Abstract
We propose two entropy-based diversity measures for evaluating population diversity in a genetic algorithm (GA) applied to the traveling salesman problem (TSP). In contrast to a commonly used entropy-based diversity measure, the proposed ones take into account high-order dependencies between the elements of individuals in the population. More precisely, the proposed ones capture dependencies in the sequences of up to m + 1 vertices included in the population (tours), whereas the commonly used one is the special case of the proposed ones with m = 1. We demonstrate that the proposed entropy-based diversity measures with appropriate values of m evaluate population diversity more appropriately than does the commonly used one.
This is a preview of subscription content, log in via an institution to check access.
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
Maekawa, K., Mori, N., Tamaki, H., Kita, H., Nishikawa, Y.: A genetic solution for the traveling salesman problem by means of a thermodynamical selection rule. In: Proceedings of 3rd IEEE Conference on Evolutionary Computation, pp. 529–534 (1996)
Mori, N., Kita, H., Nishikawa, Y.: Adaptation to a Changing Environment by Means of the Feedback Thermodynamical Genetic Algorithm. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 149–158. Springer, Heidelberg (1998)
Nagata, Y.: Fast EAX Algorithm Considering Population Diversity for Traveling Salesman Problems. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2006. LNCS, vol. 3906, pp. 171–182. Springer, Heidelberg (2006)
Nagata, Y., Kobayashi, S.: Powerful genetic algorithm using edge assembly crossover for the traveling salesman problem. INFORMS Journal on Computing (in press) (published as an article in advance)
Tsai, H., Yang, J., Tsai, Y., Kao, C.: An evolutionary algorithm for large traveling salesman problems. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 34(4), 1718–1729 (2004)
Tsujimura, Y., Gen, M.: Entropy-based genetic algorithm for solving tsp. In: Proceedings of 2nd International Conference on Knowledge-Based Intelligent Electronic Systems, pp. 285–290. IEEE (1998)
Vallada, E., Ruiz, R.: Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem. Omega 38(1), 57–67 (2010)
Wang, Y., Lü, Z., Hao, J.-K.: A Study of Multi-parent Crossover Operators in a Memetic Algorithm. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part I. LNCS, vol. 6238, pp. 556–565. Springer, Heidelberg (2010)
Yao, X.: An empirical study of genetic operators in genetic algorithms. Microprocessing and Microprogramming 38(1-5), 707–714 (1993)
Zhang, C., Su, S., Chen, J.: Efficient Population Diversity Handling Genetic Algorithm for QoS-Aware Web Services Selection. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3994, pp. 104–111. Springer, Heidelberg (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nagata, Y., Ono, I. (2013). High-Order Sequence Entropies for Measuring Population Diversity in the Traveling Salesman Problem. In: Middendorf, M., Blum, C. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2013. Lecture Notes in Computer Science, vol 7832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37198-1_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-37198-1_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37197-4
Online ISBN: 978-3-642-37198-1
eBook Packages: Computer ScienceComputer Science (R0)