遗传算法matlab程序tsp
时间: 2023-09-18 20:06:33 浏览: 69
遗传算法在解决旅行商问题(TSP)的应用非常广泛。下面是一个使用MATLAB编写的遗传算法程序来解决TSP问题的示例:
```matlab
clear all;
clc;
% 初始化参数
numCities = 20; % 城市数量
numGenerations = 100; % 迭代次数
populationSize = 50; % 种群大小
% 生成随机城市坐标
cities = rand(numCities, 2);
% 计算城市之间的距离矩阵
distMatrix = pdist2(cities, cities);
% 初始化种群
population = zeros(populationSize, numCities);
for i = 1:populationSize
population(i, :) = randperm(numCities);
end
bestFitness = inf;
bestRoute = [];
% 进化循环
for generation = 1:numGenerations
% 计算种群中每个个体的适应度
fitness = zeros(populationSize, 1);
for i = 1:populationSize
route = population(i, :);
fitness(i) = calculateFitness(route, distMatrix);
end
% 找出最佳个体及其适应度
[minFitness, minIndex] = min(fitness);
% 更新全局最佳个体及其适应度
if minFitness < bestFitness
bestFitness = minFitness;
bestRoute = population(minIndex, :);
end
% 选择、交叉和变异操作
newPopulation = zeros(populationSize, numCities);
for i = 1:2:populationSize
% 选择操作使用轮盘赌选择方法
parent1 = selectParent(population, fitness);
parent2 = selectParent(population, fitness);
% 交叉操作使用部分映射交叉 (PMX)
child = crossover(parent1, parent2);
% 变异操作使用交换变异
child = mutate(child);
% 更新种群
newPopulation(i, :) = child;
newPopulation(i+1, :) = parent1;
end
population = newPopulation;
% 显示当前迭代的最佳个体及其适应度
disp(['Generation ', num2str(generation), ': Best Fitness = ', num2str(minFitness)]);
end
% 显示最佳路径
disp('Best Route:');
disp(bestRoute);
% 适应度函数:计算路径的总距离
function fitness = calculateFitness(route, distMatrix)
fitness = 0;
numCities = length(route);
for i = 1:numCities-1
fitness = fitness + distMatrix(route(i), route(i+1));
end
fitness = fitness + distMatrix(route(end), route(1));
end
% 选择操作:轮盘赌选择
function parent = selectParent(population, fitness)
roulette = cumsum(fitness) / sum(fitness);
r = rand();
[~, parentIndex] = max(roulette >= r);
parent = population(parentIndex, :);
end
% 交叉操作:部分映射交叉 (PMX)
function child = crossover(parent1, parent2)
numCities = length(parent1);
child = zeros(1, numCities);
% 选择交叉点
crossoverPoint1 = randi([2, numCities-1]);
crossoverPoint2 = randi([crossoverPoint1+1, numCities]);
% 复制父代1中的交叉区间到子代
child(crossoverPoint1:crossoverPoint2) = parent1(crossoverPoint1:crossoverPoint2);
% 对子代中未填充的位置进行映射
for i = crossoverPoint1:crossoverPoint2
mappedValue = parent2(i);
while ismember(mappedValue, child)
index = find(parent1 == mappedValue);
mappedValue = parent2(index);
end
child(i) = mappedValue;
end
% 复制父代2中未映射的值到子代
child(child == 0) = parent2(parent2 ~= child);
end
% 变异操作:交换变异
function mutatedChild = mutate(child)
numCities = length(child);
mutatedChild = child;
% 选择变异点
mutationPoint1 = randi([1, numCities]);
mutationPoint2 = randi([1, numCities]);
% 交换变异点的值
temp = mutatedChild(mutationPoint1);
mutatedChild(mutationPoint1) = mutatedChild(mutationPoint2);
mutatedChild(mutationPoint2) = temp;
end
```
请注意,这只是一个基本示例,具体的实现细节和参数设置可能需要根据实际情况进行调整。此外,还可以通过使用其他的选择、交叉和变异操作来进一步改进算法的性能。