Neighborhood Search Considering Continuous Space Search

A.T. Gómez, B.E.J. BODMANN

Abstract


The objective of this work is to present and discuss a dynamical optimization procedure based on the algorithm of self-consistent parametric inference, where the movement of one feasible solution to another is implemented in continuous mode. The approach is based on a generic parametrization of search space and uses the definition of a model independent metric, which guides progress of the procedure. One of the principal contributions of the proposed method is, if a solution is found it is optimal for the parametrization considered. This feature is guaranteed and proven by self consistency.

References


[1] A.T. Gómez, “Modelo para Seq¨uênciamento de Partes e Ferramentas em um Sistema de Manufatura Flexível com Restrições às Datas de Vencimento e a Capacidade do Magazine”, Ph.D. thesis, Instituto Nacional de Pesquisas Espaciais. São José dos Campos, SP, Brazil, 1996.

A.G. Rodrigues, A.T. Gómez, Utilização de metaheurísticas para a modelagem de problemas de seleção de partes e ”scheduling” em um sistema de manufatura flexível. Scientia, 11 (2000) 17-47.

B.E.J. Bodmann, A.T. Gómez, The self-consistent parametric inference algorithm (SPI): optimization in continuous search space, in “Proceedings of the International Conference on Industrial Engineering and Production Management”, IEPM’99 Book 1, pp. 66-77, 1999.

V.J. Rayward-Smith, I.H. Osman, C.R. Reeves and G.D. Smith, “Modern Heuristic Search Methods”, Wiley, Chichester, 1996.

G. Roepsdorff, “Path Integral Approach to Quantum Physics”, Springer Verlag, Berlin, Heidelberg, New York, 1996.

P.E. Hart, J. Nilsson, B. Raphael, A formal basis for the heuristic determination of minimum cost paths, IEEE Transactions on SSC, 4 (1968), 100-107. also SIGART Newsletter, 37 (1972) 28-29.

J.C. Furtado, “Algoritmo Genético Construtivo na Otimização de Problemas Combinatórias de Agrupamentos”, Ph.D Thesis, pp. 16-34, Instituto Nacional de Pesquisas Espaciais, São José dos Campos, SP, Brazil, 1998.

M. Tanner, “Tools for Statistical Inference”, Springer Verlag, New York, Berlin, Heidelberg, Tokyo, 1996.

G.B. Wetherill, “Intermediate Statistical Methods”, pp. 71-73, Chapman and Hall Ltd., London, New York, 1981.

R. Fletcher, “Practical Methods of Optimization”, Wiley & Sons, New York, 1987.

J. Kohlas, “Zuverl¨assigkeit und Verf¨ugbarkeit: Mathematische Modelle, Methoden und Algorithmen”, Teubner Verlag, Stuttgart, 1987.

J. Guddart, F. Guerra Vasquez, H. Jongen, “Parametric Optimization: Singularities, Pathfollowing and Jumps”, Teubner Verlag, Stuttgart, 1990.

E. Coffman, J. Lenstra, A. Rinnooy Kan, “Handbooks in Operation Research and Management Science”, Elsevier, Amsterdam, 1992.

L. Fould, “Graph Theory and Applications”, Springer Verlag, New York, 1992.

J. Aubin, “Optima and Equilibria”, Springer Verlag, Berlin, 1993.

M. Gr¨otschel, L. Lovász, A. Schrijver, “Geometric Algorithms and Combinatorial Optimization”, Springer Verlag, New York, 1993.

J. Hiriart-Urruty, C. Lemarchal, “Convex Analysis and Minimization Algorithms”, Springer Verlag, New York, 1993).

E. Kreyszig, “Introductory Functional Analysis with Applications”, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore, 1978.

J.B. Marion, S.T. Thornton, “Classical Dynamics of Particles and Systems”, pp. 225-227, Saunders College Publishing, San Diego, New York, 1995.




DOI: https://doi.org/10.5540/tema.2002.03.02.0111

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

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