An interactive simulation and analysis software for solving TSP using Ant Colony Optimization algorithms Aybars Ug ˘ur * , Dog ˘an Aydin Department of Computer Engineering, University of Ege, 35100 Bornova-Izmir, Turkey article info Article history: Received 24 March 2008 Received in revised form 30 April 2008 Accepted 12 May 2008 Available online 30 June 2008 Keywords: Simulation software Traveling salesman problem Ant Colony Optimization Local search heuristics Combinatorial optimization, visualization abstract Traveling salesman problem (TSP) is one of the extensively studied combinatorial optimization problems and tries to find the shortest route for salesperson which visits each given city precisely once. Ant colony optimization (ACO) algorithms have been used to solve many optimization problems in various fields of engineering. In this paper, a web-based simulation and analysis software (TSPAntSim) is developed for solving TSP using ACO algorithms with local search heuristics. Algorithms are tested on benchmark prob- lems from TSPLIB and test results are presented. Importance of TSPAntSim providing also interactive visualization with real-time analysis support for researchers studying on optimization and people who have problems in form of TSP is discussed. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Traveling salesman problem (TSP) is the one of the well-known and extensively studied problems in discrete or combinatorial optimization and asks for the shortest roundtrip of minimal total cost visiting each given city (node) exactly once. Cost can be dis- tance, time, money, energy, etc. TSP is an NP-hard problem and researchers especially mathematicians and scientists have been studying to develop efficient solving methods since 1950’s. Be- cause, it is so easy to describe and so difficult to solve. Graph the- ory defines the problem as finding the Hamiltonian cycle with the least weight for a given complete weighted graph. The traveling salesman problem is widespread in engineering applications. It has been employed in designing hardware devices and radio electronic devices, in communications, in the architec- ture of computational networks, etc. [1]. In addition, some indus- trial problems such as machine scheduling, cellular manufacturing and frequency assignment problems can be formu- lated as a TSP. One direct solving method is to select the route which has min- imum total cost of all possible permutations of N cities. The num- ber of permutations can be very large for even 40 cities. Every tour is represented in 2n different ways (for symmetrical TSP). Since there are n! possible ways to permute n numbers, the size of the search space is then jSj¼ n!=ð2nÞ¼ðn  1Þ!=2. Rather than enu- merating all possibilities, many approximation algorithms based on genetic algorithms (GA) [2], simulated annealing [3], tabu search [4], ant colony optimization [5–8] and neural networks [9] have been developed to yield good solutions within a reasonable time. Also, some exact algorithms based on the branch-and-cut method [10–12] have been proposed that enable even large TSP in- stances to be solved. Ant Colony Optimization (ACO) is a population-based approach which has been successfully applied to several NP-hard combina- torial optimization problems, firstly to traveling salesman prob- lem. ACO algorithms have been applied to various fields of engineering problems as a general optimization tool. Some pub- lished studies about using ACO algorithms to solve engineering problems can be found in [13–17]. ACO algorithms have virtual ants as agents that communicate indirect way and uses randomly propagation rules that make difficult to understand algorithms and agents behavior. ACO algorithms have many critical parameters that influence the performance dramatically and whose values are hard to estimate by researchers before. Many simulation and analysis tools have been developed for ge- netic algorithms [18–20], neural networks [21,22] and other meta- heuristics [23–25] or artificial intelligence methods [26,27] in the literature. But, there was not a comprehensive simulation and analysis software that has animation and tracing capabilities espe- cially for researchers in the area of ACO. In this paper, an interactive simulation and analysis software is developed for solving TSP using Ant Colony Optimization algo- rithms. This web-based tool employing virtual ants and 2D interac- tive graphics is used to produce near-optimal solutions to the TSP 0965-9978/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2008.05.004 * Corresponding author. E-mail addresses: aybars.ugur@ege.edu.tr (A. Ug ˘ur), dogan.aydin@ege.edu.tr (D. Aydin). Advances in Engineering Software 40 (2009) 341–349 Contents lists available at ScienceDirect Advances in Engineering Software journal homepage: www.elsevier.com/locate/advengsoft