Abstract
Genetic Algorithms (GAs) for the Travelling Salesman Problem (TSP) are often based on permutation representations, which makes it difficult to design effective evolutionary operators without causing feasibility problems to chromosomes. This paper attempts to develop a binary representation based hybrid GA to solve the TSP. The basic idea is to design a pre-TSP problem (PTSPP), where the input is the coordinates of a point in the map of cities, and the output is a feasible route connecting all cities. An effective deterministic algorithm is developed for this PTSPP to search the local optimum starting from the coordinates of a given point. The new GA is then designed to randomly choose and evolve the coordinates of generations of points for the PTSPP, and also to find out the global optimum or suboptima for the TSP. The preliminary experiments show the potential of the proposed hybrid GA to solve the TSP.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Reinelt, G. (2004) TSPLIB, Travelling Salesman Problem, Universität Heidelberg, found on http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/
Holland, J.H. (1975) Adaptation in Natural and Artificial Systems, Ann Arbor, MI: University of Michigan Press
Mitchell, M., (1998) An Introduction to Genetic Algorithms, Cambridge, MA: MIT Press
Ingo, W. (1999) Evolutionäre Algorithmen, found on http://www.informaticadidactica.de/ HyFISCH/Spitzenforschung/Wegener.htm
Thomas, A. (2001) Solving the Travelling Sales Man Problem using a Genetic Algorithm, found on http://www.generation5.org/content/2001/gatsp.asp
Sengoku, H. and Yoshihara, I. (1998) A Fast TSP Solver Using GA on JAVA, Hitachi Ltd & Tohoku University, found on http://www-cse.uta.edu/ %7Ecook/ai1/lectures/ applets/gatsp/TSP.html
Jürgen, H. University of Mannheim (2002) Lecture slides for Evolutionary Algorithm, found on http://webrum.uni-mannheim.de/math/scovis/Vorlesung/EA/WS0304/EAScript3.pdf
Warson, J., Ross, C., Eisele, V., Denton, J., Bins, J., Guerra, C., Whitley, D., and Howe, A. (2001). The Travelling Salesman Problem, Edge Assembly Crossover, and 2-opt, Colorado University, Fort Collins
Jog, P., and Suh, J.Y, and Van Gucht, D. (1989). The Effects of Poplation Size, Heuristic Crossover and Local Improvement on a genetic Algorithm for the Travelling Salesman Problem, Proceedings of the 3rd International Conference on Genetic Algorithms, Indiana University, USA.
Julstrom, B. A. (1999). Coding TSP Tours as permutations via an insertion heuristic, Proceedings of the 1999 ACM symposium on Applied computing, St. Cloud State University, St. Cloud.
Whitley, D., and Strakweather, T., and Fuquay, DA. (1989). Scheduling Problems and Travelling Salesman: The Genetic Edge Recombination Operator, Proceedings of the 3rd International Conference on Genetic Algorithms, Indiana University, USA.
Sywerda, G. (1989) Uniform crossover in genetic algorithms, Proceedings of the 3rd International Conference on Genetic Algorithms, Indiana University, USA.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Hu, XB., Di Paolo, E. (2008). A Hybrid Genetic Algorithm for the Travelling Salesman Problem. In: Krasnogor, N., Nicosia, G., Pavone, M., Pelta, D. (eds) Nature Inspired Cooperative Strategies for Optimization (NICSO 2007). Studies in Computational Intelligence, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78987-1_32
Download citation
DOI: https://doi.org/10.1007/978-3-540-78987-1_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78986-4
Online ISBN: 978-3-540-78987-1
eBook Packages: EngineeringEngineering (R0)