算法优化与并行计算下的旅行商问题求解

# 1. 引言

- **1.1 问题背景**
- **1.2 目的与意义**
- **1.3 研究现状**

# 2. 旅行商问题简介

### 2.1 问题描述
The travelling salesman problem (TSP) is a classic algorithmic problem in the fields of computer science and operations research. It involves finding the shortest possible route that visits a set of given cities and returns to the original city, without visiting any city twice.

### 2.2 NP完全性证明
The TSP is a well-known NP-hard problem, meaning that there are no known polynomial-time algorithms to solve all instances of the problem optimally. This has led to the development of various heuristic and exact algorithms to find near-optimal solutions.

### 2.3 求解方法概述
There are several approaches to solving the TSP, including exact algorithms such as branch and bound, as well as heuristic algorithms like genetic algorithm