Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization Article Received: 20 September 2005 Accepted: 02 October 2005 DOI:
Cite this article as: Hedar, AR. & Fukushima, M. J Glob Optim (2006) 35: 521. doi:10.1007/s10898-005-3693-z Abstract
In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions, the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated problem. The FSA method invokes a multi-start diversification scheme in order to achieve an efficient exploration process. To deal with the considered problem, a filter-set-based procedure is built in the FSA structure. Finally, an intensification scheme is applied as a final stage of the proposed method in order to overcome the slow convergence of SA-based methods. The computational results obtained by the FSA method are promising and show a superior performance of the proposed method, which is a point-to-point method, against population-based methods.
Keywords Approximate descent direction constrained global optimization filter set metaheuristics simulated annealing References
Aarts, E., Korst, J. 2000 Selected topics in simulated annealing Ribeiro, C.C. Hansen, P. eds. Essays and Surveys in Metaheuristics. Kluwer Academic Publishers Boston, MA Google Scholar
Audet, C. and Dennis Jr., J.E. (2004), A pattern search filter method for nonlinear programming without derivatives, SIAM Journal on Optimization (to appear).
Chen, Y.X. (2001), Optimal anytime search for constrained nonlinear programming, M.Sc. Thesis, Department of Computer Science, University of Illinois.
Coello Coello, C.A. 2002 Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art Computer Methods in Applied Mechanics and Engineering 191 1245 1287 CrossRef Google Scholar
Coello Coello, C.A., Montes, E.M. 2002 Constraint-handling in genetic algorithms through the use of dominance-based tournament selection Advanced Engineering Informatics 16 193 203 CrossRef Google Scholar
Deb, K. 2000 An efficient constraint handling method for genetic algorithms Computer Methods in Applied Mechanics and Engineering 186 311 338 CrossRef Google Scholar
Fletcher, R., Leyffer, S. 2002 Nonlinear programming without a penalty function Mathematical Programming 91 239 269 CrossRef Google Scholar
Floudas, C.A. Pardalos, P.M. Adjiman, C.S. Esposito, W.R. Gumus, Z. Harding, S.T. Klepeis, J.L. Meyer, C.A. Schweiger, C.A. eds. 1999Handbook of Test Problems for Local and Global Optimization Kluwer Academic Publishers Boston, MA Google Scholar
Hamida, S.B. and Schoenauer, M. (2002), ASCHEA: new rsults using adaptive segregational constraint handling, In: Proceedings of the Congress on Evolutionary Computation (CEC2002), Piscataway, New Jersey, IEEE Service Center, pp. 884–889.
Hedar, A., Fukushima, M. 2002 Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization Optimization Methods and Software 17 891 912 CrossRef Google Scholar
Hedar, A., Fukushima, M. 2003 Minimizing multimodal functions by simplex coding genetic algorithm Optimization Methods and Software 18 265 282 CrossRef Google Scholar
Hedar, A., Fukushima, M. 2004 Heuristic pattern search and its hybridization with simulated annealing for nonlinear global optimization Optimization Methods and Software 19 291 308 CrossRef Google Scholar
Hedar, A. and Fukushima, M. (2005), Tabu search directed by direct search methods for nonlinear global optimization, European Journal of Operational Research (to appear).
Hock, W., Schittkowski, K. 1981Test Examples for Nonlinear Programming Codes Springer-Verlag Berlin, Heidelberg Google Scholar
Kelley, C.T. 1999 Detection and remediation of stagnation in the Nelder–Mead algorithm using a sufficient decrease condition SIAM Journal on Optimization 10 43 55 CrossRef Google Scholar
Kelley, C.T. 1999Iterative Methods for Optimization SIAM Philadelphia, PA Google Scholar
Kirkpatrick, S., Gelatt, C.D., Jr, Vecchi, M.P. 1983 Optimisation by simulated annealing Science 220 671 680 Google Scholar
Koziel, S., Michalewicz, Z. 1999 Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization Evolutionary Computation 7 19 44 Google Scholar
Laarhoven, P.J. 1988Theoretical and Computational Aspects of Simulated Annealing Stichting Mathematisch Centrum Amsterdam Google Scholar
Laarhoven, P.J., Aarts, E.H. 1987Simulated Annealing: Theory and Applications D. Reidel Publishing Company Dordrecht, Holland Google Scholar
Laguna, M. and Martí, R. (2002), Experimental testing of advanced scatter search designs for global optimization of multimodal functions, Journal of Global Optimization (to appear).
Laguna, M., Martí, R. 2003Scatter Search: Methodology and Implementations in C Kluwer Academic Publishers Boston Google Scholar
Martí, R. 2002 Multi-start methods Glover, F. Kochenberger, G. eds. Handbook of MetaHeuristics. Kluwer Academic Publishers Boston, MA 355 368 Google Scholar
Martí, R., Moreno, J.M. 2003 Métodos multi-arranque Inteligencia Artificial 19 49 60 Google Scholar
Montes, E.M. and Coello Coello, C.A. (2003), A simple multimembered evolution strategy to solve constrained optimization problems, Technical Report EVOCINV-04-2003, Evolutionary Computation Group at CINVESTAV, Sección de Computación, Departamento de Ingeniería Eléctrica, CINVESTAV-IPN, México D.F., México.
Michalewicz, Z., Schoenauer, M. 1996 Evolutionary algorithms for constrained parameter optimization problems Evolutionary Computation 4 1 32 Google Scholar
Nelder, J.A., Mead, R. 1965 A simplex method for function minimization The Computer Journal 7 308 313 Google Scholar
Romeijn, H.E., Smith, R.L. 1994 Simulated annealing for global constrained optimization Journal of Global Optimization 5 101 126 CrossRef Google Scholar
Runarsson, T.P., Yao, X. 2000 Stochastic ranking for constrained evolutionary optimization IEEE Transactions on Evolutionary Computation 4 284 294 CrossRef Google Scholar
Schoen, F. 2002 Two phase methods for global optimization Pardalos, P.M. Romeijn, H.E. eds. Handbook of Global Optimization Kluwer Academic Publishers Boston, MA 151 178 Google Scholar
Wah, B.W. and Chen, Y.X. (2000), Optimal anytime constrained simulated annealing for constrained global optimization, In: Dechter, R. (ed.), LNCS 1894, Springer-Verlag, pp. 425–440.
Wah, B.W., Wang, T. 2000 Tuning strategies of constrained simulated annealing for nonlinear global optimization International Journal on Artificial Intelligence Tools 9 3 25 CrossRef Google Scholar
Wang, T. (2000), Global optimization of constrained nonlinear programming, Ph.D. Thesis, Department of Computer Science, University of Illinois.
Wang, P.P., Chen, D.S. 1996 Continuous optimization by a variant of simulated annealing Computational Optimization and Applications 6 59 71 CrossRef Google Scholar