Niching is the technique of finding and preserving multiple stable niches, or favorable parts of the solution space possibly around multiple optima, for the purpose of solving multimodal optimization problems. Chaos optimization algorithm (COA) is one of the global optimization techniques, but as far as we know, a niching variant of COA has not been developed . In this paper, a novel niching chaos optimization algorithm (NCOA) is proposed. The circle map with a proper parameter setting is employed considering the fact that the performance of COA is affected by the chaotic map. In order to achieve niching, NCOA utilizes several techniques including simultaneously contracted multiple search scopes, deterministic crowding and clearing. The effects of some components and parameters of NCOA are investigated through numerical experiments. Comparison with other state-of-the-art multimodal optimization algorithms demonstrates the competitiveness of the proposed NCOA.
This is a preview of subscription content, log in to check access
This work was supported by the National Natural Science Foundation of China (No. 61375081) and the special fund project of Harbin science and technology innovation talents research (No. RC2013XK010002).
Compliance with ethical standards
Conflicts of interest
The authors declares that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
Supplementary material 1 (mp4 8254 KB)
Chen J, Xin B, Peng ZH, Dou LH, Zhang J (2009) Optimal contraction theorem for exploration-exploitation tradeoff in search and optimization. IEEE Trans Syst Man Cybern Part A Syst Hum 39(3):680–691CrossRefGoogle Scholar
Chen JY, Lin QZ, Ji Z (2011) Chaos-based multi-objective immune algorithm with a fine-grained selection mechanism. Soft Comput 15(7):1273–1288CrossRefGoogle Scholar
Devaney RL (2003) An introduction to chaotic dynamical systems, 2nd edn. Westview Press, ColoradoMATHGoogle Scholar
Li JP, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evol Comput 10(3):207–234CrossRefGoogle Scholar
Li X (2007) A multimodal particle swarm optimizer based on fitness euclidean-distance ratio. In: GECCO 2007—Genetic and Evolutionary Computation Conference, London, England, vol 1, pp 78–85Google Scholar
Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14(1):150–169CrossRefGoogle Scholar
Liang JJ, Qu BY, Mao XB, Niu B, Wang DY (2014) Differential evolution based on fitness euclidean-distance ratio for multimodal optimization. Neurocomputing 137:252–260CrossRefGoogle Scholar
Miller BL, Shaw MJ (1996) Genetic algorithms with dynamic niche sharing for multimodal function optimization. In: ICEC 96–Proceedings of 1996 IEEE international conference on evolutionary computation. Nagoya, Japan, pp 786–791Google Scholar
Parrott D, Li XD (2006) Locating and tracking multiple dynamic optima by a particle swarm model using speciation. IEEE Trans Evol Comput 10(4):440–458CrossRefGoogle Scholar
Pétrowski A (1996) Clearing procedure as a niching method for genetic algorithms. In: ICEC 96–Proceedings of 1996 IEEE international conference on evolutionary computation. Nagoya, Japan, pp 798–803Google Scholar
Qu BY, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inf Sci 197:131–143CrossRefGoogle Scholar
Qu BY, Suganthan PN, Das S (2013) A distance-based locally informed particle swarm model for multimodal optimization. IEEE Trans Evol Comput 17(3):387–402CrossRefGoogle Scholar
Sareni B, Krähenbühl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2(3):97–106CrossRefGoogle Scholar
Sheng WG, Tucker A, Liu XH (2010) A niching genetic \(k\)-means algorithm and its applications to gene expression data. Soft Comput 14(1):9–19CrossRefGoogle Scholar
Stoean C, Preuss M, Stoean R, Dumitrescu D (2010) Multimodal optimization by means of a topological species conservation algorithm. IEEE Trans Evol Comput 14(6):842–864CrossRefGoogle Scholar
Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076–1085MathSciNetMATHGoogle Scholar
Yang DX, Li G, Cheng GD (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34:1366–1375MathSciNetCrossRefGoogle Scholar
Yang YM, Wang YN, Yuan XF, Yin F (2012) Hybrid chaos optimization algorithm with artificial emotion. Appl Math Comput 218(11):6585–6611MATHGoogle Scholar
Yang DX, Liu ZJ, Zhou JL (2014) Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization. Commun Nonlinear Sci Numer Simul 19(4):1229–1246MathSciNetCrossRefGoogle Scholar
Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14CrossRefGoogle Scholar