人工蚁群算法的实现与性能分析

目录.................................................... 错误！未定义书签。摘要. (ii)

Abstract (iii)

第一章引言 (1)

1.1 非对称TSP问题（ATSP）及其求解方法概述 (1)

1.2 人工蚁群算法的主要思想和特点 (1)

1.3 主要工作 (2)

第二章 ATSP问题分析 (3)

2.1 ATSP问题的数学模型 (3)

2.2 ATSP问题与TSP问题的比较 (3)

第三章求解ATSP问题的人工蚁群算法 (4)

3.1 ATSP问题的蚁群算法表示 (4)

3.2 人工蚁群算法的实现 (4)

3.2.1 人工蚁群算法的流程图 (5)

3.2.2 蚁群的规模、算法终止条件 (6)

3.2.3 路径选择方法和信息素的更新方法 (7)

第四章实验和分析 (10)

4.1 测试环境 (10)

4.2 测试用例 (10)

4.3 实验结果及参数分析 (10)

4.3.1 br17.atsp的测试结果 (10)

4.3.2 ft53.atsp的测试结果 (12)

4.3.3 ftv33.atsp的测试结果 (13)

4.3.4 ftv35.atsp的测试结果 (15)

4.3.5 br17.atsp相关参数修改后的测试结果 (16)

第五章总结 (19)

致谢 (20)

参考文献 (21)

摘要

旅行商问题(TSP问题)是组合优化的著名难题。它具有广泛的应用背景,如计算机、网络、电气布线、加工排序、通信调度等。已经证明TSP问题是NP难题,鉴于其重要的工程与理论价值,TSP常作为算法性能研究的典型算例。TSP的最简单形象描述是:给定n个城市,有一个旅行商从某一城市出发,访问各城市一次且仅有一次后再回到原出发城市,要求找出一条最短的巡回路径。TSP分为对称TSP和非对称TSP两大类,若两城市往返距离相同,则为对称TSP,否则为非对称TSP 。本文研究的是对称的ATSP。

实质上，ATSP问题是在TSP问题上发展而来的，它们的区别就在于两座城市之间的往返距离是否相同。例如，有A,B两个城市，在TSP问题中，从A到B的距离是等于从B到A得距离的，是一个单向选择的连通问题。而在ATSP问题中，从A到B的距离就不一定等于从B到A的距离，所以这是双向选择的联通问题。

本文主要阐述了用人工蚁群算法的原理和一些与其相关联的知识结构点。通过对算法原理的理解，及在函数优化问题上的应用，与优化组合问题的研究来了解ATSP问题以及人工蚁群算法解决实际问题上的应用与研究。

关键词：ATSP ；组合优化；人工蚁群算法；TSP

Abstract

Traveling salesman problem (TSP) is the Famous combination of the optimization problem. It has broad applications, such as computer, network, electrical wiring, processing, sort and communication scheduling,and etc.Has already proved TSP is a difficult NP problem, givening its important engineering and theoretical valued, TSP is often used as the typical example of algorithm performance study.The most simple image description of TSP is: given n city, a traveling salesman start from one city, Visit other cities once and only once again return to the start city , asked to identify a shortest path of the tour.TSP can be classificated symmetric TSP and asymmetric TSP two big kinds.If two cities from the same distance,that is symmetric TSP, or for the asymmetric TSP.This paper studies the ATSP problem.

In essence, ATSP problem is based on the TSP problem.The difference lies in two cities round trip distance between the same or different.For example,there are two cities,A and B , in TSP problem,from A to B is equal to the distance from B to have A distance,it s a one-way choice the connected problems.But in ATSP problem,from A to B doesn't necessarily equal to the distance from the distance B to A, so this is the two-way choice connectivity problem. This paper mainly expounds the employing workers group of the principle and some associated knowledge structure of the points.Through the understanding of the principle of the algorithm，and in the application of the function optimization problems,And the optimized combination problems research to understand ATSP problems and one worker ants group algorithm of solving practical problems with the application of research.

Keywords：ATSP ; Combinatorial optimization ; People ants group of algorithm ; TSP