Abstract
Multimodal Optimization is one of the most challenging tasks for optimization, since many real-world problems may have multiple acceptable solutions. Different from single objective optimization problem, multimodal optimization needs to both find multiple optima/peaks at the same time, and maintain these found optima until the end of a run. A novel swarm intelligent method, Modified Self-adaptive Brain Storm Optimization (MSBSO) algorithm is proposed to solve multimodal optimization problems in this paper. In order to find potential multiple optima, a modified disruption strategy is used for BSO algorithms to maintain the identified optima until the end of the search. Besides, the self-adaptive cluster number control is applied to improve Max-fitness Clustering Method with no need for a predefined subpopulation size M. Eight multimodal benchmark functions are used to validate the performance and effectiveness. Compared with the other swarm intelligent algorithms reported in the literature, the new algorithm can outperform others on most of the test functions.
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References
Yu, X., Gen, M.: Multimodal optimization. In: Introduction to Evolutionary Algorithms. DECENGIN, vol. 0, pp. 165–191. Springer, London (2010). https://doi.org/10.1007/978-1-84996-129-5_5
Bessaou, M., Pétrowski, A., Siarry, P.: Island model cooperating with speciation for multimodal optimization. In: Schoenauer, M., et al. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 437–446. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-45356-3_43
Bošković, B., Brest, J.: Clustering and differential evolution for multimodal optimization. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 698–705, June 2017. https://doi.org/10.1109/CEC.2017.7969378
Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: 2007 IEEE Swarm Intelligence Symposium, pp. 120–127, April 2007. https://doi.org/10.1109/SIS.2007.368035
Cheng, S., Chen, J., Lei, X., Shi, Y.: Locating multiple optima via brain storm optimization algorithms. IEEE Access 6, 17039–17049 (2018). https://doi.org/10.1109/ACCESS.2018.2811542
Cheng, S., Lu, H., Song, W., Chen, J., Shi, Y.: Dynamic multimodal optimization using brain storm optimization algorithms. In: Qiao, J., et al. (eds.) BIC-TA 2018. CCIS, vol. 951, pp. 236–245. Springer, Singapore (2018). https://doi.org/10.1007/978-981-13-2826-8_21
Cheng, S., Qin, Q., Chen, J., Shi, Y.: Brain storm optimization algorithm: a review. Artif. Intell. Rev. 46(4), 445–458 (2016). https://doi.org/10.1007/s10462-016-9471-0
Cheng, S., Qin, Q., Chen, J., Wang, G.G., Shi, Y.: Brain storm optimization in objective space algorithm for multimodal optimization problems. In: Tan, Y., Shi, Y., Niu, B. (eds.) ICSI 2016. LNCS, vol. 9712, pp. 469–478. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41000-5_47
Della Cioppa, A., De Stefano, C., Marcelli, A.: Where are the niches? Dynamic fitness sharing. IEEE Trans. Evol. Comput. 11(4), 453–465 (2007)
Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512), vol. 1, pp. 84–88, July 2000. https://doi.org/10.1109/CEC.2000.870279
Gao, W., Yen, G.G., Liu, S.: A cluster-based differential evolution with self-adaptive strategy for multimodal optimization. IEEE Trans. Cybern. 44(8), 1314–1327 (2014). https://doi.org/10.1109/TCYB.2013.2282491
Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms on Genetic Algorithms and Their Application, pp. 41–49. L. Erlbaum Associates Inc., Hillsdale (1987). http://dl.acm.org/citation.cfm?id=42512.42519
Guo, X., Wu, Y., Xie, L.: Modified brain storm optimization algorithm for multimodal optimization. In: Tan, Y., Shi, Y., Coello, C.A.C. (eds.) ICSI 2014. LNCS, vol. 8795, pp. 340–351. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11897-0_40
Harik, G.: Finding multimodal solutions using restricted tournament selection. In: Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 24–31. Morgan Kaufmann (1995)
Huang, T., Zhan, Z., Jia, X., Yuan, H., Jiang, J., Zhang, J.: Niching community based differential evolution for multimodal optimization problems. In: 2017 IEEE Symposium Series on Computational Intelligence (SSCI), pp. 1–8, November 2017. https://doi.org/10.1109/SSCI.2017.8280801
Li, J.P., Balazs, M., Parks, G., Clarkson, P.: A species conserving genetic algorithm for multimodal function optimization. Evol. Comput. 10, 207–234 (2002). https://doi.org/10.1162/106365602760234081
Li, X., Epitropakis, M.G., Deb, K., Engelbrecht, A.: Seeking multiple solutions: an updated survey on niching methods and their applications. IEEE Trans. Evol. Comput. 21(4), 518–538 (2017). https://doi.org/10.1109/TEVC.2016.2638437
Li, X., Engelbrecht, A., Epitropakis, M.G.: Benchmark functions for CEC’2013 special session and competition on niching methods for multimodal function optimization (2013). http://goanna.cs.rmit.edu.au/~xiaodong/cec13-niching/competition/
Mehmood, Y., Aziz, N., Riaz, F., Iqbal, H., Shahzad, W.: PSO-based clustering techniques to solve multimodal optimization problems: a survey. In: 2018 1st International Conference on Power, Energy and Smart Grid (ICPESG), pp. 1–6, April 2018. https://doi.org/10.1109/ICPESG.2018.8417315
Passaro, A., Starita, A.: Particle swarm optimization for multimodal functions: a clustering approach. J. Artif. Evol. Appl. 2008, 8 (2008). https://doi.org/10.1155/2008/482032
Peng, H., Deng, C., Wu, Z.: SPBSO: self-adaptive brain storm optimization algorithm with pbest guided step-size. J. Intell. Fuzzy Syst. 36, 5423–5434 (2019). https://doi.org/10.3233/JIFS-181310
Petrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 798–803, May 1996. https://doi.org/10.1109/ICEC.1996.542703
Qu, B.Y., Suganthan, P.N., Liang, J.J.: Differential evolution with neighborhood mutation for multimodal optimization. IEEE Trans. Evol. Comput. 16(5), 601–614 (2012). https://doi.org/10.1109/TEVC.2011.2161873
Shi, Y.: Brain storm optimization algorithm. In: Tan, Y., Shi, Y., Chai, Y., Wang, G. (eds.) ICSI 2011. LNCS, vol. 6728, pp. 303–309. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21515-5_36
Shi, Y.: An optimization algorithm based on brainstorming process. Int. J. Swarm Intell. Res. (IJSIR) 2(4), 35–62 (2011). https://doi.org/10.4018/ijsir.2011100103
Shi, Y.: Developmental swarm intelligence: developmental learning perspective of swarm intelligence algorithms. Int. J. Swarm Intell. Res. (IJSIR) 5(1), 36–54 (2014). https://doi.org/10.4018/ijsir.2014010102
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753), vol. 2, pp. 1382–1389, June 2004. https://doi.org/10.1109/CEC.2004.1331058
Wang, X., et al.: A multilevel sampling strategy based memetic differential evolution for multimodal optimization. Neurocomputing 334, 79–88 (2019). https://doi.org/10.1016/j.neucom.2019.01.006
Yin, X., Germay, N.: A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization. In: Albrecht, R.F., Reeves, C.R., Steele, N.C. (eds.) Artificial Neural Nets and Genetic Algorithms, pp. 450–457. Springer, Vienna (1993). https://doi.org/10.1007/978-3-7091-7533-0_65
Yu, Y., Wu, L., Yu, H., Li, S., Wang, S., Gao, S.: Brain storm optimization with adaptive search radius for optimization. In: 2017 International Conference on Progress in Informatics and Computing (PIC), pp. 394–398, December 2017. https://doi.org/10.1109/PIC.2017.8359579
Zhan, Z., Wang, Z., Lin, Y., Zhang, J.: Adaptive radius species based particle swarm optimization for multimodal optimization problems. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 2043–2048, July 2016. https://doi.org/10.1109/CEC.2016.7744039
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This work is supported by the Guangdong-Hong Kong Joint Innovation Platform of Big Data and Computational Intelligence under Grant 2018B050502006.
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Dai, Zy., Fang, W., Li, Q., Chen, Wn. (2020). Modified Self-adaptive Brain Storm Optimization Algorithm for Multimodal Optimization. In: Pan, L., Liang, J., Qu, B. (eds) Bio-inspired Computing: Theories and Applications. BIC-TA 2019. Communications in Computer and Information Science, vol 1159. Springer, Singapore. https://doi.org/10.1007/978-981-15-3425-6_30
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