Natural Computing

, Volume 8, Issue 1, pp 171–196 | Cite as

Niching with derandomized evolution strategies in artificial and real-world landscapes

  • Ofer M. Shir
  • Thomas Bäck


We introduce a framework of derandomized evolution strategies (ES) niching techniques. A survey of these techniques, based on 5 variants of derandomized ES, is presented, based on the fixed niche radius approach. The core mechanisms range from the very first derandomized approach to self-adaptation of ES to the sophisticated Open image in new window Covariance Matrix Adaptation (CMA). They are applied to artificial as well as real-world multimodal continuous landscapes, of different levels of difficulty and various dimensions, and compared with the maximum-peak-ratio (MPR) performance analysis tool. While characterizing the performance of the different derandomized variants in the context of niching, some conclusions concerning the niching formation process of the different mechanisms are drawn, and the hypothesis of a trade-off between learning time and niching acceleration is numerically confirmed. Niching with (1 + λ)-CMA core mechanism is shown to experimentally outperform all the other variants, especially on the real-world problem. Some theoretical arguments supporting the advantage of a plus-strategy for niching are discussed. For the real-world application in hand, taken from the field of Quantum Control, we show that the niching framework can overcome some degeneracy in the search space, and obtain different conceptual designs using problem-specific diversity measurements.


Niching Derandomized evolution strategies CMA Quantum control Laser pulse shaping 



The authors would like to thank Christian Siedschlag and Marc Vrakking, of Amolf-FOM Amsterdam, for the collaboration on the laser problem, and Michael Emmerich, of Leiden University, for the fruitful discussions on niching.

This work is part of the research programme of the ‘Stichting voor Fundamenteel Onderzoek de Materie (FOM)’, which is financially supported by the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)’.


  1. Avigad G, Moshaiov A, Brauner N (2004) Concept-based interactive brainstorming in engineering design. J Adv Comput Intell Intell Inform 8(5):454–459Google Scholar
  2. Bäck T (1994) Selective pressure in evolutionary algorithms: A characterization of selection mechanisms. In: Michalewicz Z, Schaffer JD, Schwefel HP, Fogel DB, Kitano H (eds) Proceedings of the first IEEE conference evolutionary computation (ICEC’94), Orlando FL, vol 1. IEEE Press, Piscataway, NJ, USA, pp 57–62Google Scholar
  3. Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, New York, NY, USAzbMATHGoogle Scholar
  4. Beyer HG, Schwefel HP (2002) Evolution strategies a comprehensive introduction. Nat Comput Int J 1(1):3–52CrossRefMathSciNetGoogle Scholar
  5. Deb K, Goldberg DE (1989) An investigation of niche and species formation in genetic function optimization. In: Proceedings of the third international conference on genetic algorithms, Morgan Kaufmann Publishers Inc., San Francisco, CA, USAGoogle Scholar
  6. Demiralp M, Rabitz H (1993) Optimally controlled quantum molecular dynamics: a perturbation formulation and the existence of multiple solutions. Phys Rev A 47(2):809–816CrossRefGoogle Scholar
  7. Goldberg DE, Richardson J (1987) Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the second international conference on genetic algorithms on genetic algorithms and their application. Lawrence Erlbaum Associates Inc, Mahwah, NJ, USA, pp 41–49Google Scholar
  8. Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195CrossRefGoogle Scholar
  9. Hansen N, Ostermeier A, Gawelczyk A (1995) On the adaptation of arbitrary normal mutation distributions in evolution strategies: the generating set adaptation. In: Proceedings of the sixth international conference on genetic algorithms (ICGA6)Google Scholar
  10. Igel C, Suttorp T, Hansen N (2006) A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2005), ACM Press, pp 453–460Google Scholar
  11. Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15(1):1–28CrossRefGoogle Scholar
  12. Kimura M (1983) The neutral theory of molecular evolution. Cambridge University Press, CambridgeGoogle Scholar
  13. Kramer O, Schwefel HP (2006) On three new approaches to handle constraints within evolution strategies. Nat Comput Int J 5(4):363–385CrossRefMathSciNetGoogle Scholar
  14. Mahfoud S (1995) Niching methods for genetic algorithms. PhD thesis, University of Illinois at Urbana, ChampaignGoogle Scholar
  15. Miller B, Shaw M (1996) Genetic algorithms with dynamic niche sharing for multimodal function optimization. In: Proceedings of the 1996 IEEE international conference on evolutionary computation (ICEC’96), New York, NY, USAGoogle Scholar
  16. Nuernberger P, Vogt G, Brixner T, Gerber G (2007) Femtosecond quantum control of molecular dynamics in the condensed phase. Phys Chem Chem Phys 9(20):2470–2497CrossRefGoogle Scholar
  17. Ostermeier A, Gawelczyk A, Hansen N (1993) A derandomized approach to self adaptation of evolution strategies. Technical report, TU, BerlinGoogle Scholar
  18. Ostermeier A, Gawelczyk A, Hansen N (1994) Step-size adaptation based on non-local use of selection information. In: PPSN. Volume 866 of lecture notes in computer science, SpringerGoogle Scholar
  19. Rabitz H, de Vivie-Riedle R, Mutzkus M, Kompa K (2000) Whither the future of controlling quantum phenomena? Science 288:824–828CrossRefGoogle Scholar
  20. Rosca-Pruna F, Vrakking M (2002) Revival structures in picosecond laser-induced alignment of i2 molecules. J Chem Phys 116(15):6579–6588CrossRefGoogle Scholar
  21. Schönemann L, Emmerich M, Preuss M (2004) On the extiction of sub-populations on multimodal landscapes. In: Proceedings of the international conference on Bioinspired optimization methods and their applications, BIOMA 2004, Jožef Stefan Institute, Slovenia, pp 31–40Google Scholar
  22. Shir OM, Bäck T (2005a) Dynamic niching in evolution strategies with covariance matrix adaptation. In: Proceedings of the 2005 congress on evolutionary computation CEC-2005, IEEE Press, Piscataway, NJ, USAGoogle Scholar
  23. Shir OM, Bäck T (2005b) Niching in evolution strategies. Technical report, Technical Report TR-2005-01, LIACS, Leiden UniversityGoogle Scholar
  24. Shir OM, Bäck T (2006) Niche radius adaptation in the CMA-ES niching algorithm. In: Parallel problem solving from nature—PPSN IX, 9th international conference, Reykjavik, Iceland, September 9–13, 2006, Proceedings. Volume 4193 of lecture notes in computer science, Springer, pp 142–151Google Scholar
  25. Shir OM, Kok JN, Vrakking MJ, Bäck T (2007) Gaining insight into laser pulse shaping by evolution strategies. In: IWINAC. Volume 4527 of lecture notes in computer science, SpringerGoogle Scholar
  26. Siedschlag C, Shir OM, Bäck T, Vrakking MJJ (2006) Evolutionary algorithms in the optimization of dynamic molecular alignment. Opt Commun 264:511–518CrossRefGoogle Scholar
  27. Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the cec 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, SingaporeGoogle Scholar
  28. Törn A, Zilinskas A (1987) Global optimization, vol 350. SpringerGoogle Scholar
  29. Warren WS, Rabitz HA, Dahleh M (1993) Coherent control of quantum dynamics: the dream is alive. Science 259:1581–1589CrossRefMathSciNetGoogle Scholar
  30. Weinacht TC, Bucksbaum PH (2002) Using feedback for coherent control of quantum systems. J Opt B 4:R35–R52Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Natural Computing GroupLeiden UniversityLeidenThe Netherlands
  2. 2.NuTech SolutionsDortmundGermany

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