遗传算法tsp matlab
时间: 2023-10-04 16:12:08 浏览: 43
遗传算法(Genetic Algorithm,简称GA)是一种基于自然选择和遗传进化论的搜索算法,适用于求解复杂的优化问题。而TSP(Traveling Salesman Problem,旅行商问题)是一种经典的组合优化问题,在旅行商问题中,旅行商要去 n 个城市,每个城市只能去一次,而且要求每个城市只去一次,最后回到起点,问旅行商如何走才能走最短的距离。
以下是在Matlab中使用遗传算法求解TSP问题的示例代码:
```matlab
% 旅行商问题(TSP)遗传算法(Matlab实现)
clear all;
close all;
clc;
% 城市坐标
city = [0.40,0.75;
0.22,0.70;
0.35,0.85;
0.80,0.60;
0.55,0.50;
0.50,0.25;
0.25,0.45;
0.70,0.30;
0.80,0.10;
0.50,0.05];
% 城市数量
n = size(city,1);
% 个体数
popSize = 100;
% 迭代次数
maxgen = 100;
% 交叉概率
pc = 0.8;
% 变异概率
pm = 0.1;
% 初始化种群
pop = zeros(popSize,n);
for i = 1:popSize
pop(i,:) = randperm(n);
end
% 计算距离矩阵
dist = zeros(n,n);
for i = 1:n
for j = 1:n
dist(i,j) = sqrt((city(i,1)-city(j,1))^2+(city(i,2)-city(j,2))^2);
end
end
% 记录历史最优解
best = zeros(maxgen,1);
% 进化
for k = 1:maxgen
% 适应度函数,计算每个个体的适应度
fitness = zeros(popSize,1);
for i = 1:popSize
d = 0;
for j = 1:n-1
d = d + dist(pop(i,j),pop(i,j+1));
end
d = d + dist(pop(i,n),pop(i,1));
fitness(i) = 1/d;
end
% 记录历史最优解
best(k) = max(fitness);
% 选择,使用轮盘赌选择算子进行选择
for i = 1:popSize
idx1 = randi(popSize);
idx2 = randi(popSize);
if fitness(idx1) > fitness(idx2)
parent1 = pop(idx1,:);
else
parent1 = pop(idx2,:);
end
idx1 = randi(popSize);
idx2 = randi(popSize);
if fitness(idx1) > fitness(idx2)
parent2 = pop(idx1,:);
else
parent2 = pop(idx2,:);
end
% 交叉,使用顺序交叉算子进行交叉
if rand < pc
child1 = zeros(1,n);
child2 = zeros(1,n);
k1 = randi(n);
k2 = randi(n);
if k1 > k2
temp = k1;
k1 = k2;
k2 = temp;
end
child1(k1:k2) = parent1(k1:k2);
child2(k1:k2) = parent2(k1:k2);
p1 = 1;
p2 = 1;
for j = 1:n
if p1 == k1
p1 = k2+1;
end
if p2 == k1
p2 = k2+1;
end
if ~ismember(parent2(j),child1)
child1(p1) = parent2(j);
p1 = p1+1;
end
if ~ismember(parent1(j),child2)
child2(p2) = parent1(j);
p2 = p2+1;
end
end
pop(i,:) = child1;
pop(i+1,:) = child2;
end
% 变异,使用交换变异算子进行变异
if rand < pm
m1 = randi(n);
m2 = randi(n);
while m1 == m2
m2 = randi(n);
end
temp = pop(i,m1);
pop(i,m1) = pop(i,m2);
pop(i,m2) = temp;
end
end
end
% 找出最优解
idx = find(best == max(best));
bestpop = pop(idx,:);
% 绘制路径
figure;
plot(city(:,1),city(:,2),'ro');
hold on;
plot(city(bestpop,1),city(bestpop,2),'b-');
title(['TSP遗传算法,最短路程为',num2str(1/best(idx))]);
xlabel('X坐标');
ylabel('Y坐标');
```
上述代码中,首先定义了城市坐标和相关参数,然后使用遗传算法求解TSP问题。具体而言,遗传算法主要包括初始化种群、计算距离矩阵、适应度函数、选择算子、交叉算子、变异算子和进化过程。最后,找出最优解,并绘制路径。