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Evolution Strategies

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Handbook of Heuristics

Abstract

Evolution strategies are classical variants of evolutionary algorithms which are frequently used to heuristically solve optimization problems, in particular in continuous domains. In this chapter, a description of classical and contemporary evolution strategies will be provided. The review includes remarks on the history of evolution strategies and how they relate to other evolutionary algorithms. Furthermore, developments of evolution strategies for nonstandard problems and search spaces will also be summarized, including multimodal, multi-criterion, and mixed-integer optimization. Finally, selected variants of evolution strategies are compared on a representative set of continuous benchmark functions, revealing strength and weaknesses of the different variants.

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References

  1. Akimoto Y, Sakuma J, Ono I, Kobayashi S (2008) Functionally specialized CMA-ES: a modification of CMA-ES based on the specialization of the functions of covariance matrix adaptation and step size adaptation. In: GECCO’08: proceedings of the 10th annual conference on genetic and evolutionary computation, New York. ACM, pp 479–486

    Google Scholar 

  2. Arnold DV (2002) Noisy optimization with evolution strategies, vol 8. Springer, Boston

    Google Scholar 

  3. Auger A, Brockhoff D, Hansen N (2011) Mirrored sampling in evolution strategies with weighted recombination. In: Proceedings of the 13th annual conference on genetic and evolutionary computation, GECCO’11, New York. ACM, pp 861–868

    Google Scholar 

  4. Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: Proceedings of the 2005 congress on evolutionary computation CEC-2005, Piscataway. IEEE Press, pp 1769–1776

    Google Scholar 

  5. Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, Oxford

    Google Scholar 

  6. Bäck T, Emmerich M, Shir OM (2008) Evolutionary algorithms for real world applications [application notes]. IEEE Comput Intell Mag 3(1):64–67

    Google Scholar 

  7. Bäck T, Hammel U, Schwefel H-P (1997) Evolutionary computation: comments on the history and current state. IEEE Trans Evol Comput 1(1):3–17

    Google Scholar 

  8. Bäck T, Schütz M (1995) Evolution strategies for mixed integer optimization of optical multilayer systems. In: Evolutionary programming IV – proceeding of fourth annual conference on evolutionary programming. MIT Press, pp 33–51

    Google Scholar 

  9. Bartz-Beielstein T (2005) Evolution strategies and threshold selection. In: Hybrid metaheuristics. Springer, pp 104–115

    Google Scholar 

  10. Ben-Tal A, El Ghaoui L, Nemirovski A (2009) Robust optimization. Princeton series in applied mathematics. Princeton University Press, Princeton

    Google Scholar 

  11. Beyer H-G (1999) On the dynamics of EAs without selection. Found Genet Algorithms 5:5–26

    Google Scholar 

  12. Beyer H-G (2000) Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice. Comput Methods Appl Mech Eng 186(2):239–267

    Google Scholar 

  13. Beyer H-G (2001) The Theory of Evolution Strategies. Springer, Berlin

    Google Scholar 

  14. Beyer H-G, Schwefel H-P (2002) Evolution strategies–a comprehensive introduction. Nat Comput 1(1):3–52

    Google Scholar 

  15. Beyer H-G, Sendhoff B (2008) Covariance matrix adaptation revisited – the CMSA evolution strategy. In: Parallel problem solving from nature – PPSN X. Lecture notes in computer science, vol 5199. Springer, Berlin, pp 123–132

    Google Scholar 

  16. Brockhoff D, Auger A, Hansen N, Arnold DV, Hohm T (2010) Mirrored sampling and sequential selection for evolution strategies. In: Schaefer R, Cotta C, Kolodziej J, Rudolph G (eds) Proceedings of the 11th international conference on Parallel problem solving from nature: part I, PPSN’10. Springer, Berlin, pp 11–21

    Google Scholar 

  17. Droste S, Wiesmann D (2003) On the design of problem-specific evolutionary algorithms. In: Advances in evolutionary computing. Springer, Berlin, pp 153–173

    Google Scholar 

  18. Emmerich M, Grötzner M, Schütz M (2001) Design of graph-based evolutionary algorithms: a case study for chemical process networks. Evol Comput 9(3):329–354

    Google Scholar 

  19. Finck S, Hansen N, Ros R, Auger A (2010) Real-parameter black-box optimization benchmarking 2010: presentation of the noisy functions. Technical report 2009/21, Research Center PPE

    Google Scholar 

  20. Fogel LJ (1999) Intelligence through simulated evolution: forty years of evolutionary programming. Wiley, New York

    Google Scholar 

  21. Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison Wesley, Reading

    Google Scholar 

  22. Grimme C, Schmitt K (2006) Inside a predator-prey model for multi-objective optimization: a second study. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM, pp 707–714

    Google Scholar 

  23. Hansen N (2016) The CMA evolution strategy: a tutorial. arXiv preprint, arXiv:1604.00772. 4 Apr 2016

    Google Scholar 

  24. Hansen N, Arnold DV, Auger A (2015) Evolution strategies. Springer, Berlin/Heidelberg, pp 871–898

    Google Scholar 

  25. Hansen N, Auger A, Finck S, Ros R (2010) Real-parameter black-box optimization benchmarking 2010: experimental setup. Technical report RR-7215, INRIA

    Google Scholar 

  26. Hansen N, Kern S (1998) Evaluating the CMA evolution strategy on multimodal test functions. In: Parallel problem solving from nature – PPSN V. Lecture notes in computer science, vol 1498. Springer, Amsterdam, pp 282–291

    Google Scholar 

  27. Hansen N, Niederberger S, Guzzella L, Koumoutsakos P (2009) A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion. IEEE Trans Evol Comput 13(1):180–197

    Google Scholar 

  28. Hansen N, Ostermeier A (1996) Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation. In: Proceedings of the 1996 IEEE international conference on evolutionary computation, Piscataway. IEEE, pp 312–317

    Google Scholar 

  29. Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195

    Google Scholar 

  30. 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), San Francisco. Morgan Kaufmann, pp 57–64

    Google Scholar 

  31. Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15(1):1–28

    Google Scholar 

  32. Jablonka E, Lamb MJ (2005) Evolution in four dimensions. MIT Press, Cumberland

    Google Scholar 

  33. Jägersküpper J (2007) Algorithmic analysis of a basic evolutionary algorithm for continuous optimization. Theor Comput Sci 379(3):329–347

    Google Scholar 

  34. John H (1992) Holland, adaptation in natural and artificial systems. MIT Press, Cambridge

    Google Scholar 

  35. Jolliffe I (2002) Principal component analysis2nd edn. Springer, New York

    Google Scholar 

  36. Klinkenberg J-W, Emmerich MT, Deutz AH, Shir OM, Bäck T (2010) A reduced-cost SMS-EMOA using kriging, self-adaptation, and parallelization. In: Multiple criteria decision making for sustainable energy and transportation systems. Springer, Berlin/Heidelberg, pp 301–311

    Google Scholar 

  37. Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto archived evolution strategy. Evol Comput 8(2):149–172

    Google Scholar 

  38. Kramer O, Schwefel H-P (2006) On three new approaches to handle constraints within evolution strategies. Nat Comput 5(4):363–385

    Google Scholar 

  39. Kruisselbrink J (2012) Evolution strategies for robust optimization. PhD thesis, Leiden University, Leiden

    Google Scholar 

  40. Kursawe F (1991) A variant of evolution strategies for vector optimization. In: Parallel problem solving from nature. Springer, Berlin/Heidelberg, pp 193–197

    Google Scholar 

  41. Laumanns M, Rudolph G, Schwefel H-P (1998) A spatial predator-prey approach to multi-objective optimization: a preliminary study. In: Parallel problem solving from nature – PPSN V. Springer, Berlin/Heidelberg, pp 241–249

    Google Scholar 

  42. Li R (2009) Mixed-integer evolution strategies for parameter optimization and their applications to medical image analysis. PhD thesis, Leiden University, Leiden

    Google Scholar 

  43. Li R, Emmerich MT, Eggermont J, Bäck T, Schütz M, Dijkstra J, Reiber JH (2013) Mixed integer evolution strategies for parameter optimization. Evol Comput 21(1): 29–64

    Google Scholar 

  44. Mahfoud S (1995) Niching methods for genetic algorithms. PhD thesis, University of Illinois at Urbana Champaign

    Google Scholar 

  45. Meyer-Nieberg S, Beyer H-G (2007) Self-adaptation in evolutionary algorithms. In: Parameter setting in evolutionary algorithms. Springer, Berlin, pp 47–75

    Google Scholar 

  46. Ostermeier A, Gawelczyk A, Hansen N (1993) A derandomized approach to self adaptation of evolution strategies. Technical report TR-93-003, TU Berlin

    Google Scholar 

  47. Ostermeier A, Gawelczyk A, Hansen N (1994) A derandomized approach to self adaptation of evolution strategies. Evol Comput 2(4):369–380

    Google Scholar 

  48. Ostermeier A, Gawelczyk A, Hansen N (1994) Step-size adaptation based on non-local use of selection information. In: Parallel problem solving from nature – PPSN III. Lecture notes in computer science, vol 866. Springer, Berlin/Heidelberg, pp 189–198

    Google Scholar 

  49. Preuss M (2015) Multimodal optimization by means of evolutionary algorithms. Natural computing series. Springer International Publishing, Cham

    Google Scholar 

  50. Rechenberg I (1973) Evolutionsstrategie: optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Friedrich Frommann Verlag, Stuttgart-Bad Cannstatt

    Google Scholar 

  51. Ros R, Hansen N (2008) A simple modification in CMA-ES achieving linear time and space complexity. In: Parallel problem solving from nature – PPSN X. Lecture notes in computer science, vol 5199. Springer, Berlin/Heidelberg, pp 296–305

    Google Scholar 

  52. Rudolph G (1992) On correlated mutations in evolution strategies. In: Parallel problem solving from nature – PPSN II. Elsevier, Amsterdam, pp 105–114

    Google Scholar 

  53. Rudolph G (1994) An evolutionary algorithm for integer programming. In: Parallel problem solving from nature – PPSN III. Springer, Berlin/Heidelberg, pp 139–148

    Google Scholar 

  54. Rudolph G (1997) Convergence properties of evolutionary algorithms. Kovac, Hamburg

    Google Scholar 

  55. Schönemann L, Emmerich M, Preuß M (2004) On the extinction of evolutionary algorithm subpopulations on multimodal landscapes. Informatica (Slovenia) 28(4):345–351

    Google Scholar 

  56. Schumer M, Steiglitz K (1968) Adaptive step size random search. IEEE Trans Autom Control 13(3):270–276

    Article  Google Scholar 

  57. Schwefel H-P (1965) Kybernetische Evolution als Strategie der experimentellen Forschung in der Strömungstechnik. Technische Universität, Berlin

    Google Scholar 

  58. Schwefel H-P (1987) Collective phenomena in evolutionary systems. In: Checkland P, Kiss I (eds) Problems of constancy and change – the complementarity of systems approaches to complexity, proceeding of 31st annual meeting, Budapest, vol 2. International Society for General System Research, pp 1025–1033

    Google Scholar 

  59. Schwefel H-PP (1993) Evolution and optimum seeking: the sixth generation. Wiley, New York

    Google Scholar 

  60. Shir OM (2008) Niching in derandomized evolution strategies and its applications in quantum control. PhD thesis, Leiden University, Leiden

    Google Scholar 

  61. Shir OM, Bäck T (2009) Niching with derandomized evolution strategies in artificial and real-world landscapes. Nat Comput Int J 8(1):171–196

    Article  MathSciNet  Google Scholar 

  62. Shir OM, Emmerich M, Bäck T (2010) Adaptive niche-radii and niche-shapes approaches for niching with the CMA-ES. Evol Comput 18(1):97–126

    Article  Google Scholar 

  63. Shir OM, Roslund J, Whitley D, Rabitz H (2014) Efficient retrieval of landscape hessian: forced optimal covariance adaptive learning. Phys Rev E 89(6):063306

    Article  Google Scholar 

  64. Shir OM, Yehudayoff A (2017) On the statistical learning ability of evolution strategies. In: Proceedings of the 14th ACM/SIGEVO conference on foundations of genetic algorithms, FOGA-2017. ACM Press, New York, pp 127–138

    Chapter  Google Scholar 

  65. Teytaud O (2011) Lower bounds for evolution strategies. Theory Random Search Heuristics 1:327–354

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Leiden, Netherlands

    Michael Emmerich

  2. Computer Science Department, Tel-Hai College, Upper Galilee, Kiryat Shmona, Israel

    Ofer M. Shir

  3. MIGAL Galilee Research Institute, Upper Galilee, Kiryat Shmona, Israel

    Ofer M. Shir

  4. Leiden Institute of Advanced Computer Science, Leiden University, Leiden, Netherlands

    Hao Wang

Authors
  1. Michael Emmerich
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  2. Ofer M. Shir
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  3. Hao Wang
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Corresponding author

Correspondence to Michael Emmerich .

Editor information

Editors and Affiliations

  1. Statistics and Operations Research Department, University of Valencia, Valencia, Spain

    Rafael Martí

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  3. Amazon.com, Inc. and University of Washington, Seattle, Washington, USA

    Mauricio G. C. Resende

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Emmerich, M., Shir, O.M., Wang, H. (2018). Evolution Strategies. In: Martí, R., Pardalos, P., Resende, M. (eds) Handbook of Heuristics. Springer, Cham. https://doi.org/10.1007/978-3-319-07124-4_13

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