Finding Multiple Solutions of Multimodal Optimization Using Spiral Optimization Algorithm with Clustering
Abstract
Multimodal optimization is one of the interesting problems in optimization which arises frequently in a wide
range of engineering and practical applications. The goal of this problem is to find all of optimum solutions in a single run. Some algorithms fail to find all solutions that have been proven their existence analytically. In our paper [1], a method is proposed to find the roots of a system of non-linear equations using a clustering technique that combine with Spiral Optimization algorithm and Sobol sequence of points. An interesting benefit using this method is that the same inputs will give the same results. Most of the time this does not happen in meta-heuristic algorithms using random factors. Now the method is modified to find solutions of multimodal optimization problems. Generally in an optimization problem, the differential form of the objective function is needed. In this paper, the proposed method is to find optimum points of general multimodal functions that its differential form is not required. Several problems with benchmark functions have been examined using our method and they give good result.
References
Sidarto, K.A., Kania, A.: Finding all soluti ons of systems of nonlinear equations using spiral dynamics inspired optimization with clustering. J. of Advanced Computational Intelligence and Intelligent Informatics (JACIII) 19(5), 697-707 (2015). DOI 10.20965/jaciii.2015.p0697
Kamyab, S., Eftekhari, M.: Feature selection using m ultimodal optim ization tech niques. Neurocomputing, 1 71, 586–597 (2016). DOI 10.1016/j.neucom.2015.06.068
Huang, L., Ng, C., Sheikh, A.H., Griffith, M.C.: Niching particle swarm optimization techniques for multimodal buckling m aximization o f com posite lam inates. Ap plied S oft C omputing, 57, 4 95–503 ( 2017). DOI 10.1016/j.asoc.2017.04.006
Zaharie, D.: A multipopulation differential evolution algorithm for multimodal optimization. In: R. Matousek (ed.) Proceedings of 10th International Conference on Soft Computing – MENDEL 2004, no. 10 in MENDEL, pp. 17–24. Brno University of Technology, VUT Press, Brno (2004)
Chica, M ., B arranquero, J. , Kajdanowicz, T., Damas, S., Cordón, O.: Multi modal optimization: An effective framework for model calibration. Information Sciences, 375, 79–97 (2017). DOI 10.1016/j.ins.2016.09.048
Chiu, C., Lin, J.T.: N ovel hybrid approach with elite group optimal computing budget allocation for the stochastic multimodal problem, Neurocomputing (2017). DOI 10.1016/j.neucom.2017.04.041
Tamura, K., Yasuda, K.: Spiral Dynam ics Inspired Optimization. J. of Advanced Co mputational Intelligence and Intelligent Informatics (JACIII) 15(8), 1116-1122 (2011). DOI 10.20965/jaciii.2011.p1116.
Tamura, K., Yasuda, K.: A Parameter Setting Method for Spiral Optimization from Stability Analysis of Dynamic Equilibrium Point. S ICE Journal of Control, Measurement, and System Integration 7(3), 173–182 (2 014). DOI 10.9746/jcmsi.7.173
Nasir, A.N.K, Ism ail, R .M.T.R., T okhi, M.O.: Adaptive spiral dynamics metaheuristic algorithm for global optimisation with application to modelling of a flexible system. Applied Mathematical Modelling 40(9-10), 5442–5461 (2016). DOI 10.1016/j.apm.2016.01.002
Li, X., Engelbrecht, A., Epitropakis, M.G.: Benchmarks Functions for CEC’2013 Special Session and Competition on Niching Methods for Multimodal Function Optimization. (Last updated 21 September 2016). Technical Report, Evolutionary Computation and Machine Learning Group, RMIT University, Australia.
Seydel, R.: Tools for Computational Finance. Springer-Verlag (2002)
Joe, S., Kuo, F.Y.: Constructing Sobol sequences with be tter two dimensional projections. SIAM J. Sci. Comput. 30(5), 2635–2654 (2008). DOI 10.1137/070709359
MENDEL open access articles are normally published under a Creative Commons Attribution-NonCommercial-ShareAlike (CC BY-NC-SA 4.0) https://creativecommons.org/licenses/by-nc-sa/4.0/ . Under the CC BY-NC-SA 4.0 license permitted 3rd party reuse is only applicable for non-commercial purposes. Articles posted under the CC BY-NC-SA 4.0 license allow users to share, copy, and redistribute the material in any medium of format, and adapt, remix, transform, and build upon the material for any purpose. Reusing under the CC BY-NC-SA 4.0 license requires that appropriate attribution to the source of the material must be included along with a link to the license, with any changes made to the original material indicated.
