Skip to main content

Methods for the Analysis of Evolutionary Algorithms

  • Chapter
  • First Online:
Analyzing Evolutionary Algorithms

Part of the book series: Natural Computing Series ((NCS))

  • 2187 Accesses

Abstract

Analyzing evolutionary algorithms is often surprisingly difficult. It can be challenging even for very simple evolutionary algorithms on very simple functions. This is due to the fact that evolutionary algorithms are a class of randomized search heuristics mimicking natural evolution that have been designed to search effectively for good solutions in a vast search space without any thought about analysis. The directed random sampling of the search space they perform gives rise to complex and hard to analyze random processes that can be described as complex Markov chains as we have discussed in Sect. 3.1. This motivates us to start our analysis with evolutionary algorithms that are as simple as possible and consider fitness functions that are as simple as possible. We do not claim that such evolutionary algorithms are actually applied in practice or that example problems bear much resemblance to real optimization problems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. S. Böttcher, B. Doerr, F. Neumann, Optimal fixed and adaptive mutation rates for the LeadingOnes problem, in Proceedings of the 11th International Conference on Parallel Problem Solving from Nature (PPSN XI), ed. by R. Schaefer, C. Cotta, J. Kołodziej, G. Rudolph. Lecture Notes in Computer Science, vol. 6238 (Springer, Berlin, 2010), pp. 1–10

    Google Scholar 

  2. D. Brockhoff, T. Friedrich, N. Hebbinghaus, C. Klein, F. Neumann, E. Zitzler, On the effects of adding objectives to plateau functions. IEEE Trans. Evol. Comput. 13(3), 591–603 (2009)

    Article  Google Scholar 

  3. M. Dietzfelbinger, B. Naudts, C.V. Hoyweghen, I. Wegener, The analysis of a recombinative hill-climber on H-IFF. IEEE Trans. Evol. Comput. 7(5), 417–423 (2003)

    Article  Google Scholar 

  4. B. Doerr, L.A. Goldberg, Adaptive drift analysis, in Proceedings of the 11th International Conference on Parallel Problem Solving from Nature (PPSN XI), Kraków, ed. by R. Schaefer, C. Cotta, J. Kołodziej, G. Rudolph. Lecture Notes in Computer Science, vol. 6238 (Springer, Berlin, 2010), pp. 32–41

    Google Scholar 

  5. B. Doerr, L.A. Goldberg, Drift analysis with tail bounds, in Proceedings of the 11th International Conference on Parallel Problem Solving from Nature (PPSN XI), Kraków, ed. by R. Schaefer, C. Cotta, J. Kołodziej, G. Rudolph. Lecture Notes in Computer Science, vol. 6238 (Springer, Berlin, 2010), pp. 174–183

    Google Scholar 

  6. B. Doerr, D. Johannsen, C. Winzen, Drift analysis and linear functions revisited, in IEEE Congress on Evolutionary Computation (CEC 2010), Barcelona (IEEE, Piscataway, 2010), pp. 1–8

    Google Scholar 

  7. B. Doerr, D. Johannsen, C. Winzen, Multiplicative drift analysis, in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2010), Portland (ACM, New York, 2010), pp. 1449–1456

    Google Scholar 

  8. B. Doerr, F. Neumann, D. Sudholt, C. Witt, Runtime analysis of the 1-ANT ant colony optimizer. Theor. Comput. Sci. 412(17), 1629–1644 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Droste, T. Jansen, I. Wegener, A rigorous complexity analysis of the (1 + 1) evolutionary algorithm for linear functions with Boolean inputs, in Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC 1998), Anchorage, ed. by D. Fogel, H.-P. Schwefel, T. Bäck, X. Yao (IEEE, Piscataway, 1998), pp. 499–504

    Google Scholar 

  10. S. Droste, T. Jansen, I. Wegener, On the optimization of unimodal functions with the (1 + 1) evolutionary algorithm, in Proceedings of the 5th International Conference on Parallel Problem Solving from Nature (PPSN 1998), Amsterdam, ed. by A. Eiben, T. Bäck, M. Schoenauer, H.-P. Schwefel. Lecture Notes in Computer Science, vol. 1498 (Springer, Berlin, 1998), pp. 13–22

    Google Scholar 

  11. T. Friedrich, P.S. Oliveto, D. Sudholt, C. Witt, Analysis of diversity-preserving mechanisms for global exploration. Evol. Comput. 17(4), 455–476 (2009)

    Article  Google Scholar 

  12. J. Garnier, L. Kallel, Statistical distribution of the convergence time of evolutionary algorithms for long-path problems. IEEE Trans. Evol. Comput. 4(1), 16–30 (2000)

    Article  Google Scholar 

  13. J. He, X. Yao, Drift analysis and average time complexity of evolutionary algorithms. Artif. Intell. 127(1), 57–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Horn, D. Goldberg, K. Deb, Long path problems, in Proceedings of the 4th International Conference on Parallel Problem Solving from Nature (PPSN IV), Jerusalem. Lecture Notes in Computer Science, vol. 866 (Springer, Berlin, 1994), pp. 149–158

    Google Scholar 

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

    Article  MATH  Google Scholar 

  17. T. Jansen, I. Wegener, On the analysis of evolutionary algorithms – a proof that crossover really can help, in Proceedings of the 7th Annual European Symposium on Algorithms (ESA 1999), Prague, ed. by J. Nesetril. Lecture Notes in Computer Science, vol. 1643 (Springer, Berlin, 1999), pp. 184–193

    Google Scholar 

  18. T. Jansen, I. Wegener, Evolutionary algorithms – how to cope with plateaus of constant fitness and when to reject strings of the same fitness. IEEE Trans. Evol. Comput. 5(6), 589–599 (2002)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. T. Jansen, I. Wegener, A comparison of simulated annealing with simple evolutionary algorithms on pseudo-Boolean functions of unitation. Theor. Comput. Sci. 386, 73–93 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. T. Jansen, C. Zarges, Analysis of evolutionary algorithms: from computational complexity analysis to algorithm engineering, in 11th ACM SIGEVO Workshop on Foundations of Genetic Algorithms (FOGA 2011), Schwarzenberg, ed. by H.-G. Beyer, W.B. Langdon (ACM, New York, 2011), pp. 1–14

    Google Scholar 

  22. T. Jansen, C. Zarges, Analyzing different variants of immune inspired somatic contiguous hypermutations. Theor. Comput. Sci. 412(6), 517–533 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. T. Jansen, K.A. De Jong, I. Wegener, On the choice of the offspring population size in evolutionary algorithms. Evol. Comput. 13(4), 413–440 (2005)

    Article  Google Scholar 

  24. P.K. Lehre, Fitness-levels for non-elitist populations, in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2011), Dublin (ACM, New York, 2011), pp. 2075–2082

    Google Scholar 

  25. R. Motwani, P. Raghavan, Randomized Algorithms (Cambridge University Press, Cambridge, 1995)

    MATH  Google Scholar 

  26. H. Mühlenbein, How genetic algorithms really work: mutation and hillclimbing, in Proceedings of the 2nd International Conference on Parallel Problem Solving from Nature (PPSN II), Brussels (Elsevier, Amsterdam, 1992), pp. 15–26

    Google Scholar 

  27. F. Neumann, C. Witt, Runtime analysis of a simple ant colony optimization algorithm. Algorithmica 54(2), 243–255 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. P.S. Oliveto, C. Witt, Simplified drift analysis for proving lower bounds in evolutionary computation. Algorithmica 59(3), 369–386 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. G. Rudolph, How mutation and selection solve long path problems in polynomial expected time. Evol. Comput. 4(2), 195–205 (1996)

    Article  Google Scholar 

  30. G. Rudolph, Convergence Properties of Evolutionary Algorithms (Kovac, Hamburg, 1997)

    Google Scholar 

  31. D. Sudholt, Computational complexity of evolutionary algorithms, hybridizations, and swarm intelligence. Ph.D. thesis, Technische Universität Dortmund, 2008

    Google Scholar 

  32. D. Sudholt, General lower bounds for the running time of evolutionary algorithms, in Proceedings of the 11th International Conference on Parallel Problem Solving from Nature (PPSN XI), Kraków, ed. by R. Schaefer, C. Cotta, J. Kołodziej, G. Rudolph. Lecture Notes in Computer Science, vol. 6238 (Springer, Berlin, 2010), pp. 124–133

    Google Scholar 

  33. D. Sudholt, A new method for lower bounds on the running time of evolutionary algorithms. Technical report abs/1109.1504v2, CoRR, 2011. http://arxiv.org/abs/1109.1504

  34. D. Sudholt, C. Thyssen, Running time analysis of ant colony optimization for shortest path problems. J. Discret. Algorithms 10, 165–180 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  35. D. Sudholt, C. Witt, Runtime analysis of a binary particle swarm optimizer. Theor. Comput. Sci. 411(21), 2084–2100 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  36. R.A. Watson, G. Hornby, J.B. Pollack, Modeling building-block interdependency, in Proceedings of the 5th International Conference on Parallel Problem Solving from Nature (PPSN 1998), Amsterdam, ed. by A. Eiben, T. Bäck, M. Schoenauer, H.-P. Schwefel. Lecture Notes in Computer Science, vol. 1498 (Springer, Berlin, 1998), pp. 97–108

    Google Scholar 

  37. I. Wegener, Methods for the analysis of evolutionary algorithms on pseudo-Boolean functions, in Evolutionary Optimization, ed. by R. Sarker, X. Yao, M. Mohammadian (Kluwer Academic, New York, 2002), pp. 349–369

    Google Scholar 

  38. I. Wegener, Simulated annealing beats Metropolis in combinatorial optimization, in Automata, Languages and Programming, 32nd International Colloquium (ICALP 2005), Lisbon, ed. by L. Caires, G. Italiano, L. Monteiro, C. Palamidessi, M. Yung. Lecture Notes in Computer Science, vol. 3580 (Springer, Berlin, 2005), pp. 589–601

    Google Scholar 

  39. C. Witt, Runtime analysis of (μ + 1) EA on simple pseudo-Boolean functions. Evol. Comput. 14(1), 65–86 (2006)

    MathSciNet  Google Scholar 

  40. C. Witt, Optimizing linear functions with randomized search heuristics – the robustness of mutation, in 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012), Paris, ed. by C. Dürr, T. Wilke. Leibniz International Proceedings in Informatics, vol. 14 (Dagstuhl Publishing, Saarbrücken, 2012), pp. 420–431

    Google Scholar 

  41. C. Zarges, On the utility of the population size for inversely fitness proportional mutation rates, in 10th ACM SIGEVO Workshop on Foundations of Genetic Algorithms (FOGA 2009), Orlando, ed. by I. Garibay, T. Jansen, R.P. Wiegand, A.S. Wu (ACM, New York, 2009), pp. 39–46

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jansen, T. (2013). Methods for the Analysis of Evolutionary Algorithms. In: Analyzing Evolutionary Algorithms. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17339-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-17339-4_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17338-7

  • Online ISBN: 978-3-642-17339-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics