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Computational Complexity of Evolutionary Algorithms

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Handbook of Natural Computing

Abstract

When applying evolutionary algorithms to the task of optimization it is important to have a clear understanding of their capabilities and limitations. By analyzing the optimization time of various variants of evolutionary algorithms for classes of concrete optimization problems, important insights can be gained about what makes problems easy or hard for these heuristics. Still more important than the derivation of such specific results is the development of methods that facilitate rigorous analysis and enable researchers to derive such results for new variants of evolutionary algorithms and more complex problems. The development of such methods and analytical tools is a significant and very active area of research. An overview of important methods and their foundations is presented together with exemplary applications. This enables one to apply these methods to concrete problems and participate in the theoretical foundation of evolutionary computing.

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References

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms, 2nd edn. MIT Press, Cambridge, MA

    MATH  Google Scholar 

  • De Jong KA (1992) Genetic algorithms are NOT function optimizers. In: Whitley LD (ed) Proceedings of the second workshop on foundations of genetic algorithms (FOGA), Morgan Kaufmann, San Francisco, CA, pp 5–17

    Google Scholar 

  • Dietzfelbinger M, Naudts B, Hoyweghen CV, Wegener I (2003) The analysis of a recombinative hill-climber on H-IFF. IEEE Trans Evolut Comput 7(5):417–423

    Article  Google Scholar 

  • Doerr B, Neumann F, Sudholt D, Witt C (2007) On the runtime analysis of the 1-ANT ACO algorithm. In: Proceedings of the genetic and evolutionary computation conference (GECCO), ACM, New York, pp 33–40

    Google Scholar 

  • Doerr B, Jansen T, Klein C (2008) Comparing global and local mutations on bit strings. In: Proceedings of the genetic and evolutionary computation conference (GECCO), ACM, New York, pp 929–936

    Google Scholar 

  • Droste S, Jansen T, Wegener I (2002a) On the analysis of the (1+1) evolutionary algorithm. Theor Comput Sci 276:51–81

    Article  MathSciNet  MATH  Google Scholar 

  • Droste S, Jansen T, Wegener I (2002b) Optimization with randomized search heuristics – the (A)NFL theorem, realistic scenarios, and difficult functions. Theor Comput Sci 287(1):131–144

    Article  MathSciNet  MATH  Google Scholar 

  • Droste S, Jansen T, Wegener I (2006) Upper and lower bounds for randomized search heuristics in black-box optimization. Theory Comput Syst 39(4): 525–544

    Article  MathSciNet  MATH  Google Scholar 

  • He J, Yao X (2004) A study of drift analysis for estimating computation time of evolutionary algorithms. Nat Comput 3(1):21–35

    Article  MathSciNet  MATH  Google Scholar 

  • Horn J, Goldberg DE, Deb K (1994) Long path problems. In: Davidor Y, Schwefel HP, Männer R (eds) Proceedings of the 3rd international conference on parallel problem solving from nature (PPSN III), Springer, Berlin, Germany, LNCS 866, pp 149–158

    Google Scholar 

  • Igel C, Toussaint M (2003) On classes of functions for which no free lunch results hold. Inf Process Lett 86:317–321

    Article  MathSciNet  MATH  Google Scholar 

  • Igel C, Toussaint M (2004) A no-free-lunch theorem for non-uniform distributions of target functions. J Math Model Algorithms 3:313–322

    Article  MathSciNet  MATH  Google Scholar 

  • Jansen T, Sudholt D (2010) Analysis of an asymmetric mutation operator. Evolut Comput 18(1):1–26

    Article  Google Scholar 

  • Jansen T, Wegener I (2000) On the choice of the mutation probability for the (1+1) EA. In: Schoenauer M, Deb K, Rudolph G, Yao X, Lutton E, Merelo-Guervos J, Schwefel HP (eds) Proceedings of the 6th international conference on parallel problem solving from nature (PPSN VI), Springer, New York, LNCS 1917, pp 89–98

    Chapter  Google Scholar 

  • Jansen T, Wegener I (2002) On the analysis of evolutionary algorithms – a proof that crossover really can help. Algorithmica 34(1):47–66

    Article  MathSciNet  MATH  Google Scholar 

  • Jansen T, De Jong KA, Wegener I (2005) On the choice of the offspring population size in evolutionary algorithms. Evolut Comput 13(4):413–440

    Article  Google Scholar 

  • Mitzenmacher M, Upfal E (2005) Probability and computing. Cambridge University Press, Cambridge, MA

    MATH  Google Scholar 

  • Motwani R, Raghavan P (1995) Randomized algorithms. Cambridge University Press, Cambridge, MA

    MATH  Google Scholar 

  • Neumann F, Wegener I (2004) Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. In: Proceedings of the genetic and evolutionary computation conference (GECCO), Springer, Berlin, Germany, LNCS 3102, pp 713–724

    Google Scholar 

  • Oliveto PS, Witt C (2008) Simplified drift analysis for proving lower bounds in evolutionary computation. In: Proceedings of the 10th international conference on parallel problem solving from nature (PPSN X), Springer, Berlin, Germany, LNCS 5199, pp 82–91

    Google Scholar 

  • Oliveto PS, He J, Yao X (2007) Time complexity of evolutionary algorithms for combinatorial optimization: a decade of results. Int J Automation Comput 4(3):281–293

    Article  Google Scholar 

  • Reichel J, Skutella M (2009) On the size of weights in randomized search heuristics. In: Garibay I, Jansen T, Wiegand RP, Wu A (eds) Proceedings of the tenth workshop on foundations of genetic algorithms (FOGA), ACM, New York, pp 21–28

    Google Scholar 

  • Rudolph G (1997) How mutation and selection solve long path problems polynomial expected time. Evolut Comput 4(2):195–205

    Article  MathSciNet  Google Scholar 

  • Schumacher C, Vose MD, Whitley LD (2001) The no free lunch and problem description length. In: Proceedings of the genetic and evolutionary computation conference (GECCO), Morgan Kaufmann, San Francisco, CA, pp 565–570

    Google Scholar 

  • Sudholt D (2008) Memetic algorithms with variable-depth search to overcome local optima. In: Proceedings of the genetic and evolutionary computation conference (GECCO), ACM, New York, pp 787–794

    Google Scholar 

  • Sudholt D, Witt C (2008a) Rigorous analyses for the combination of ant colony optimization and local search. In: Proceedings of ant colony and swarm intelligence (ANTS), Springer, Berlin, Germany, LNCS 5217, pp 132–143

    Google Scholar 

  • Sudholt D, Witt C (2008b) Runtime analysis of binary PSO. In: Proceedings of the genetic and evolutionary computation conference (GECCO), ACM, New York, pp 135–142

    Google Scholar 

  • Williams D (1991) Probability with martingales. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Witt C (2006) Runtime analysis of the (μ+1) EA on simple pseudo-boolean functions. Evolut Comput 14(1):65–86

    MathSciNet  Google Scholar 

  • Witt C (2009) Why standard particle swarm optimizers elude a theoretical runtime analysis. In: Garibay I, Jansen T, Wiegand RP, Wu A (eds) Proceedings of the tenth workshop on foundations of genetic algorithms (FOGA), ACM, New York, pp 13–20

    Google Scholar 

  • Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1(1):67–82

    Article  Google Scholar 

  • Yao AC (1977) Probabilistic computations: towards a unified measure of complexity. In: Proceedings of the 17th IEEE symposium on foundations of computer science (FOCS), New York, pp 222–227

    Google Scholar 

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Acknowledgment

This material is based upon works supported by Science Foundation Ireland under Grant No. 07/SK/I1205.

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Jansen, T. (2012). Computational Complexity of Evolutionary Algorithms. In: Rozenberg, G., Bäck, T., Kok, J.N. (eds) Handbook of Natural Computing. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92910-9_26

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