Unsupervised fuzzy clustering-based genetic algorithms to Traveling Salesman Problem

In this paper a new genetic algorithm based on an unsupervised fuzzy clustering is proposed for Traveling Salesman Problem (TSP). The proposed algorithm involves on three phases. In the first phase, the cities are divided into several sub-tours by the clustering algorithm. In the second phase, each partition of cities is considered as a smaller scale TSP problem and this smaller size TSP problem is solved by a genetic algorithm which gets an optimal sub-tour of the cities of this partition. In the third phase, a new technique for connecting all these sub-tours into an appropriate tour of whole cities. As well as, this appropriate tour is improved by a genetic algorithm for cluster centers and a heuristic method. The computer simulations on some standard test problems show good performance for the proposed algorithm.

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

[2]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[3]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[4]  James P. Ignizio,et al.  Neural networks and operations research: An overview , 1992, Comput. Oper. Res..

[5]  Federico Greco.  Traveling Salesman Problem , 2008 .

[6]  Richard Szeliski,et al.  An Analysis of the Elastic Net Approach to the Traveling Salesman Problem , 1989, Neural Computation.

[7]  Lixia Han,et al.  A new encoding based genetic algorithm for the traveling salesman problem , 2006 .

[8]  D. Fogel.  An evolutionary approach to the traveling salesman problem , 1988, Biological Cybernetics.

[9]  Shyi-Ming Chen,et al.  Parallelized genetic ant colony systems for solving the traveling salesman problem , 2011, Expert Syst. Appl..

[10]  K. Katayama,et al.  Iterated local search approach using genetic transformation to the traveling salesman problem , 1999 .

[11]  Karan Bhatia,et al.  Genetic Algorithms and the Traveling Salesman Problem , 1994 .

[12]  M Dorigo,et al.  Ant colonies for the travelling salesman problem. , 1997, Bio Systems.

[13]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[14]  Kalyanmoy Deb,et al.  Ordering Genetic Algorithms and Deception , 1992, PPSN.

[15]  Abdelaziz Bouroumi,et al.  Unsupervised fuzzy learning and cluster seeking , 2000, Intell. Data Anal..

[16]  J. Monnot,et al.  The Traveling Salesman Problem and its Variations , 2014 .

[17]  Miguel Casquilho,et al.  Travelling Salesman Problem , 2012 .

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

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

[20]  S. Chatterjee,et al.  Genetic algorithms and traveling salesman problems , 1996 .

[21]  Pedro Larrañaga,et al.  Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators , 1999, Artificial Intelligence Review.

[22]  B. Freisleben,et al.  Genetic local search for the TSP: new results , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).