Preventing Premature Convergence and Proving the Optimality in Evolutionary Algorithms

  • Charlie Vanaret
  • Jean-Baptiste Gotteland
  • Nicolas Durand
  • Jean-Marc Alliot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8752)

Abstract

Evolutionary Algorithms (EA) usually carry out an efficient exploration of the search-space, but get often trapped in local minima and do not prove the optimality of the solution. Interval-based techniques, on the other hand, yield a numerical proof of optimality of the solution. However, they may fail to converge within a reasonable time due to their exponential complexity and their inability to quickly compute a good approximation of the global minimum. The contribution of this paper is a hybrid algorithm called Charibde in which a particular EA, Differential Evolution, cooperates with a branch and bound algorithm endowed with interval propagation techniques. It prevents premature convergence toward local optima and is highly competitive with both deterministic and stochastic existing approaches. We demonstrate its efficiency on a benchmark of highly multimodal problems, for which we provide previously unknown global minima and certification of optimality.

References

  1. 1.
    Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)MATHGoogle Scholar
  2. 2.
    Sotiropoulos, G.D., Stavropoulos, C.E., Vrahatis, N.M.: A new hybrid genetic algorithm for global optimization. In: Proceedings of Second World Congress on Nonlinear Analysts, pp. 4529–4538. Elsevier Science Publishers Ltd. (1997)Google Scholar
  3. 3.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  4. 4.
    Zhang, X., Liu, S.: A new interval-genetic algorithm. Int. Conf. Nat. Comput. 4, 193–197 (2007)Google Scholar
  5. 5.
    Lei, Y., Chen, S.: A reliable parallel interval global optimization algorithm based on mind evolutionary computation. In: 2012 Seventh ChinaGrid Annual Conference, pp. 205–209 (2009)Google Scholar
  6. 6.
    Alliot, J.M., Durand, N., Gianazza, D., Gotteland, J.B.: Finding and proving the optimum: cooperative stochastic and deterministic search. In: 20th European Conference on Artificial Intelligence (2012)Google Scholar
  7. 7.
    Hansen, E.: Global Optimization Using Interval Analysis. Dekker, New York (1992)MATHGoogle Scholar
  8. 8.
    Chabert, G., Jaulin, L.: Contractor programming. Artif. Intell. 173, 1079–1100 (2009)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Benhamou, F., Goualard, F., Granvilliers, L., Puget, J.F.: Revising hull and box consistency. In: International Conference on Logic Programming, pp. 230–244. MIT press, Cambridge (1999)Google Scholar
  10. 10.
    Araya, I., Trombettoni, G., Neveu, B.: Exploiting monotonicity in interval constraint propagation. In: Proceedings of the AAAI, pp. 9–14 (2010)Google Scholar
  11. 11.
    Storn, R., Price, K.: Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Price, K., Storn, R., Lampinen, J.: Differential Evolution - A Practical Approach to Global Optimization. Natural Computing. Springer, New York (2006)Google Scholar
  13. 13.
    Rall, L.B.: Automatic Differentiation: Techniques and Applications. LNCS, vol. 120. Springer, Heidelberg (1981)CrossRefMATHGoogle Scholar
  14. 14.
    Kearfott, R.B.: Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers. Computing 57, 57–149 (1996)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Whitley, D., Mathias, K., Rana, S., Dzubera, J.: Evaluating evolutionary algorithms. Artif. Intell. 85, 245–276 (1996)CrossRefGoogle Scholar
  16. 16.
    Mishra, S.K.: Some new test functions for global optimization and performance of repulsive particle swarm method. Technical report, University Library of Munich, Germany (2006)Google Scholar
  17. 17.
    Sekaj, I.: Robust parallel genetic algorithms with re-initialisation. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 411–419. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Kim, Y.H., Lee, K.H., Yoon, Y.: Visualizing the search process of particle swarm optimization. In: Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation, pp. 49–56. ACM (2009)Google Scholar
  19. 19.
    Coello Coello, C.A.: Use of a self-adaptive penalty approach for engineering optimization problems. Comput. Ind. 41, 113–127 (1999)CrossRefGoogle Scholar
  20. 20.
    Zhang, J., Zhou, Y., Deng, H.: Hybridizing particle swarm optimization with differential evolution based on feasibility rules. In: ICGIP 2012, vol. 8768 (2013)Google Scholar
  21. 21.
    Aguirre, A., Muñoz Zavala, A., Villa Diharce, E., Botello Rionda, S.: COPSO: constrained optimization via PSO algorithm. Technical report, CIMAT (2007)Google Scholar
  22. 22.
    Duenez-Guzman, E., Aguirre, A.: The Baldwin effect as an optimization strategy. Technical report, CIMAT (2007)Google Scholar
  23. 23.
    Keane, A.J.: A brief comparison of some evolutionary optimization methods. In: Proceedings of the Conference on Applied Decision Technologies. Modern Heuristic Search Methods, Uxbridge, 1995, pp. 255–272. Wiley, Chichester (1996)Google Scholar
  24. 24.
    Mishra, S.K.: Minimization of Keane‘s bump function by the repulsive particle swarm and the differential evolution methods. Technical report, North-Eastern Hill University, Shillong (India) (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Charlie Vanaret
    • 1
    • 2
  • Jean-Baptiste Gotteland
    • 1
    • 2
  • Nicolas Durand
    • 1
    • 2
  • Jean-Marc Alliot
    • 2
  1. 1.Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l’AérienEcole Nationale de l’Aviation CivileToulouseFrance
  2. 2.Institut de Recherche en Informatique de ToulouseToulouseFrance

Personalised recommendations