基本蚁群算法

摘要

许多实际工程问题可以抽象为相应的组合优化问题，TSP问题是作为所有组合优化问题的范例而存在的，它已成为并将继续成为测试组合优化新算法的标准问题。从理论上讲，使用穷举法可以求解出TSP问题的最优解；但是对现有的计算机来说，让它在如此庞大的搜索空间中寻求最优解，几乎是不可能的。所以，各种求TSP问题近似解的算法应运而生了，本文所描述的蚁群算法（AC）也在其中。

目前已出现了很多的启发式算法，而蚁群算法作为一种新型的启发式算法，已成功地应用于求解TSP问题。蚂蚁通过分泌信息素来加强较好路径上信息素的浓度，同时按照路径上的信息素浓度来选择下一步的路径：好的路径将会被越来越多的蚂蚁选择，因此更多的信息素将会覆盖较好的路径；最终所有的蚂蚁都集中到了好的路径上。蚂蚁的这种基于信息素的正反馈原理正是整个算法的关键所在。

本文介绍了基本蚁群算法概念、原理及蚁群算法的特点，再根据蚁群算法的缺点做出了优化。采用轮盘赌选择代替了基本框架中通过启发式函数和信息素选择路径，改进蚁群算法的信息素传递参数，让整个算法更快速的找到最优解。其次，采用最大最小优化系统限制最大值和最小值，让整个系统更快收敛，得到最优解。

关键字：蚁群算法，TSP问题，启发式函数，轮盘算法，最大最小优化

ABSTRACT

Many practical engineering problems can be abstracted as corresponding combinatorial optimization problem, TSP problem is an example of all as a combinatorial optimization problem, it has become and will continue to be a new combinatorial optimization algorithm of standard test problems. In theory, using the exhaustion method can solve the TSP problem optimal solution; But for the existing computer, let it in such a large search space to seek the optimal solution, it is almost impossible. So, all kinds of algorithm arises at the historic moment, the approximate solution of the TSP problem described in this paper, ant colony algorithm (AC) is among them.

Has appeared a lot of heuristic algorithm and ant colony algorithm as a kind of new heuristic algorithm, has been successfully used in solving TSP problems. Ant secretion by pheromones to strengthen the good path pheromone concentration, at the same time according to the path to choose the next path pheromone concentration: good paths will be more and more ants to choose, so that more information will cover good path; Eventually all the ants on a good path. This positive feedback based on the pheromone of ant principle is the key to the whole algorithm.

This paper introduces the basic concept of ant colony algorithm, principle and characteristics of ant colony algorithm, according to the disadvantages of ant colony algorithm optimization. Adopting roulette selection instead of the basic framework by heuristic function and choose path pheromone, pheromone passing parameters of improved ant colony algorithm, make the whole algorithm find the optimal solution more quickly. Second, limiting the maximum and the minimum maximum minimum optimization system, make the whole system faster convergence and the optimal solution is obtained.

Keywords: ant colony algorithm, the TSP problem, a heuristic function, roulette algorithm, maximum_minimum optimization

目录

摘要 (1)

ABSTRACT (2)

第1章绪论 (5)

1.1 研究目的和意义 (5)

1.2 国内外研究现状 (6)

1.2.1 国外研究现状 (6)

1.2.2 国内研究现状 (7)

1.3 本文研究内容 (7)

（1）基本蚁群算法 (8)

（2）蚁群算法的优化 (8)

（3）蚁群算法在TSP问题中的应用 (8)

1.4 开发环境与工具 (8)

1.5 论文的组织结构 (8)

第2章蚁群算法 (9)

2.1 蚁群算法简介 (9)

2.2 蚁群算法的原理 (10)

2.2.1 蚂蚁觅食规则 (10)

2.2.2 蚂蚁移动规则 (11)

2.2.3 蚂蚁避障规则 (11)

2.2.4 蚂蚁撒信息素规则 (11)

2.3 蚁群算法的特点及优缺点 (11)

2.3.1 蚁群算法的特点 (11)

2.3.2 蚁群算法的优点 (12)

2.3.3 蚁群算法的缺点 (13)

2.5 蚁群算法的核心函数 (13)

（1）初始化 (13)

（2）选择下一个城市，返回城市编号 (14)

（3）更新环境信息素 (16)

（4）检查终止条件 (17)