% 初始化种群 pop = zeros(pop_size, num_city); for i = 1:pop_size pop(i, :) = randperm(num_city); end 以上代码中的num-city 是什么意思呢
时间: 2024-05-21 08:18:12 浏览: 11
`num_city` 是一个整数变量,表示旅行商(TSP)中城市的数量。在SP问题中,有一定数量的城市被访问,这些城市之间的距离需要被计算。在这代码中,`num_city 被用来初始化种群中每个个体的染色体长度,即需要访问的城市数量。`randperm(num_city)` 返回一个包含 `num_city` 个随机排列的数组,表示一个个体对城市的访问顺序。种群中的每个个体都代表了一种访问城市的路径。
相关问题
遗传算法求解20个城市tsp问题 matlab代码
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。
3维多旅行商matlab实现
多旅行商问题(MTSP)是旅行商问题(TSP)的扩展,它需要解决多个旅行商的路径问题。对于三维空间,可以考虑使用遗传算法等启发式算法来解决MTSP。下面是一个使用遗传算法来解决3维多旅行商问题的Matlab实现示例:
```matlab
function [best_path, best_cost] = mtsp_genetic_algorithm(city_locations, num_salesmen, pop_size, num_gen, crossover_prob, mutation_prob)
% city_locations: 表示城市坐标位置的矩阵,每一行代表一个城市的坐标
% num_salesmen: 旅行商数量
% pop_size: 种群个数
% num_gen: 迭代次数
% crossover_prob: 交叉概率
% mutation_prob: 变异概率
% 计算城市之间的距离矩阵
num_cities = size(city_locations, 1);
dist_matrix = zeros(num_cities, num_cities);
for i = 1:num_cities
for j = i+1:num_cities
dist_matrix(i,j) = sqrt(sum((city_locations(i,:)-city_locations(j,:)).^2));
dist_matrix(j,i) = dist_matrix(i,j);
end
end
% 初始化种群
pop = zeros(num_cities, num_salesmen, pop_size);
for i = 1:pop_size
for j = 1:num_salesmen
pop(:,j,i) = randperm(num_cities)';
end
end
% 迭代求解
for gen = 1:num_gen
% 计算适应度
fitness = zeros(pop_size, 1);
for i = 1:pop_size
cost = 0;
for j = 1:num_salesmen
route = pop(:,j,i);
cost = cost + dist_matrix(route(1),route(end));
for k = 1:length(route)-1
cost = cost + dist_matrix(route(k),route(k+1));
end
end
fitness(i) = 1/cost;
end
% 选择操作
parents = zeros(num_cities, num_salesmen, 2);
for i = 1:2
% 轮盘赌选择
idx = randperm(pop_size);
for j = 1:pop_size
if rand < fitness(idx(j))/sum(fitness(idx))
parents(:,:,i) = pop(:,:,idx(j));
break;
end
end
end
% 交叉操作
if rand < crossover_prob
% 随机选择两个旅行商
salesmen_idx = randperm(num_salesmen,2);
% 随机选择两个交叉点
cross_idx = sort(randperm(num_cities,2));
% 交叉
temp1 = parents(cross_idx(1):cross_idx(2),salesmen_idx(1),1);
temp2 = parents(cross_idx(1):cross_idx(2),salesmen_idx(2),2);
parents(cross_idx(1):cross_idx(2),salesmen_idx(1),1) = temp2;
parents(cross_idx(1):cross_idx(2),salesmen_idx(2),2) = temp1;
end
% 变异操作
if rand < mutation_prob
% 随机选择一个旅行商
salesman_idx = randperm(num_salesmen,1);
% 随机选择两个变异点
mut_idx = sort(randperm(num_cities,2));
% 变异
temp = parents(:,salesman_idx,1);
temp(mut_idx(1)) = parents(mut_idx(2),salesman_idx,1);
temp(mut_idx(2)) = parents(mut_idx(1),salesman_idx,1);
parents(:,salesman_idx,1) = temp;
end
% 合并操作
new_pop = zeros(num_cities, num_salesmen, pop_size);
new_pop(:,:,1:2) = parents;
for i = 3:pop_size
% 轮盘赌选择
idx = randperm(pop_size);
for j = 1:pop_size
if rand < fitness(idx(j))/sum(fitness(idx))
new_pop(:,:,i) = pop(:,:,idx(j));
break;
end
end
end
% 更新种群
pop = new_pop;
end
% 计算最优解
best_cost = Inf;
for i = 1:pop_size
cost = 0;
for j = 1:num_salesmen
route = pop(:,j,i);
cost = cost + dist_matrix(route(1),route(end));
for k = 1:length(route)-1
cost = cost + dist_matrix(route(k),route(k+1));
end
end
if cost < best_cost
best_cost = cost;
best_path = pop(:,:,i);
end
end
end
```
需要注意的是,这是一种基本的实现方式,可能存在一些不足之处,需要根据实际情况进行调整和改进。