Summary
A variation of an adaptive random search algorithm for the optimization of functions of continuous variables is presented. The scheme does not require any assumptions about the function to be optimized, apart from the availability of evaluations at selected test points. The main design criterion of the Reactive Affine Shaker (RASH) scheme consists of the adaptation of a search region by an affine transformation. The modification takes into account the local knowledge derived from trial points generated with a uniform probability in the search region. The aim is to scout for local minima in the attraction basin where the initial point falls, by adapting the step size and direction to maintain heuristically the largest possible movement per function evaluation. The design is complemented by the analysis of some strategic choices, like the double-shot strategy and the initialization, and by experimental results showing that, in spite of its simplicity, RASH is a promising building block to consider for the development of more complex optimization algorithms.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Battiti, R., Tecchiolli, G.: Learning with first, second and no derivatives: A case study in high energy physics. Neurocomp. 6, 181–206 (1994)
Battiti, R., Tecchiolli, G.: The reactive tabu search. ORSA Journal on Computing 6(2), 126–140 (1994)
Brunelli, R., Tecchiolli, G.: On random minimization of functions. Biological Cybernetics 65(6), 501–506 (1991)
Chelouah, R., Siarry, P.: Tabu search applied to global optimization. European Journal of Operational Research 123, 256–270 (2000)
Corana, A., Marchesi, M., Martini, C., Ridella, S.: Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans. Math. Softw. 13(3), 262–280 (1987)
Dixon, L.C.W., Szegő, G.P. (eds.): Towards Global Optimization 2. North-Holland, Amsterdam (1978)
Glover, F.W., Kochenberger, G.A.: Handbook of Metaheuristics. International Series in Operations Research and Management Science, vol. 57. Kluwer Academic Publishers, Norwell (2003)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Kluwer Academic Publishers, Boston (1989)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1-2), 43–62 (2001)
Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. ACM 8(2), 212–229 (1961)
Hoos, H.H., Stützle, T.: Stochastic Local Search Foundations and Applications. Morgan Kaufmann / Elsevier (2004)
Pardalos, P.M., Resende, M.G.C. (eds.): Handbook of Applied Optimization. Oxford University Press, NY, USA (2002)
Siarry, P., Berthiau, G., Durbin, F., Haussy, J.: Enhanced simulated annealing for globally minimizing functions of many-continuous variables. ACM Transactions on Mathematical Software 23(2), 209–228 (1997)
Solis, F.J., Wets, R.J.-B.: Minimization by random search techniques. Mathematics of Operations Research 6(1), 19–30 (1981)
Tsoi, A.C., Lim, M.: Improved simulated annealing technique. In: Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Piscataway, NJ (USA), pp. 594–597. IEEE Press, Los Alamitos (1988)
Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Brunato, M., Battiti, R. (2008). RASH: A Self-adaptive Random Search Method. In: Cotta, C., Sevaux, M., Sörensen, K. (eds) Adaptive and Multilevel Metaheuristics. Studies in Computational Intelligence, vol 136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79438-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-79438-7_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79437-0
Online ISBN: 978-3-540-79438-7
eBook Packages: EngineeringEngineering (R0)