Abstract
Optimization has been one of significant research fields in the past few decades, most of the real-world problems are multimodal optimization problems. The prime target of multimodal optimization is to find multiple global and local optima of a problem in one single run. The multimodal optimization problems have drawn attention to evolutionary algorithms. Firefly algorithm is a recently proposed stochastic optimization technique. This algorithm is a global search algorithm. On the other hand, because this algorithm has multimodal characteristics, it has the capacity and capability to change into multimodal optimization method. The aim of this article is to show that firefly algorithm is able to find multiple solutions in multimodal problems. Therefore, in this study, a new technique, is introduced for multimodal optimization. In the proposed algorithm, the multimodal optima are detected through separately evolving sub-populations. A stability criterion is used to determine the stability and instability of the sub-population. If a sub-population is regarded as stable, it has an optima stored in an external memory called Archive. After some iterations, the archive includes all of the optimums. The proposed algorithm utilizes a simulated annealing local optimization algorithm to increase search power, accuracy and speed of the algorithm. The proposed algorithm is tested on a set of criterion functions. The results show that the proposed algorithm has a high ability to find the multimodal optimal points.
Similar content being viewed by others
References
Beasley D, Bull DR, Martin RR (1993) A sequential niche technique for multimodal function optimization. Evolut Comput 1:101–125
Brits R, Engelbrecht AP, van den Bergh F (2007) Locating multiple optima using particle swarm optimization. Appl Math Comput 189:1859–1883
De Castro LN, Von Zuben FJ (2002) Learning and optimization using the clonal selection principle. IEEE Trans Evolut Comput 6:239–251
Durkota K (2011) Implementation of a discrete firefly algorithm for the QAP problem within the sage framework. Czech Technical University, BSc thesis
Goh CK, Tan KC, Liu D, Chiam SC (2010) A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design. Eur J Oper Res 202:42–54
Kennedy J (2010) Particle swarm optimization. In: C. Sammut, GI Webb (eds) Encyclopedia of machine learning. Springer, pp 760–766
Krishnanand K, Ghose D (2009) Glowworm swarm optimization for simultaneous capture of multiple local optima of multimodal functions. Swarm Intell 3:87–124
Li X (2007) Multimodal function optimization based on fitness-Euclidean distance ratio. In: Proceedings on genetic and evolutionary computation conference, pp 78–85
Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evolut Comput 14:150–169
Liang Y, Leung K-S (2011) Genetic algorithm with adaptive elitist-population strategies for multimodal function optimization. Appl Soft Comput 11:2017–2034
Liang JJ, Qu B-Y, Mao X, Niu B, Wang D (2014) Differential evolution based on fitness Euclidean-distance ratio for multimodal optimization. Neurocomputing 137:252–260
Lung RI, Dumitrescu D (2004) Roaming optimization: a new evolutionary technique for multimodal optimization. Studia Univ Babes-Bolyai Inform 49:99–109
Lung RI, Dumitrescu D (2005) A new subpopulation model for evolutionary multimodal optimization. In: Seventh international symposium on symbolic and numeric algorithms for scientific computing, 2005. SYNASC 2005, p 4
Mahfoud SW (1992) Crowding and preselection revisited. Urbana 51:61801
Mahfoud SW (1994) Crossover interactions among niches. In: International conference on evolutionary computation, pp 188–193
Mengshoel OJ, Goldberg DE (1999) Probabilistic crowding: deterministic crowding with probabilistic replacement. In: Proceedings of the genetic and evolutionary computation conference (GECCO-99), pp 409–416
Otani T, Suzuki R, Arita T (2011) DE/isolated/1: a new mutation operator for multimodal optimization with differential evolution. In: AI 2011: advances in artificial intelligence. Springer, pp 321–330
Parrott D, Li X (2006) Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Trans Evolut Comput 10:440–458
Pétrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: International conference on evolutionary computation, pp 798–803
Price K, Storn RM, Lampinen JA (2006) Differential evolution: a practical approach to global optimization. Springer Science & Business Media, Berlin
Qu BY, Suganthan PN (2010) Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection. Inf Sci 180:3170–3181
Qu BY, Gouthanan P, Suganthan PN (2010) Dynamic grouping crowding differential evolution with ensemble of parameters for multi-modal optimization. In: Swarm, evolutionary, and memetic computing. Springer, pp 19–28
Shir OM, Bäck T (2006) Niche radius adaptation in the cma-es niching algorithm. In: Parallel problem solving from nature-PPSN IX. Springer, pp 142–151
Wang H, Moon I, Yang S, Wang D (2012) A memetic particle swarm optimization algorithm for multimodal optimization problems. Inf Sci 197:38–52
Yang XS (2010a) Nature-inspired metaheuristic algorithms. Luniver Press, UK
Yang XS (2010b) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-Inspir Comput 2:78–84
Yang XS (2011a) Metaheuristic optimization: algorithm analysis and open problems. In: Experimental algorithms. Springer, Berlin, pp 21–32
Yang XS (2011b) Review of meta-heuristics and generalised evolutionary walk algorithm. Int J Bio-Inspir Comput 3:77–84
Yang XS (2013) Multiobjective firefly algorithm for continuous optimization. Eng Comput 29:175–184
Yang X (2014) Chapter 8-firefly algorithms. Elsevier, Oxford, pp 111–127
Yang XS, Gandomi AH, Talatahari S, Alavi AH (2012) Metaheuristics in water, geotechnical and transport engineering. Newnes
Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evolut Comput 14:1–14
Yin X, Germay N (1993) A fast genetic algorithm with sharing scheme using cluster analysis methods in multimodal function optimization. In: Neural nets and genetic algorithms, Proceedings of the International Conference in Innsbruck, Austria, pp 450–457
Zaman MA, Sikder U (2015) Bouc–Wen hysteresis model identification using modified firefly algorithm. J Magn Magn Mater 395:229–233
Zhang Y, Wu L, Wang S (2013) Solving two-dimensional HP model by firefly algorithm and simplified energy function. Math Probl Eng 2013: 9
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nekouie, N., Yaghoobi, M. A new method in multimodal optimization based on firefly algorithm. Artif Intell Rev 46, 267–287 (2016). https://doi.org/10.1007/s10462-016-9463-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-016-9463-0