A novel discrete particle swarm optimization to solve traveling salesman problem

Particle swarm optimization (PSO), which simulates the unpredictable flight of a bird flock, is one of the intelligent computation algorithms. PSO is well-known to solve the continuous problems, yet by proper modification, it can also be applied to discrete problems, such as the classical test model: traveling salesman problem (TSP). In this paper, a novel discrete PSO call C3DPSO for TSP, with modified update formulas and a new parameter c3 (called mutation factor, to help to keep the balance between exploitation and exploration), is proposed. In the new algorithm, the particle is not a permutation of numbers but a set of edges, which is different from most other algorithms for TSP. However, it still keeps the most important characteristics of PSO that the whole swarm is guided by pbest and gbest. According to some benchmarks in TSP lib, it is proved that the proposed PSO works well even with 200 cities.

[1]  Luca Maria Gambardella,et al.  Ant colony system: a cooperative learning approach to the traveling salesman problem , 1997, IEEE Trans. Evol. Comput..

[2]  Yue Shi,et al.  A modified particle swarm optimizer , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[3]  Chunguang Zhou,et al.  Hybrid ant colony algorithm for traveling salesman problem , 2003 .

[4]  Richard Bellman,et al.  Dynamic Programming Treatment of the Travelling Salesman Problem , 1962, JACM.

[5]  Peter J. Angeline,et al.  Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences , 1998, Evolutionary Programming.

[6]  Maurice Clerc,et al.  Discrete Particle Swarm Optimization, illustrated by the Traveling Salesman Problem , 2004 .

[7]  Chunguang Zhou,et al.  Fuzzy discrete particle swarm optimization for solving traveling salesman problem , 2004, The Fourth International Conference onComputer and Information Technology, 2004. CIT '04..

[8]  T. Krink,et al.  Particle swarm optimisation with spatial particle extension , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Mehmet Fatih Tasgetiren,et al.  A Discrete Particle Swarm Optimization Algorithm for Single Machine Total Earliness and Tardiness Problem with a Common Due Date , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[10]  James Kennedy,et al.  Particle swarm optimization , 1995, Proceedings of ICNN'95 - International Conference on Neural Networks.

[11]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[12]  Kevin D. Seppi,et al.  Adaptive diversity in PSO , 2006, GECCO '06.

[13]  Yanchun Liang,et al.  Particle swarm optimization-based algorithms for TSP and generalized TSP , 2007, Inf. Process. Lett..

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

[15]  Richard W. Prager,et al.  Limitations of neural networks for solving traveling salesman problems , 1995, IEEE Trans. Neural Networks.

[16]  R. K. Suresh,et al.  Discrete Particle Swarm Optimization (DPSO) Algorithm for Permutation Flowshop Scheduling to Minimize Makespan , 2005, ICNC.

[17]  R. Eberhart,et al.  Fuzzy adaptive particle swarm optimization , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[18]  Cliff T. Ragsdale,et al.  A new approach to solving the multiple traveling salesperson problem using genetic algorithms , 2006, Eur. J. Oper. Res..

[19]  T. Munakata,et al.  Temperature control for simulated annealing. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Jun Liu,et al.  A Modified Particle Swarm Optimization Algorithm and its Application For Solving Traveling Salesman Problem , 2005, 2005 International Conference on Neural Networks and Brain.

[21]  Leonardo Zambito,et al.  The Traveling Salesman Problem: A Comprehensive Survey , 2006 .

[22]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[23]  Sanghamitra Bandyopadhyay,et al.  New operators of genetic algorithms for traveling salesman problem , 2004, ICPR 2004.

[24]  S.G. Ponnambalam,et al.  A Hybrid Discrete Particle Swarm Optimization Algorithm to Solve Flow Shop Scheduling Problems , 2006, 2006 IEEE Conference on Cybernetics and Intelligent Systems.

[25]  Thomas Kiel Rasmussen,et al.  Hybrid Particle Swarm Optimiser with breeding and subpopulations , 2001 .

[26]  Wei Pang,et al.  Modified particle swarm optimization based on space transformation for solving traveling salesman problem , 2004, Proceedings of 2004 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.04EX826).