Soft Computing

, Volume 17, Issue 7, pp 1121–1144 | Cite as

Design and analysis of migration in parallel evolutionary algorithms

Focus

Abstract

Parallelization is becoming a more important issue for solving difficult optimization problems. Island models combine phases of independent evolution with migration where genetic information is spread out to neighbored islands. This can lead to an increased diversity within the population. Despite many successful applications, the reasons behind the success of island models are not well understood. We perform a first rigorous runtime analysis for island models and construct a function where phases of independent evolution as well as communication among the islands are essential. A simple island model with migration finds a global optimum in polynomial time, while panmictic populations as well as island models without migration need exponential time, with very high probability. Our results lead to new insights into the usefulness of migration, how information is propagated in island models, and how to set parameters such as the migration interval. This is a novel contribution to the theoretical foundation of parallel EAs. Further, we provide empirical results that complement the theoretical results, investigate the robustness with respect to the choice of the migration interval and compare various migration topologies using statistical tests.

Keywords

Parallel evolutionary algorithms Island model Migration Distributed evolutionary algorithms Spatial structures Multi-deme model Runtime analysis 

References

  1. Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs, and mathematical tables. 9th Dover printing, 10th GPO printing edition. Dover, New YorkGoogle Scholar
  2. Alba E (2002) Parallel evolutionary algorithms can achieve super-linear performance. Inf Process Lett 82(1):7–13MathSciNetMATHCrossRefGoogle Scholar
  3. Alba E (2005) Parallel metaheuristics: a new class of algorithms. Wiley-Interscience, New YorkGoogle Scholar
  4. Baswana S, Biswas S, Doerr B, Friedrich T, Kurur PP, Neumann F (2009) Computing single source shortest paths using single-objective fitness functions. In: Proceedings of the 10th international workshop on foundations of genetic algorithms (FOGA ’09). ACM Press, New York, pp 59–66Google Scholar
  5. Böttcher S, Doerr B, Neumann F (2011) Optimal fixed and adaptive mutation rates for the leadingones problem. In: 11th international conference on parallel problem solving from nature (PPSN 2010). LNCS, vol 6238. Springer, Berlin, pp 1–10Google Scholar
  6. Cantú-Paz E (1997) A survey of parallel genetic algorithms. Technical report, Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana Champaign, UrbanaGoogle Scholar
  7. Cantú-Paz E, Goldberg DE (1999) On the scalability of parallel genetic algorithms. Evol Comput 7(4):429–449CrossRefGoogle Scholar
  8. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms, 2nd edn. The MIT Press, MassachusettsGoogle Scholar
  9. Doerr B, Gnewuch M, Hebbinghaus N, Neumann F (2007) A rigorous view on neutrality. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2007). IEEE Press, New Jersey, pp 2591–2597Google Scholar
  10. Droste S, Jansen T, Wegener I (2002) On the analysis of the (1+1) evolutionary algorithm. Theoret Comput Sci 276:51–81MathSciNetMATHCrossRefGoogle Scholar
  11. Friedrich T, Oliveto PS, Sudholt D, Witt C (2009) Analysis of diversity-preserving mechanisms for global exploration. Evol Comput 17(4):455–476CrossRefGoogle Scholar
  12. Giacobini M, Tomassini M, Tettamanzi A (2003) Modelling selection intensity for linear cellular evolutionary algorithms. In: Proceedings of the sixth international conference on artificial evolution, evolution artificielle. Springer, Berlin, pp 345–356Google Scholar
  13. Giacobini M, Alba E, Tettamanzi A, Tomassini M (2005a) Selection intensity in cellular evolutionary algorithms for regular lattices. IEEE Trans Evol Comput 9:489–505CrossRefGoogle Scholar
  14. Giacobini M, Tomassini M, Tettamanzi A (2005b) Takeover time curves in random and small-world structured populations. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2005). ACM Press, New York, pp 1333–1340Google Scholar
  15. He J, Yao X (2006) Analysis of scalable parallel evolutionary algorithms. In: Proceedings of the IEEE congress on evolutionary computation (CEC 2006), July 2006, pp 120–127Google Scholar
  16. Jägersküpper J, Storch T (2007) When the plus strategy outperforms the comma strategy and when not. In: Proceedings of the IEEE symposium on foundations of computational intelligence, FOCI 2007. IEEE, New Jersey, pp 25–32Google Scholar
  17. Jansen T, Wegener I (2005) Real royal road functions: where crossover provably is essential. Discrete Appl Math 149(1–3):111–125MathSciNetMATHCrossRefGoogle Scholar
  18. Jansen T, De Jong KA, Wegener I (2005) On the choice of the offspring population size in evolutionary algorithms. Evol Comput 13:413–440CrossRefGoogle Scholar
  19. Kötzing T, Sudholt D, Theile M (2011) How crossover helps in pseudo-Boolean optimization. In: Proceedings of the 13th annual genetic and evolutionary computation conference (GECCO 2011). ACM Press, New York, pp 989–996Google Scholar
  20. Lässig J, Sudholt D (2010a) The benefit of migration in parallel evolutionary algorithms. In: Proceedings of the annual genetic and evolutionary computation conference (GECCO 2010), pp 1105–1112Google Scholar
  21. Lässig J, Sudholt D (2010b) Experimental supplements to the theoretical analysis of migration in the island model. In: 11th international conference on parallel problem solving from nature (PPSN 2010). LNCS, vol 6238. Springer, Berlin, pp 224–233Google Scholar
  22. Lässig J, Sudholt D (2010c) General scheme for analyzing running times of parallel evolutionary algorithms. In: 11th international conference on parallel problem solving from nature (PPSN 2010). Springer, Berlin, pp 234–243Google Scholar
  23. Lässig J, Sudholt D (2011) Adaptive population models for offspring populations and parallel evolutionary algorithms. In: Proceedings of the 11th workshop on foundations of genetic algorithms (FOGA 2011). ACM Press, New York, pp 181–192Google Scholar
  24. Luque G, Alba E (2010) Selection pressure and takeover time of distributed evolutionary algorithms. In: Proceedings of the annual genetic and evolutionary computation conference (GECCO 2010). ACM, New York, pp 1083–1088Google Scholar
  25. Luque G, Alba E (2011) Parallel genetic algorithms theory and real world applications. In: Studies in computational intelligence, vol 367. Springer, BerlinGoogle Scholar
  26. McMinn P (2013) An identification of program factors that impact crossover performance in evolutionary test input generation for the branch coverage of C programs. Inf Softw Technol (to appear). http://philmcminn.staff.shef.ac.uk/papers/2012-ist.pdf.
  27. Mitzenmacher M, Upfal E (2005) Probability and computing. Cambridge University Press, OxfordGoogle Scholar
  28. Neumann F, Oliveto PS, Rudolph G, Sudholt D (2011) On the effectiveness of crossover for migration in parallel evolutionary algorithms. In: Proceedings of the 13th annual genetic and evolutionary computation conference (GECCO 2011). ACM Press, New York, pp 1587–1594Google Scholar
  29. Rudolph G (2000) On takeover times in spatially structured populations: array and ring. In: Proceedings of the 2nd Asia-Pacific conference on genetic algorithms and applications. Global-Link Publishing Company, Hong Kong, pp 144–151Google Scholar
  30. Rudolph G (2006) Takeover time in parallel populations with migration. In: Proceedings of the second international conference on bioinspired optimization methods and their applications (BIOMA 2006), pp 63–72Google Scholar
  31. Skolicki Z, De Jong K (2005) The influence of migration sizes and intervals on island models. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2005). ACM Press, New York, pp 1295–1302Google Scholar
  32. Sudholt D (2005) Crossover is provably essential for the Ising model on trees. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2005). ACM Press, New York, pp 1161–1167Google Scholar
  33. Sudholt D (2010) General lower bounds for the running time of evolutionary algorithms. In: 11th international conference on parallel problem solving from nature (PPSN 2010). LNCS, vol 6238. Springer, Berlin, pp 124–133Google Scholar
  34. Teytaud F, Teytaud O (2010) Log(lambda) modifications for optimal parallelism. In: 11th international conference on parallel problem solving from nature (PPSN 2010). LNCS, vol 6238, pp 254–263Google Scholar
  35. Tomassini M (2005) Spatially structured evolutionary algorithms: artificial evolution in space and time. Springer, BerlinGoogle Scholar
  36. Watson RA, Jansen T (2007) A building-block royal road where crossover is provably essential. In: Proceedings of the genetic and evolutionary computation conference (GECCO 2007). ACM Press, New York, pp 1452–1459Google Scholar
  37. Wegener I (2002) Methods for the analysis of evolutionary algorithms on pseudo-Boolean functions. In: Sarker R, Yao X, Mohammadian M (eds) Evolutionary optimization. Kluwer, Dordrecht, pp 349–369Google Scholar
  38. Wineberg M, Christensen S (2009) Statistical analysis for evolutionary computation: introduction. In: Companion of GECCO 2009. ACM Press, New York, pp 2949–2976Google Scholar
  39. Witt C (2006) Runtime analysis of the (μ+1) EA on simple pseudo-Boolean functions. Evol Comput 14(1):65–86MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer ScienceUniversity of Applied Sciences Zittau/GörlitzGörlitzGermany
  2. 2.Department of Computer ScienceUniversity of SheffieldSheffieldUK

Personalised recommendations