Abstract
In a traveling salesman problem (TSP), the contribution of a variable to fitness depends on the state of other variables. This characteristic can be referred to as entire linkage, utilizing which evolutionary algorithms can significantly enhance performance, especially in cases of large scale problems. In this paper, a construction graph-based evolutionary algorithm (CGEA) to learn variable interactions in TSP is presented. The proposed method employs real adjacency matrix-coding based on construction graph to make population individuals as carriers of variable interaction degrees through evolution. Iteratively, variable interactions are discovered by a parameterless search scheme, called matrix recombination-difference. In order to explore features of CGEA, an entire linkage index (ELI) is proposed to measure the entire linkage level of TSP. The experimental results show CGEA is promising for TSP, especially with a high entire linkage level.
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Notes
- 1.
Notes: Results of S-CLPSO were provided by Chen.
References
Matai, R., Mittal, M.L., Singh, S.: Traveling Salesman Problem: An Overview of Applications, Formulations, and Solution Approaches. Intech Open Access Publisher, Rijeka (2010)
Sun, Y., Kirley, M., Halgamuge, S.: Quantifying variable interactions in continuous optimization problems. IEEE Trans. Evol. Comput. 99, 1 (2016)
Eiben, A.E., Smith, J.: From evolutionary computation to the evolution of things. Nature 521(7553), 476–482 (2015)
Huang, H., Yang, X., Hao, Z., Wu, C., Liang, Y., Zhao, X.: Hybrid chromosome genetic algorithm for generalized traveling salesman problems. In: Wang, L., Chen, K., Ong, Y.S. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 137–140. Springer, Heidelberg (2005). doi:10.1007/11539902_16
Homaifar, A., Guan, S., Liepins, G.: A new approach to the traveling salesman problem by genetic algorithm. In: 5th International Conference on Genetic Algorithms, 1CGA 1993. University of Illinois at Urbana-Champaign, Champaign, IL, pp. 460–466 (1993)
Onwubolu, G.C., Davendra, D.: Differential Evolution: a Handbook for Global Permutation-Based Combinatorial Optimization. Spinger Publishing Company, Incorporated, Heidelberg (2009)
Samanlioglu, F., Kurz, M.B., Ferrell, W.G., et al.: A hybrid random-key genetic algorithm for a symmetric travelling salesman problem. Int. J. Oper. Res. 2(1), 47–63 (2006)
Pang, W., Wang, K., Zhou, C., et al.: Fuzzy discrete particle swarm optimization for solving traveling salesman problem. In: 2004 The Fourth International Conference on Computer and Information Technology, CIT 2004, pp. 796–800. IEEE (2004)
Chen, W., Zhang, J., Chung, H.H., et al.: A novel set-based particle swarm optimization method for discrete optimization problems. IEEE Trans. Evol. Comput. 14(2), 278–300 (2010)
Ma, Y., Gong, Y., Chen, W., et al.: A set-based locally informed discrete particle swarm optimization. In: Proceedings of the 15th Annual Conference Companion on Genetic and Evolutionary Computation, pp. 71–72. ACM (2013)
Liu, Y., Chen, W.N., Zhan, Z.H., et al.: A set-based discrete differential evolution algorithm. In: 2013 IEEE International Conference on Systems, Man, and Cybernetics (SMC), pp. 1347–1352. IEEE (2013)
Dorigo, M., Sttzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)
Gutjahr, W.J.: A generalized convergence result for the graph-based ant system metaheuristic. Probab. Eng. Inf. Sci. 17(04), 545–569 (2003)
Yan, L., Mei, Y., Ma, H., et al.: Evolutionary web service composition: a graph-based memetic algorithm. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 201–208. IEEE (2016)
Peng, G., Wang, H., Dong, J., et al.: Knowledge-based resource allocation for collaborative simulation development in a multi-tenant cloud computing environment. IEEE Trans. Serv. Comput. 99, 1 (1939)
TSPLIB. http://www.iwr.uni-heidelberg.de
Sttzle, T., Hoos, H.H.: MAX-MIN ant system. Future Gener. Comput. Syst. 16(8), 889–914 (2000)
Yu, Y., Qian, H., Hu, Y.Q.: Derivative-free optimization via classification. In: Proceedings of Thirtieth AAAI Conference on Artificial Intelligence. Phoenix (2016)
Acknowledgement
First of all, the writers are very thankful to Pro. Chen who provided computation results of some TSP instances by S-CLPSO.
This work is supported by National Natural Science Foundation of China (61370102), Guangdong Natural Science Funds for Distinguished Young Scholar (2014A030306050), the Ministry of Education - China Mobile Research Funds (MCM20160206) and Guangdong High-level personnel of special support program (2014TQ01X664).
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Li, G., Hao, Z.f., Wei, H., Huang, H. (2017). A Construction Graph-Based Evolutionary Algorithm for Traveling Salesman Problem. In: Shi, Y., et al. Simulated Evolution and Learning. SEAL 2017. Lecture Notes in Computer Science(), vol 10593. Springer, Cham. https://doi.org/10.1007/978-3-319-68759-9_53
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