Abstract
In this paper, a hybrid evolution strategy is proposed to solve mixed discrete continuous constrained problems. We consider that the functions of the problems are differentiable with respect to the continuous variables but are not with respect to the discrete ones. Evolutionary algorithms are well suited to solve these difficult optimization problems but the number of evaluations is generally very high. The presented hybrid method combines the advantages of evolutionary algorithms for the discrete variables and those of classical gradient-based methods for the continuous variables in order to accelerate the search. The algorithm is based on a dual formulation of the optimization problem. The efficiency of the method is demonstrated through an application to two complex mechanical design problems with mixed-discrete variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bäck, T.: Evolutionary algorithms in theory and practice. Oxford University Press, New York (1996)
Bäck, T., Schütz, M.: Evolution strategies for mixed-integer optimization of optical multilayer systems. In: McDonnell, J.R., Reynolds, R.G., Fogel, D.B. (eds.) Proceedings of the Fourth Annual Conference on Evolutionary Programming, pp. 33–51. MIT Press, Cambridge (1995)
Fletcher, R.: A new approach to variable metric algorithms. Computer Journal 13(3), 317–322 (1970)
Giraud, L., Lafon, P.: Optimization of mechanical design problems with genetic algorithms. In: Proceeding of the 2nd International Conférence IDMME 1998, Compiègne, France, pp. 98–90 (Mai 1998)
Lafon, P.: Conception optimale de systèmes mécaniques: Optimisation en variables mixtes. Thèse 3ème cycle, no d’ordre 273, Institut National des Sciences Appliquées de Toulouse (1994)
Michalewicz, Z., Schoenauer, M.: Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation 4, 1–32 (1996)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin (1996)
Minoux, M.: Programmation Mathématique: Théorie et Algorithms. Tome1 et 2. Edition DUNOD (1983)
Moreau-Giraud, L., Lafon, P.: Evolution strategies for optimal design of mechanical systems. In: Third World Congress of Structural and Multidisciplinary Optimization (WCSMO-3), Buffalo, Etats-Unis (Mai 1999)
Myung, H., Kim, J.-H., Fogel, D.B.: Preliminary investigations into a two-stage method of evolutionary optimization on constrained problems. In: Mac Donnel, J.R., Reynolds, R.G., Fogel, D.B. (eds.) Proceedings of the Fourth Annual Conference on Evolutionary programming, pp. 449–463 (1995)
Rockafellar, R.T.: Augmented lagrange multiplier functions and duality in nonconvex programmings. SIAM Journal Control 12, 268–285 (1974)
Schwefel, H.P.: Numerical optimization of computer models. Wiley, Chichester (1981)
Vasconscelos, J.A., Saldanha, R.R., Krähenbühl, L., Nicolas, A.: Genetic algorithm coupled with a deterministic method for optimization in electromagnetics. IEEE Transaction on magnetics 33(2), 1860–1863 (1997)
Wilde, D.J.: Monotonicity and dominance in optimal hydrolic cylinder design. ASME Journal of Engineering Optimzation 97, 1390–1394 (1975)
Zhou, J., Mayn, R.W.: Monotonicity analysis and the reduced gradient method in constrained optimization. ASME Journal of Mechanisms, Transmissions, and Automation in Design 113, 90–94 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Moreau-Giraud, L., Lafon, P. (2000). A Hybrid Evolution Strategy for Mixed Discrete Continuous Constrained Problems. In: Fonlupt, C., Hao, JK., Lutton, E., Schoenauer, M., Ronald, E. (eds) Artificial Evolution. AE 1999. Lecture Notes in Computer Science, vol 1829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721187_9
Download citation
DOI: https://doi.org/10.1007/10721187_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67846-5
Online ISBN: 978-3-540-44908-9
eBook Packages: Springer Book Archive