Abstract
This paper proposes a new multistart algorithm to find the global minimum of constrained problems. This algorithm, which in this paper is called the repulsion algorithm, efficiently selects initial design points for local searches. A Bayesian approach provides the stopping rules. The method uses information from the previous sampling points and the corresponding sequences generated by local searches to select new initial points. This approach increases the probability of finding all local minima with fewer local searches. Numerical example problems show that compared with traditional multistart methods, the repulsion algorithm reduces significantly the number of local searches required to find the global minimum.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Betro, B.; Schoen, F. 1987: Sequential stopping rules for the multistart algorithm in global optimization.Math. Prog. 38, 271–286
Boender, C.G.E.; Rinnooy-Kan, A. 1987: Bayesian stopping rules for multistart global optimization methods.Math. Prog. 37, 59–80
Cassis, J.H.; Schmit, L.A. 1976: Optimum structural design with dynamic constraints.J. Struct. Div., ASCE 102, 2053–2071
Chew, S.H.; Zheng, Q. 1988: Integral global optimization.Lecture Notes in Economics and Mathematical Systems 298. Berlin, Heidelberg, New York: Springer
Floudas, C.A.; Pardalos, P.M. 1990: A collection of test problems for constrained global optimization algorithmsLecture Notes in Computer Science 455. Berlin, Heidelberg, New York: Springer
Golinski, J. 1970: Optimal synthesis problems solved by means of nonlinear programming and random methods.J. Mech. 5, 287–309
Hajela, P. 1990: Genetic search — an approach to the nonconvex optimization problem.AIAA J. 28, 1205–1210
Johnson, E.H. 1976: Disjoint design spaces in the optimization of harmonically excited structures.AIAA J. 14, 259–261
Kavlie, D.; Moe, J. 1971: Automated design of frame structures.J. Struct. Div., ASCE 97, 33–62
Levy, A.V.; Gomez, S. 1985: The tunneling method applied to global optimization. In: Boggs, P.T.; Byro, R.H. and Schnabel, R.B. (eds.)Numerical optimization, SIAM Conference, Philadelphia, USA
Mills-Curran, W.C.; Schmit, L.A. 1985: Structural optimization with dynamic behavior constraints.AIAA J. 23, 136–138
Moses, F.; Onoda, S. 1969: Minimum weight design of structures with application to elastic grillages.Int. J. Num. Meth. Eng. 1, 311–331
Ratschek, H.; Rukne, J. 1988:New computer methods for global optimization. New York: John Wiley
Rinnooy-Kan, A.; Timmer, G.T. 1986: Stochastic global optimization methods. Part I: clustering methods; Part II: multilevel methods.Math. Prog. 39, 27–78
Sepulveda, A.E.; Jin, I.M. 1992: Design of structure/control systems with transient response constraints exhibiting relative minima.Proc. 4th AIAA/USAF/NASA/OAI Symp. on Multidisciplinary Analysis and Optimization, AIAA-92-4736-CP (held in Cleveland OH), pp. 371–378
Sepulveda, A.E.; Schmit, L.A. 1993: Approximation-based global optimization strategy for structural synthesis.AIAA J. 31 180–188
Vanderplaats, G.N.; Hansen, S.R. 1989:DOT user's manual, version 2.04, Goleta, CA: VMA Engineering.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sepulveda, A.E., Epstein, L. The repulsion algorithm, a new multistart method for global optimization. Structural Optimization 11, 145–152 (1996). https://doi.org/10.1007/BF01197028
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01197028