Ant colony system: a cooperative learning approach to the traveling salesman problem

This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSPs. Ants cooperate using an indirect form of communication mediated by a pheromone they deposit on the edges of the TSP graph while building solutions. We study the ACS by running experiments to understand its operation. The results show that the ACS outperforms other nature-inspired algorithms such as simulated annealing and evolutionary computation, and we conclude comparing ACS-3-opt, a version of the ACS augmented with a local search procedure, to some of the best performing algorithms for symmetric and asymmetric TSPs.

[1]  Gebräuchliche Fertigarzneimittel,et al.  V , 1893, Therapielexikon Neurologie.

[2]  J. Willems The Belgian National Fund for Scientific Research , 1945, Nature.

[3]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[4]  Shen Lin Computer solutions of the traveling salesman problem , 1965 .

[5]  Nicos Christofides,et al.  Distribution management : mathematical modelling and practical analysis , 1971 .

[6]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

[7]  Daniel J. Rosenkrantz,et al.  An Analysis of Several Heuristics for the Traveling Salesman Problem , 1977, SIAM J. Comput..

[8]  Christos H. Papadimitriou,et al.  Local Search for the Asymmetric Traveling Salesman Problem , 1980, Oper. Res..

[9]  Richard Durbin,et al.  An analogue approach to the travelling salesman problem using an elastic net method , 1987, Nature.

[10]  L. D. Whitley,et al.  Scheduling Problems and Traveling Salesmen: The Genetic Edge Recombination Operator , 1989, ICGA.

[11]  Darrell Whitley,et al.  Scheduling problems and traveling salesman: the genetic edge recombination , 1989 .

[12]  Edward W. Felten,et al.  Large-step markov chains for the TSP incorporating local search heuristics , 1992, Oper. Res. Lett..

[13]  J. Deneubourg,et al.  Trails and U-turns in the Selection of a Path by the Ant Lasius niger , 1992 .

[14]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[15]  Marco Dorigo,et al.  Distributed Optimization by Ant Colonies , 1992 .

[16]  Marco Dorigo,et al.  An Investigation of some Properties of an "Ant Algorithm" , 1992, PPSN.

[17]  Jon Jouis Bentley,et al.  Fast Algorithms for Geometric Traveling Salesman Problems , 1992, INFORMS J. Comput..

[18]  D. Fogel Applying evolutionary programming to selected traveling salesman problems , 1993 .

[19]  Jean-Yves Potvin,et al.  THE TRAVELING SALESMAN PROBLEM: A NEURAL NETWORK PERSPECTIVE , 1993 .

[20]  David S. Johnson,et al.  Data structures for traveling salesmen , 1993, SODA '93.

[21]  Cheng-Yan Kao,et al.  Applying the genetic approach to simulated annealing in solving some NP-hard problems , 1993, IEEE Trans. Syst. Man Cybern..

[22]  G. Reinelt The traveling salesman: computational solutions for TSP applications , 1994 .

[23]  Ben J. A. Kröse,et al.  Learning from delayed rewards , 1995, Robotics Auton. Syst..

[24]  Luca Maria Gambardella,et al.  Ant-Q: A Reinforcement Learning Approach to the Traveling Salesman Problem , 1995, ICML.

[25]  Rich Caruana,et al.  Removing the Genetics from the Standard Genetic Algorithm , 1995, ICML.

[26]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[27]  Luca Maria Gambardella,et al.  Results of the first international contest on evolutionary optimisation (1st ICEO) , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[28]  Luca Maria Gambardella,et al.  Solving symmetric and asymmetric TSPs by ant colonies , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[29]  Bernd Freisleben,et al.  A genetic local search algorithm for solving symmetric and asymmetric traveling salesman problems , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[30]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[31]  Bernd Freisleben,et al.  New Genetic Local Search Operators for the Traveling Salesman Problem , 1996, PPSN.

[32]  Luca Maria Gambardella,et al.  A Study of Some Properties of Ant-Q , 1996, PPSN.

[33]  Léon J. M. Rothkrantz,et al.  Ant-Based Load Balancing in Telecommunications Networks , 1996, Adapt. Behav..

[34]  Corso Elvezia Ant Colonies for the QAP , 1997 .

[35]  Thomas Stützle,et al.  Improvements on the Ant-System: Introducing the MAX-MIN Ant System , 1997, ICANNGA.

[36]  T. Stützle,et al.  MAX-MIN Ant System and local search for the traveling salesman problem , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[37]  Vittorio Maniezzo,et al.  The Ant System Applied to the Quadratic Assignment Problem , 1999, IEEE Trans. Knowl. Data Eng..