Skip to main content
SpringerLink
Log in

Metaheuristic Optimization: Algorithm Analysis and Open Problems

  • Conference paper
Experimental Algorithms (SEA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6630))

Included in the following conference series:

Abstract

Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming increasingly popular. Despite their popularity, mathematical analysis of these algorithms lacks behind. Convergence analysis still remains unsolved for the majority of metaheuristic algorithms, while efficiency analysis is equally challenging. In this paper, we intend to provide an overview of convergence and efficiency studies of metaheuristics, and try to provide a framework for analyzing metaheuristics in terms of convergence and efficiency. This can form a basis for analyzing other algorithms. We also outline some open questions as further research topics.

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

Access this chapter

Log in via an institution
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 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Auger, A., Doerr, B.: Theory of Randomized Search Heuristics: Foundations and Recent Developments. World Scientific, Singapore (2010)

    MATH  Google Scholar 

  2. Auger, A., Teytaud, O.: Continuous lunches are free plus the design of optimal optimization algorithms. Algorithmica 57(1), 121–146 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bell, W.J.: Searching Behaviour: The Behavioural Ecology of Finding Resources. Chapman & Hall, London (1991)

    Google Scholar 

  4. Bertsimas, D., Tsitsiklis, J.: Simulated annealing. Stat. Science 8, 10–15 (1993)

    Article  MATH  Google Scholar 

  5. Blum, C., Roli, A.: Metaheuristics in combinatorial optimization: Overview and conceptural comparison. ACM Comput. Surv. 35, 268–308 (2003)

    Article  Google Scholar 

  6. Chatterjee, A., Siarry, P.: Nonlinear inertia variation for dynamic adapation in particle swarm optimization. Comp. Oper. Research 33, 859–871 (2006)

    Article  MATH  Google Scholar 

  7. Clerc, M., Kennedy, J.: The particle swarm - explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evolutionary Computation 6, 58–73 (2002)

    Article  Google Scholar 

  8. Dorigo, M.: Optimization, Learning and Natural Algorithms. PhD thesis. Politecnico di Milano, Italy (1992)

    Google Scholar 

  9. Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley, Chichester (2005)

    Google Scholar 

  10. Floudas, C.A., Pardalos, P.M.: A Collection of Test Problems for Constrained Global Optimization Algorithms. LNCS, vol. 455. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  11. Floudas, C.A., Pardolos, P.M.: Encyclopedia of Optimization, 2nd edn. Springer, Heidelberg (2009)

    Book  Google Scholar 

  12. Gamerman, D.: Markov Chain Monte Carlo. Chapman & Hall/CRC (1997)

    Google Scholar 

  13. Geyer, C.J.: Practical Markov Chain Monte Carlo. Statistical Science 7, 473–511 (1992)

    Article  Google Scholar 

  14. Ghate, A., Smith, R.: Adaptive search with stochastic acceptance probabilities for global optimization. Operations Research Lett. 36, 285–290 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Granville, V., Krivanek, M., Rasson, J.P.: Simulated annealing: A proof of convergence. IEEE Trans. Pattern Anal. Mach. Intel. 16, 652–656 (1994)

    Article  Google Scholar 

  16. Gutowski, M.: Lévy flights as an underlying mechanism for global optimization algorithms. ArXiv Mathematical Physics e-Prints (June 2001)

    Google Scholar 

  17. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proc. of IEEE International Conference on Neural Networks, Piscataway, NJ, pp. 1942–1948 (1995)

    Google Scholar 

  18. Kennedy, J., Eberhart, R.C.: Swarm intelligence. Academic Press, London (2001)

    Google Scholar 

  19. Holland, J.: Adaptation in Natural and Artificial systems. University of Michigan Press, Ann Anbor (1975)

    Google Scholar 

  20. Kirkpatrick, S., Gellat, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220, 670–680 (1983)

    Article  MathSciNet  Google Scholar 

  21. Matthews, C., Wright, L., Yang, X.S.: Sensitivity Analysis, Optimization, and Sampling Methodds Applied to Continous Models. National Physical Laboratory Report, UK (2009)

    Google Scholar 

  22. Neumann, F., Witt, C.: Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity. Springer, Heidelberg (2010)

    Book  MATH  Google Scholar 

  23. Nolan, J.P.: Stable distributions: models for heavy-tailed data. American University (2009)

    Google Scholar 

  24. Pavlyukevich, I.: Lévy flights, non-local search and simulated annealing. J. Computational Physics 226, 1830–1844 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Rebennack, S., Arulselvan, A., Elefteriadou, L., Pardalos, P.M.: Complexity analysis for maximum flow problems with arc reversals. J. Combin. Optimization 19(2), 200–216 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Reynolds, A.M., Rhodes, C.J.: The Lévy fligth paradigm: random search patterns and mechanisms. Ecology 90, 877–887 (2009)

    Article  Google Scholar 

  27. Steinhöfel, K., Albrecht, A.A., Wong, C.-K.: Convergence analysis of simulated annealing-based algorithms solving flow shop scheduling problems. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 277–290. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  28. Sobol, I.M.: A Primer for the Monte Carlo Method. CRC Press, Boca Raton (1994)

    MATH  Google Scholar 

  29. Talbi, E.G.: Metaheuristics: From Design to Implementation. Wiley, Chichester (2009)

    Book  MATH  Google Scholar 

  30. Viswanathan, G.M., Buldyrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P., Stanley, H.E.: Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996)

    Article  Google Scholar 

  31. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimisation. IEEE Transaction on Evolutionary Computation 1, 67–82 (1997)

    Article  Google Scholar 

  32. Yang, X.S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press (2008)

    Google Scholar 

  33. Yang, X.S.: Engineering Optimization: An Introduction with Metaheuristic Applications. John Wiley & Sons, Chichester

    Google Scholar 

  34. Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Computation 2, 78–84 (2010)

    Article  Google Scholar 

  35. Yang, X.S., Deb, S.: Engineering optimization by cuckoo search. Int. J. Math. Modelling & Num. Optimization 1, 330–343 (2010)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics and Scientific Computing, National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK

    Xin-She Yang

Authors
  1. Xin-She Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Division of Economics and Business, Colorado School of Mines, Engineering Hall 310, 816 15th Street, 80401, Golden, CO, USA

    Steffen Rebennack

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yang, XS. (2011). Metaheuristic Optimization: Algorithm Analysis and Open Problems. In: Pardalos, P.M., Rebennack, S. (eds) Experimental Algorithms. SEA 2011. Lecture Notes in Computer Science, vol 6630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20662-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20662-7_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20661-0

  • Online ISBN: 978-3-642-20662-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation