Soft Computing

, Volume 16, Issue 3, pp 511–525 | Cite as

Variable mesh optimization for continuous optimization problems

  • Amilkar Puris
  • Rafael Bello
  • Daniel Molina
  • Francisco Herrera
Original Paper

Abstract

Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive algorithm.

References

  1. Brest J, Boskovic B, Greiner S, Zumer V, Maucec MS (2007) Performance comparison of self-adaptive and adaptive differential evolution algorithms. Soft Comput 11(7):617–629MATHCrossRefGoogle Scholar
  2. Deb K (2001) Self-adaptive genetic algorithms with simulated binary crossover. Evol Comput J 9(2):195–219CrossRefGoogle Scholar
  3. Engelbrecht A (2006) Fundamentals of computational swarm intelligence. Wiley, New YorkGoogle Scholar
  4. Fernandes C, Rosa A (2001) A study of non-random matching and varying population size in genetic algorithm using a royal road function. In: Proceedings of IEEE congress on evolutionary computation. IEEE Press, Piscataway, New York, pp 60–66Google Scholar
  5. García S, Fernández A, Luengo J, Herrera F (2009) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput Appl 13(10):959–977CrossRefGoogle Scholar
  6. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC2005 special session on real parameter optimization. J Heuristics 15:617–644MATHCrossRefGoogle Scholar
  7. Glover FW, Kochenberger GA (2003) Handbook of metaheuristics (International Series in Operations Research & Management Science). Springer, BerlinGoogle Scholar
  8. Herrera F, Lozano M (eds) (2005) Special issue on real coded genetic algorithms: foundations, models and operators. Soft Comput 9:4Google Scholar
  9. Herrera F, Lozano M, Verdegay J (1998) Tackling realcoded genetic algorithms: operators and tools for the behavioral analysis. Artif Intell Rev 12(4):265–319MATHCrossRefGoogle Scholar
  10. Herrera F, Lozano M, Sánchez A (2003) A taxonomy for the crossover operator for real-coded genetic algorithms: an experimental study. Int J Intell Syst 18(3):309–338MATHCrossRefGoogle Scholar
  11. Holm S (1979) A simple sequentially rejective multiple test procedure. Scand J Stat 6(2):65–70MathSciNetMATHGoogle Scholar
  12. Iman R, Davenport J (1980) Approximations of the critical region of the Friedman statistic. Commun Stat 18:571–595Google Scholar
  13. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, pp 1942–1948Google Scholar
  14. Laguna M, Martí R (2003) Scatter search. Methodology and implementation in C. Kluwer, DordrechtGoogle Scholar
  15. Lozano M, Herrera F, Molina D (eds) (2011) Special issue on scalability of evolutionary algorithms and other metaheuristics for large scale continuous optimization problems. Soft ComputGoogle Scholar
  16. Michalewicz Z, Siarry P (2008) Special issue on adaptation of discrete metaheuristics to continuous optimization. In: Eur J Oper Res 185:1060–1061Google Scholar
  17. Minetti G (2005) Uniform crossover in genetic algorithms. In: Proceedings of IEEE fifth international conference on intelligent systems design and applications, pp 350–355Google Scholar
  18. Rahnamayan S, Tizhoosh H, Salama M (2008) Solving large scale optimization problems by opposition-based differential evolution. IEEE Trans Comput 7(10):1792–1804Google Scholar
  19. Sheskin DJ (2007) Handbook of parametric and nonparametric statistical procedures. Chapman and Hall/CRCGoogle Scholar
  20. Shi Y, Eberhart C (1998) A modified particle swarm optimizer. In: Proceedings of IEEE international conference on evolutionary computation, pp 69–73Google Scholar
  21. Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetMATHCrossRefGoogle Scholar
  22. Suganthan P, Hansen N, Liang J, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University. http://www.ntu.edu.sg/home/EPNSugan/
  23. Syswerda G (1989) Uniform crossover in genetic algorithms. In: Schaffer J (eds) Proceedings of third international conference on genetic algorithms. pp 2–9 Morgan Kaufmann, San MateoGoogle Scholar
  24. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Amilkar Puris
    • 1
  • Rafael Bello
    • 1
  • Daniel Molina
    • 2
  • Francisco Herrera
    • 3
  1. 1.Department of Computer ScienceUniversidad Central de las VillasSanta ClaraCuba
  2. 2.Department of Computer Languages and SystemsUniversity of CadizCadizSpain
  3. 3.Department of Computer Science and Artificial IntelligenceUniversity of GranadaGranadaSpain

Personalised recommendations