基于混合遗传和退火算法求解不同种类箱子问题的matlab

以下是基于混合遗传和退火算法求解不同种类箱子问题的 Matlab 代码。在代码中，我们使用了遗传算法和退火算法的优点来求解该问题，以获得更好的结果。

%% 遗传算法参数
pop_size = 100; % 种群数量
gen_num = 100; % 迭代次数
mut_rate = 0.01; % 变异率
cross_rate = 0.8; % 交叉率

%% 退火算法参数
T0 = 100; % 初始温度
Tf = 0.01; % 终止温度
delta = 0.95; % 降温系数
num_of_iter = 50; % 迭代次数

%% 初始化箱子和物品
boxes = [5 5 5; 4 4 4; 3 3 3]; % 不同种类的箱子
items = [2 2 2; 3 3 3; 1 1 1; 4 4 4]; % 不同种类的物品

%% 将物品随机分配到箱子中
pop = zeros(pop_size, size(items, 1));
for i=1:pop_size
pop(i,:) = randperm(size(items, 1));
end

%% 遗传算法求解
for g=1:gen_num
% 计算适应度
fitness = zeros(pop_size, 1);
for i=1:pop_size
fitness(i) = calculate_fitness(pop(i,:), items, boxes);
end

% 选择
[parents, fitness] = select_parents(pop, fitness);

% 交叉
children = crossover(parents, cross_rate);

% 变异
children = mutate(children, mut_rate);

% 合并新种群
pop = [parents; children];

% 评估新种群
fitness = zeros(pop_size, 1);
for i=1:pop_size
fitness(i) = calculate_fitness(pop(i,:), items, boxes);
end

% 挑选最优解
[best_fitness, best_index] = max(fitness);
best_solution = pop(best_index,:);
end

%% 退火算法求解
T = T0;
while T > Tf
for i=1:num_of_iter
% 随机交换两个物品的位置
new_solution = best_solution;
idx = randperm(length(new_solution), 2);
new_solution(idx) = new_solution(fliplr(idx));

% 计算新解的适应度
new_fitness = calculate_fitness(new_solution, items, boxes);

% 计算接受概率
deltaE = new_fitness - best_fitness;
P = exp(-deltaE/T);

% 判断是否接受新解
if rand() < P
best_solution = new_solution;
best_fitness = new_fitness;
end
end

% 降温
T = T * delta;
end

%% 输出结果
disp('最优解：');
disp(best_solution);
disp('适应度：');
disp(best_fitness);

%% 遗传算法中的选择函数
function [parents, fitness] = select_parents(pop, fitness)
% 轮盘赌选择
prob = fitness / sum(fitness);
cum_prob = cumsum(prob);
parents = zeros(size(pop));

for i=1:size(pop, 1)
r = rand();
for j=1:size(pop, 1)
if r < cum_prob(j)
parents(i,:) = pop(j,:);
break;
end
end
end
end

%% 遗传算法中的交叉函数
function children = crossover(parents, cross_rate)
children = zeros(size(parents));

for i=1:2:size(parents,1)
if rand() < cross_rate
% 选择交叉点
cross_point = randi(size(parents,2));

% 交叉
children(i,:) = [parents(i,1:cross_point) parents(i+1,cross_point+1:end)];
children(i+1,:) = [parents(i+1,1:cross_point) parents(i,cross_point+1:end)];
else
children(i,:) = parents(i,:);
children(i+1,:) = parents(i+1,:);
end
end
end

%% 遗传算法中的变异函数
function children = mutate(children, mut_rate)
for i=1:size(children,1)
if rand() < mut_rate
% 选择变异点
mut_point = randi(size(children,2));

% 变异
idx = randperm(size(children,2), 2);
children(i,idx) = children(i,fliplr(idx));
end
end
end

%% 计算适应度函数
function fitness = calculate_fitness(solution, items, boxes)
% 计算每个箱子的可用空间
space = zeros(size(boxes, 1), 1);
for i=1:length(solution)
space(solution(i)) = space(solution(i)) + prod(items(i,:));
end

% 计算适应度
fitness = sum((space ./ prod(boxes, 2)) .^ 2);
end