Soft Computing

, Volume 22, Issue 2, pp 621–633 | Cite as

A niching chaos optimization algorithm for multimodal optimization

  • Cholmin Rim
  • Songhao PiaoEmail author
  • Guo Li
  • Unsun Pak
Methodologies and Application


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.


Multimodal optimization Chaos optimization algorithm (COA) Evolutionary algorithms (EAs) Niching method 

Mathematics Subject Classification

65K05 68T20 90C59 



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.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Supplementary material

Supplementary material 1 (mp4 8254 KB)


  1. 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
  2. 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
  3. Devaney RL (2003) An introduction to chaotic dynamical systems, 2nd edn. Westview Press, ColoradozbMATHGoogle Scholar
  4. Li B, Jiang WS (1998) Optimizing complex function by chaos search. Cybern Syst 29(4):409–419CrossRefzbMATHGoogle Scholar
  5. 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
  6. 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
  7. Li X (2010) Niching without niching parameters: particle swarm optimization using a ring topology. IEEE Trans Evol Comput 14(1):150–169CrossRefGoogle Scholar
  8. 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
  9. May RM (1976) Simple mathematical models with very complicated dynamics. Nature 261:459–467CrossRefzbMATHGoogle Scholar
  10. 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
  11. 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
  12. 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
  13. Qu BY, Liang JJ, Suganthan PN (2012) Niching particle swarm optimization with local search for multi-modal optimization. Inf Sci 197:131–143CrossRefGoogle Scholar
  14. 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
  15. Sareni B, Krähenbühl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evol Comput 2(3):97–106CrossRefGoogle Scholar
  16. 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
  17. 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
  18. Tavazoei MS, Haeri M (2007) Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms. Appl Math Comput 187(2):1076–1085MathSciNetzbMATHGoogle Scholar
  19. Xu ZR, Iizuka H, Yamamoto M (2015) Attraction basin sphere estimation approach for niching CMA-ES. Soft Comput. doi: 10.1007/s00500-015-1865-4 Google Scholar
  20. Yang DX, Li G, Cheng GD (2007) On the efficiency of chaos optimization algorithms for global optimization. Chaos Solitons Fractals 34:1366–1375MathSciNetCrossRefGoogle Scholar
  21. Yang YM, Wang YN, Yuan XF, Yin F (2012) Hybrid chaos optimization algorithm with artificial emotion. Appl Math Comput 218(11):6585–6611zbMATHGoogle Scholar
  22. 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
  23. Yazdani S, Nezamabadi-pour H, Kamyab S (2014) A gravitational search algorithm for multimodal optimization. Swarm Evol Comput 14:1–14CrossRefGoogle Scholar
  24. Yu EL, Suganthan PN (2010) Ensemble of niching algorithms. Inf Sci 180(15):2815–2833MathSciNetCrossRefGoogle Scholar
  25. Yuan XF, Yang YM, Wang H (2012) Improved parallel chaos optimization algorithm. Appl Math Comput 219(8):3590–3599MathSciNetzbMATHGoogle Scholar
  26. Yuan XF, Xiang YZ, He YQ (2014) Parameter extraction of solar cell models using mutative-scale parallel chaos optimization algorithm. Solar Energy 108:238–251CrossRefGoogle Scholar
  27. Yuan XF, Dai XS, Wu LH (2015) A mutative-scale pseudo-parallel chaos optimization algorithm. Soft Comput 19(5):1215–1227CrossRefGoogle Scholar
  28. Zhu Q, Yuan XF, Wang H (2012) An improved chaos optimization algorithm-based parameter identification of synchronous generator. Electr Eng 94:147–153CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyHarbin Institute of TechnologyHarbinPeople’s Republic of China
  2. 2.Department of Electronics and AutomationKim Il Sung UniversityPyongyangDemocratic People’s Republic of Korea

Personalised recommendations