Abstract
We present a hybrid genetic algorithm that incorporates the Generalized Partition Crossover (GPX) operator to produce an algorithm that is competitive with the state of the art for the Traveling Salesman Problem (TSP). GPX is respectful, transmits alleles and is capable of tunneling directly to new local optima. Our results show that the hybrid genetic algorithm quickly finds optimal and near optimal solution on problems ranging from 500 to 1817 cities using a population size of 10. It is also superior to Chained-LK given similar computational effort. Additional analysis shows that all the edges found in the globally optimal solution are present in a population after only a few generations in almost every run. Furthermore the number of unique edges in the population is also less than twice the problem size.
This effort was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-08-1-0422. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
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
Applegate, D., Cook, W., Rohe, A.: Chained Lin-Kernighan for large traveling salesman problems. INFORMS Journal on Computing 15(1), 82–92 (2003)
Whitley, D., Hains, D., Howe, A.: Tunneling between optima: partition crossover for the traveling salesman problem. In: Proceedings of the 11th Annual conference on Genetic and evolutionary computation, pp. 915–922. ACM, New York (2009)
Radcliffe, N., Surry, P.: Fitness variance of formae and performance predictions. In: Whitley, D., Vose, M. (eds.) FOGA - 3, pp. 51–72. Morgan Kaufmann, San Francisco (1995)
Croes, G.: A method for solving traveling-salesman problems. Operations Research, 791–812 (1958)
Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling-salesman problem. Operations Research, 498–516 (1973)
Boese, K.D., Kahng, A.B., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Operations Research Letters 16, 101–113 (1994)
Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: A case study in local optimization. In: Aarts, E.H.L., Lenstra, J. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley and Sons Ltd., Chichester (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Whitley, D., Hains, D., Howe, A. (2010). A Hybrid Genetic Algorithm for the Traveling Salesman Problem Using Generalized Partition Crossover. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15844-5_57
Download citation
DOI: https://doi.org/10.1007/978-3-642-15844-5_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15843-8
Online ISBN: 978-3-642-15844-5
eBook Packages: Computer ScienceComputer Science (R0)