用分支限界法求 tsp,给出代码
时间: 2024-10-17 09:15:01 浏览: 20
分支限界法(Branch and Bound,简称BB算法)是一种用于解决组合优化问题如旅行商问题(Travelling Salesman Problem,TSP)的有效搜索策略。TSP的目标是最短路径,使得旅行商访问每个城市恰好一次并返回起点。
以下是使用Python实现一个简单版本的分支限界算法解TSP的伪代码示例:
```python
# 假设我们有一个包含城市距离的邻接矩阵distances
def branch_and_bound(distances, current_city, visited_cities, best_path=None):
# 初始化最低成本(上界)
if not best_path or total_cost(best_path) > total_cost(visited_cities + [current_city]):
best_path = visited_cities + [current_city]
unvisited_cities = list(set(range(len(distances))) - set(visited_cities))
# 枝节点:尝试所有未访问城市的下一个访问点
for next_city in unvisited_cities:
new_visited_cities = visited_cities.copy()
new_visited_cities.append(next_city)
# 检查当前扩展是否优于已知最优解
if total_cost(new_visited_cities) < total_cost(best_path):
branch_and_bound(distances, next_city, new_visited_cities, best_path)
# 回溯过程中更新最佳解
if total_cost(best_path) < total_cost(current_best):
current_best = best_path
# 辅助函数计算路径总成本
def total_cost(path):
cost = 0
for i in range(len(path) - 1):
cost += distances[path[i]][path[i+1]]
return cost
# 示例调用
start_city = 0
branch_and_bound(distances, start_city, [], best_path=start_city)
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