分支限界法旅行商问题算法伪代码

分支限界法（Branch and Bound）是一种用于求解组合优化问题，如旅行商问题（Traveling Salesman Problem, TSP）的有效算法。旅行商问题的目标是找到一条经过所有城市恰好一次的最短路径，使得旅行商回到起点。以下是使用分支限界法解决TSP的一个简化版的伪代码：

function BranchAndBound(TSPInstance, current_city, lower_bound, upper_bound, path):
    if current_city == TSPInstance.total_cities:  // 如果已访问所有城市
        return calculate_path_length(path)  // 返回路径长度

    best_solution = Infinity  // 初始化最佳解决方案
    for next_city in unvisited_cities(current_city):  // 遍历未访问的城市
        new_path = path + [next_city]  // 添加下一个城市到路径
        new_lower_bound = lower_bound[current_city] + distance(current_city, next_city)  // 更新下界
        new_upper_bound = lower_bound[next_city] + distance(next_city, TSPInstance.start_city)  // 更新上界

        solution = BranchAndBound(TSPInstance, next_city, update_lower_bound(lower_bound, next_city), new_upper_bound, new_path)
        if solution < best_solution:
            best_solution = solution
            // Update best path if a better one is found

    return best_solution

function main(TSPInstance):
    initial_lower_bound = zeros(TSPInstance.total_cities)  // 初始下界全为0
    best_path = []  // 初始化空路径
    best_solution = BranchAndBound(TSPInstance, TSPInstance.start_city, initial_lower_bound, Infinity, best_path)
    print("Best solution:", best_solution, "Path:", best_path)