matlab电动汽车路径优化的遗传算法求解代码

以下是一个简单的 MATLAB 代码示例，用遗传算法优化电动汽车路径：

function [bestRoute, bestFitness] = gaEVPathOptimization()

% 参数设置
numCities = 20; % 城市数量
numGenerations = 1000; % 迭代次数
popSize = 100; % 种群数量
eliteRatio = 0.1; % 精英比例
mutationRate = 0.02; % 变异率

% 随机生成城市坐标
cities = 10 * rand(numCities, 2);

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

% 进化循环
for i = 1:numGenerations
    
    % 计算适应度
    fitness = zeros(popSize, 1);
    for j = 1:popSize
        fitness(j) = evaluateFitness(population(j,:), cities);
    end
    
    % 找出精英个体
    eliteNum = round(eliteRatio * popSize);
    [sortedFitness, sortedIdx] = sort(fitness, 'descend');
    elitePopulation = population(sortedIdx(1:eliteNum),:);
    
    % 选择
    parent1 = elitePopulation(randi(eliteNum), :);
    parent2 = elitePopulation(randi(eliteNum), :);
    child = crossover(parent1, parent2);
    
    % 变异
    if rand < mutationRate
        child = mutate(child);
    end
    
    % 替换
    idx = randi(popSize);
    population(idx,:) = child;
    
end

% 计算最佳路径和适应度
bestFitness = Inf;
for i = 1:popSize
    f = evaluateFitness(population(i,:), cities);
    if f < bestFitness
        bestFitness = f;
        bestRoute = population(i,:);
    end
end

% 绘制最佳路径
figure;
plot(cities(:,1), cities(:,2), 'o');
hold on;
plot(cities([bestRoute, bestRoute(1)], 1), cities([bestRoute, bestRoute(1)], 2), '-r');
title(sprintf('Total distance: %0.2f', bestFitness));

end

function fitness = evaluateFitness(route, cities)

% 计算路径距离
distance = 0;
for i = 1:length(route)-1
    distance = distance + norm(cities(route(i),:) - cities(route(i+1),:));
end
distance = distance + norm(cities(route(end),:) - cities(route(1),:));

% 计算适应度
fitness = 1 / distance;

end

function child = crossover(parent1, parent2)

% 交叉操作：部分映射交叉
n = length(parent1);
child = zeros(1, n);
start = randi(n);
stop = randi(n);
if start > stop
    temp = start;
    start = stop;
    stop = temp;
end
child(start:stop) = parent1(start:stop);
idx = 1;
for i = 1:n
    if ~ismember(parent2(i), child)
        while child(idx) ~= 0
            idx = idx + 1;
        end
        child(idx) = parent2(i);
    end
end

end

function child = mutate(parent)

% 变异操作：随机交换两个基因
n = length(parent);
idx1 = randi(n);
idx2 = randi(n);
temp = parent(idx1);
parent(idx1) = parent(idx2);
parent(idx2) = temp;
child = parent;

end

这个示例代码使用遗传算法来优化电动汽车经过一系列城市的路径。在代码中，我们首先随机生成了一些城市坐标，并将它们表示为一个 $n \times 2$ 的矩阵。然后，我们初始化了一个由 $popSize$ 个个体组成的种群，每个个体表示一个遍历所有城市的路径。在进化循环中，我们计算每个个体的适应度（路径总长度的倒数），并选择一些精英个体进行繁殖。每次繁殖操作都会选择两个精英个体，进行交叉和变异操作，然后将产生的子代替换掉种群中的某个个体。经过多次迭代后，我们可以找到最佳路径和最短距离，并绘制出来。