使用matlab实现退火算法eil51解决TSP问题

退火算法是一种不确定性搜索算法，用于在大规模问题中寻找全局最优解。TSP问题是一个经典的组合优化问题，需要在给定的点集中找到一条最短的路径，使得每个点恰好被经过一次。下面是使用MATLAB实现退火算法解决TSP问题的示例代码，其中eil51数据集被用作测试数据集。

clc; clear; close all;
% Load TSP data
data = load('eil51.tsp');
n = size(data,1);
% Calculate distance matrix
distances = zeros(n,n);
for i=1:n
    for j=1:n
        distances(i,j) = norm(data(i,:)-data(j,:));
    end
end
% Set initial parameters
t0 = 100;
tf = 1;
alpha = 0.99;
max_iterations = 500;
% Initialize current solution
current_solution = randperm(n);
current_cost = calculate_cost(current_solution,distances);
% Initialize best solution
best_solution = current_solution;
best_cost = current_cost;
% Initialize iteration counter
iteration = 0;
% Main loop
while t0 > tf && iteration < max_iterations
    % Generate new solution
    new_solution = generate_solution(current_solution);
    new_cost = calculate_cost(new_solution,distances);
    % Calculate acceptance probability
    delta = new_cost-current_cost;
    if delta < 0
        probability = 1;
    else
        probability = exp(-delta/t0);
    end
    % Decide whether to accept new solution
    if rand() < probability
        current_solution = new_solution;
        current_cost = new_cost;
    end
    % Update best solution
    if current_cost < best_cost
        best_solution = current_solution;
        best_cost = current_cost;
    end
    % Update temperature
    t0 = t0*alpha;
    % Increment iteration counter
    iteration = iteration + 1;
end
% Plot best solution
best_solution = [best_solution best_solution(1)];
figure;
plot(data(:,1),data(:,2),'k.','MarkerSize',20);
hold on;
plot(data(best_solution,1),data(best_solution,2),'r-','LineWidth',2);
title(['Best solution: ' num2str(best_cost)]);
xlabel('x'); ylabel('y');

% Subfunctions
function cost = calculate_cost(solution,distances)
    n = length(solution);
    cost = 0;
    for i=1:n-1
        cost = cost + distances(solution(i),solution(i+1));
    end
    cost = cost + distances(solution(n),solution(1));
end

function new_solution = generate_solution(current_solution)
    n = length(current_solution);
    i = randi(n);
    j = randi(n);
    while j==i
        j = randi(n);
    end
    if i > j
        temp = i;
        i = j;
        j = temp;
    end
    new_solution = current_solution;
    new_solution(i:j) = fliplr(new_solution(i:j));
end

该代码中，calculate_cost函数用于计算给定解决方案的总成本。generate_solution函数用于生成新解决方案，它随机选择两个不同的点，并将它们之间的路径翻转。主循环通过逐渐降低温度来模拟冷却过程，并根据概率接受新解决方案。在循环中，当前解决方案和成本被更新，最佳解决方案和成本也被更新。最后，使用MATLAB的绘图功能绘制最佳解决方案的路径。