Abstract
This article proposes a novel crossover operator of hybrid genetic algorithms (HGAs) with a Lin-Kernighan (LK) heuristic for solving large-scale traveling salesman problems (TSPs). The proposed crossover, tentatively named sub-tour recombination crossover (SRX), collects many short sub-tours from both parents under some set of rules, and reconnects them to construct a new tour of the TSP. The method is evaluated from the viewpoint of tour quality and CPU time for ten well-known benchmarks, e.g., dj38, qa194, …, ch71009.tsp, in the TSP website of the Georgia Institute of Technology. We compare the SRX with three conventional crossover operators, a variant of the maximal preservative crossover operator (MPX3), a variant of the greedy sub-tour crossover operator (GSX2), and a variant of the edge recombination crossover operator (ERX6), and show that the SRX succeeded in finding a better solution and running faster than the conventional methods mentioned above.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Lin S, Kernighan B (1973) An effective heuristic algorithm for the traveling salesman problem. Operations Res 21(2):498–516
Mühlenbein H, Gorges-Schleuter M, Krämer O (1988) Evolution algorithms in combinatorial optimization. Parallel Comput 7:65–85
Sengoku H, Yoshihara I (1998) A fast TSP solver using GA on JAVA. Proceedings of the 3rd International Symposium on Artificial Life and Robotics (AROB-3), pp 283–288
Whitley D, Starkweather T, Fuquay D (1989) Scheduling problems and traveling salesman: the genetic edge recombination operator. Proceedings of the 3rd ICGA, pp 133–140
Nguyen HD (2004) Hybrid genetic algorithms for combinatorial optimization problems. PhD dissertation, University of Miyazaki
Nguyen HD, Yoshihara I, Yamamori K, et al (2002) Greedy genetic algorithms for symmetric and asymmetric TSPs. IPSJ Tech Rep SIG-MPS 43(SIG10), pp 165–175
Nguyen HD, Yoshihara I, Yasunaga M (2000) Modified edge recombination operators of genetic algorithms for the traveling salesman problem. Proceedings of the 3rd Asia-Pacific Conference on Simulation, Evolution, and Learning. SEAL 2000, pp 2815–2820
National TSPs, http://www.tsp.gatech.edu/world/countries.html (Accessed: 10 Jan. 2010)
Applegate D, Cook W, Rohe A (2003) Chained Lin-Kernighan for large traveling salesman problems. INFORMS J Comput 15(1):82–92
Baraglia R, Hidalgo JI, Perego R (2001) A hybrid heuristic for the traveling salesman problems. IEEE Trans EC 5(6):613–622
Nguyen HD, Yoshihara I, Yamamori K, et al (2007) Implementation of an effective hybrid GA for large-scale traveling salesman problems. IEEE Trans SMC 37(1):92–99
Concorde TSP Solver, http://www.tsp.gatech.edu/concorde/
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was presented in part at the 15th International Symposium on Artificial Life and Robotics, Oita, Japan, February 4–6, 2010
About this article
Cite this article
Kuroda, M., Yamamori, K., Munetomo, M. et al. Development of a novel crossover of hybrid genetic algorithms for large-scale traveling salesman problems. Artif Life Robotics 15, 547–550 (2010). https://doi.org/10.1007/s10015-010-0866-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10015-010-0866-8