pop(min_idx,:);
fprintf('gen = %d, best_dist = %f\n', gen, best_dist);
end
% 精英选择
elite_size = round(pop_size * elite_rate);
[~, elite_idx] = sort(dist);
elite_pop = pop(elite_idx(1:elite_size),:);
% 交叉操作
cross_size = round(pop_size * cross_rate);
cross_pop = zeros(cross_size, num_city);
for i = 1:cross_size
parent1 = elite_pop(randi(elite_size),:);
parent2 = elite_pop(randi(elite_size),:);
cut_pos = randi(num_city-1);
child = [parent1(1:cut_pos) parent2(cut_pos+1:end)];
cross_pop(i,:) = child;
end
% 变异操作
mutate_size = round(pop_size * mutate_rate);
mutate_pop = zeros(mutate_size, num_city);
for i = 1:mutate_size
parent = elite_pop(randi(elite_size),:);
pos1 = randi(num_city);
pos2 = randi(num_city);
child = parent;
child(pos1) = parent(pos2);
child(pos2) = parent(pos1);
mutate_pop(i,:) = child;
end
% 新一代种群
new_pop = [elite_pop; cross_pop; mutate_pop];
new_size = size(new_pop, 1);
if new_size > pop_size
new_pop = new_pop(1:pop_size,:);
elseif new_size < pop_size
new_pop = [new_pop; pop(randperm(pop_size-new_size),:)];
end
pop = new_pop;
end
% 绘制最优路径
figure;
plot(city_x(best_path), city_y(best_path), 'o-');
title(sprintf('最短距离: %f', best_dist));
```
该代码使用了一个简单的遗传算法来求解20个城市的TSP问题。首先计算了城市之间的距离矩阵,然后使用遗传算法进行迭代优化,直到达到指定的迭代次数。遗传算法的参数包括种群大小、精英率、交叉率和变异率等。在每次迭代中,计算种群中每个个体的适应度,并选择精英个体进行交叉和变异操作,生成新一代种群。最终输出最优路径,并绘制图形展示。