Skip to main content

Advertisement

SpringerLink
Log in

An investigation on niching multiple species based on population replacement strategies for multimodal functions optimization

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

This paper studies the niching mechanism based on population replacement in the process of evolution to solve the multimodal functions optimization (MMFO) problems. In order to niche multiple species for the MMFO tasks, the overlapping population replacement is surely needed because the offspring population most probably does not inherit all of the genetic information contained in its parental population, and the basic procedure for niching genetic algorithms with overlapping population replacement is presented. Then four niching schemes, the nearest neighbors replacement crowding (NNRC), the species conservation technique (SCT), the HFC-I (implicit hierarchical fair competition), and the CPE (clearing procedure with elitist) are investigated. These niching schemes are characterized with regard to different niching strategies and parameterizations, and the corresponding niching procedures are outlined. Finally, experiments are carried out on a suite of test functions to compare different niching strategies regarding niching efficiency and scalability. Experimental results illustrate the intrinsic difference of the four niching schemes. The NNRC and HFC-I have a mechanism of multiple species coevolution via adapting multiple species to different niches, while the SCT and CPE tend to make use of a mandatory mechanism to conserve species just like the grid searching over the solution space based on species distance or clearing radius. All niching methods are able to deal with complex MMFO problems, while the NNRC and HFC-I show a better performance in terms of niching efficiency and scalability, and are more robust regarding the algorithm parameterization.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Notes

  1. The niching convergence and equilibrium is measured by population entropy. First, the real-valued variables are discretized into 32 intervals or \( 32 \times 32 \) grids in the 1-d or 2-d definition domain of a function. Second, the population entropy is computed by \( E_{\text{pop}} = - \sum\nolimits_{i = 0}^{K - 1} {\sum\nolimits_{j = 0}^{K - 1} {p_{ij} \log p_{ij} } } , \) where \( p_{ij} \) is the approximate proportion of individuals in the \( i \times j \) grid, \( i,j = 1,2, \ldots ,K,\;K = 31. \) If the relative decrease rate of the population entropy (smoothed for algorithms with fitness proportional selection) per 1000 fitness evaluations was smaller than the threshold (5%), the algorithm is taken as reaching niching convergence and equilibrium.

References

  • Bäck T, Fogel DB, Michalewicz Z (2000) Evolutionary Computation. Institute of Physics Publishing, Bristol and Philadelphia

    Google Scholar 

  • Ballester P, Carter J (2003) Real-parameter genetic algorithms for finding multiple optimal solutions in multi-modal optimization. In: Erick Cantú-Paz et al (eds) Proceedings of the 2003 genetic and evolutionary computation conference (GECCO 2003), Lecture Notes in Computer Science 2, Springer, Berlin, pp 706–717

  • Beasley D, Bull DR, Martin RR (1993) A sequential niche technique for multimodal function optimization. Evolut Comput 1(2):10–125

    Article  Google Scholar 

  • Beyer H-G (2001) The theory of evolution strategies. Springer, Berlin

    Google Scholar 

  • Cedeño W, Vemuri V (1999) Analysis of speciation and niching in multi-niche crowding genetic algorithms. Theor Comput Sci 229(1–2):177–197

    Article  MATH  Google Scholar 

  • Cioppa AD, De Stefano C, Marcelli A (2004) On the role of population size and niche radius in fitness sharing. IEEE Trans Evolut Comput 8(6):580–592

    Article  Google Scholar 

  • De Jong KA (1975) An Analysis of The Behavior of A Class of Genetic Adaptive Systems. Dissertation, University of Michigan, Ann Arbor. (University Microfilms No. 76-9381)

  • Eiben AE, Smith JE (2003) Introduction to Evolutionary Computing. Springer, Berlin

    MATH  Google Scholar 

  • Eshelman LJ, Shaffer JD (1993) Real coded genetic algorithms and interval schemata. In: Whitley LD (ed) Foundations of genetic algorithms II. Morgan Kaufmann, San Mateo, pp 187–202

    Google Scholar 

  • Gan J, Warwick K (2001) Dynamic niche clustering: a fuzzy variable radius niching technique for multimodal optimization in GAs. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), vol 1. 27–30 May 2001, pp 215–222

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley Publishing Company, New York

    MATH  Google Scholar 

  • Goldberg DE, Richardson JJ (1987) Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the second international conference on genetic algorithms (ICGA 2), pp 41–49

  • Goldberg DE, Deb K, Korb B (1990) Messy genetic algorithms revisited: studies in mixed size and scale. Complex Syst 4(4):415–444

    MATH  Google Scholar 

  • Goldberg DE, Deb K, Horn J (1992) Massive multimodality, deception, and genetic algorithms. Parallel Problem Solving from Nature, 2, pp 37–46. (Also IlliGAL Report No. 92007)

  • Gudla PK, Ganguli R (2005) An automated hybrid genetic-conjugate gradient algorithm for multimodal optimization problems. Applied Mathematics and Computation 167(2):1457–1474

    Article  MATH  MathSciNet  Google Scholar 

  • Harik GR (1995) Finding multimodal solutions using restricted tournament selection. In: Proceedings of the sixth international conference on genetic algorithms (ICGA 6), pp 24–31 (Also IlliGAL Report No. 94002)

  • Herrera F, Lozano M, Sànchez AM (2003) A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study. Int J Intell Syst 18(3):309–338

    Article  MATH  Google Scholar 

  • Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 2nd edn. MIT Press, Cambridge

    Google Scholar 

  • Horn J (1997) The Nature of niching: genetic algorithms and the evolution of optimal, cooperative populations. Dissertation, University of Illinois at Urbana-Champaign, Urbana, IL61801. (Also IlliGAL Report No. 97008)

  • Hu J, Goodman E (2004) Robust and efficient genetic algorithms with hierarchical niching and sustainable evolutionary computation model. In: Deb K et al (eds) Proceedings of genetic and evolutionary computation conference (GECCO 2004), Seattle, Washington, USA, June 2004; Part 1, Lecture Notes in Computer Science, vol 3,102, Springer, Berlin, pp 1220–1232

  • Hu J, Goodman ED, Seo K, Fan Z, Rosenberg R (2005) The hierarchical fair competition (HFC) framework for sustainable evolutionary algorithms. Evolut Comput 13(2):241–277

    Article  Google Scholar 

  • Iwamatsu M (2006) Multi-species particle swarm optimizer for multimodal function optimization. IEICE Trans Inf Syst E89-D(3):1181–1187

    Article  Google Scholar 

  • Jelasity M, Ortigosa PM, Garcia I (2001) UEGO, an abstract clustering technique for multimodal global optimization. J Heuristics 7(3):215–233

    Article  MATH  MathSciNet  Google Scholar 

  • Lee C-G, Cho D-H, Jung H-K (1999) Niching genetic algorithm with restricted competition selection for multimodal function optimization. IEEE Transactions on Magnetics 35(3), Part 1, pp 1722–1725

    Google Scholar 

  • Li M, Kou J (2005) A novel type of niching methods based on steady-state genetic algorithm. In: Wang L, Chen K, Ong YS (eds) Advances in natural computation: first international conference (ICNC 2005), lecture notes in computer science, vol 3612/2005, Springer, Berlin, pp 37–47

  • Li M, Kou J (2008) Crowding with nearest neighbors replacement for multiple species niching and building blocks preservation in binary multimodal functions optimization. J Heuristics 14(3):243–270

    Article  MATH  Google Scholar 

  • Li J-P, Balazs ME, Parks GT, Clarkson PJ (2002) A species conserving genetic algorithm for multimodal function optimization. Evolut Comput 10(3):207–234

    Article  Google Scholar 

  • Lin C-Y, Yang Y-J (1998) Cluster identification techniques in genetic algorithms for multimodal optimization. Comput Aided Civil Infrastruct Eng 13(1):53–62(10)

    Google Scholar 

  • Mahfoud SW (1995) Niching methods for genetic algorithms. Dissertation, University of Illinois at Urbana-Champaign, Urbana, IL61801 (Also IlliGAL Report No. 95001)

  • Pelikan M, Goldberg DE (2000) Genetic algorithms, clustering, and the breaking of symmetry. In: Proceedings of parallel problem solving from Nature VI, Springer, Berlin, pp 385–394 (Also IlliGAL Report No. 2000013)

  • Peña JM, Lozano JA, Larrañaga P (2005) Globally multimodal problem optimization via an estimation of distribution algorithm based on unsupervised learning of Bayesian networks. Evolut Comput 13(1):43–66

    Article  Google Scholar 

  • Pétrowski A (1996) A clearing procedure as a niching method for genetic algorithms. In: Proceedings of the IEEE international conference evolutionary computation, Nagoya, Japan, pp 798–803

  • Reeves CR, Rowe JE (2003) Genetic algorithms: principles and perspectives—a guide to GA theory. Kluwer Academic Publishers, Boston

    Google Scholar 

  • Sareni B, Krähenbühl L (1998) Fitness sharing and niching methods revisited. IEEE Trans Evolut Comput 2(3):97–106

    Article  Google Scholar 

  • Siarry P, Pétrowski A, Bessaou M (2000) Island model cooperating with speciation for multimodal optimization. In: Schoenauer M et al (eds) Proceedings of 6th international conference on parallel problem solving from nature (PPSN-VI}), parallel problem solving from nature, Paris, France. Springer, Berlin, pp 437–446

  • Siarry P, Pétrowski A, Bessaou M (2002) A multipopulation genetic algorithm aimed at multimodal optimization. Adv Eng Softw 33(4):207–213

    Article  MATH  Google Scholar 

  • Van Hoyweghen C, Naudts B, Goldberg DE (2002) Spin-flip symmetry and synchronization. Evolut Comput 10(4):317–344

    Article  Google Scholar 

  • Yin X, Germany N (1993) A fast algorithm with sharing scheme using cluster analysis methods in multimodal function optimization. In: Albrecht RF, Reeves CR, Steel NC (eds) Proceedings of the international conference on artificial neural nets and genetic algorithms. Springer, Berlin, pp 450–457

  • Yuan B, Gallagher M (2003) On building a principled framework for evaluating and testing evolutionary algorithms: a continuous landscape generator. In: Sarkar R et al (ed) Proceedings of the 2003 congress on evolutionary computation (CEC 2003), vol 1, 8–12 Dec 2003, pp 451–458

Download references

Acknowledgments

The work was supported by the National Science Foundation of China (Grant No. 70571057) and by the Program for New Century Excellent Talents in Universities of China (NCET-05-0253). The authors are very grateful to the two anonymous reviewers whose invaluable comments and suggestions substantially helped improve the quality of the paper.

Author information

Authors and Affiliations

  1. School of Management, Tianjin University, 300072, Tianjin, People’s Republic of China

    Minqiang Li, Dan Lin & Jisong Kou

Authors
  1. Minqiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dan Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jisong Kou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Minqiang Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, M., Lin, D. & Kou, J. An investigation on niching multiple species based on population replacement strategies for multimodal functions optimization. Soft Comput 14, 49–69 (2010). https://doi.org/10.1007/s00500-008-0389-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-008-0389-6

Keywords

Search

Navigation