Keywords
heuristics
combinatorial optimization
How to Cite
Abstract
This paper presents an innovating Monte Carlo method for exploring n-dimensional non-linear functions defined in a compact domain which is transformed to the hypercube [0;1]n. This approach uses the beta distribution for generating random samples. Te distribution parameters, named Alpha and beta, are dynamically adjusted so that, in the first iterations, the beta distribution looks like the uniform distribution. ; in the last iterations, the beta distribution is centered in the known minimum and the variance is near zero, so that only the neighborhood around the optimum is sampled. The method proposed is tested through four well known benchmark functions.
BAZARAA, M.; SHERALI, H. y SHETTY, C.M. Nonlinear optimization. New Jersey: Wiley, 2006.
BEYER, H. y SCHWEFEL, H. Evolution strategies. Natural Computing. 2002, vol. 1, núm. 1, pp. 3-52.
DIXON, L. C. W. y SZEGÖ, G. P. (eds.). Towards global optimization, parts 1 and 2. Amsterdam: North-Holland, 1978.
DUGAN, N. y ERKOÇ, Ş. Genetic algorithm–Monte Carlo hybrid geometry optimization method for atomic clusters. Computational Materials Science. 2009, vol. 45, núm. 1, pp. 127-132.
HIMMENLBLAU, D. Applied nonlinear optimization. New York: McGraw Hill, 1972.
KADRI, O.; GHARBI, F. y TRABELSI, A. Monte Carlo optimization of some parameters in gamma irradiation processing. Nuclear Instruments and Methods in Physics Research. 2006, vol. 245, núm. 2, pp. 459-463.
KIRKPATRICK, S.; GELATT, C.D. y VECCHI, M.P. Optimization by simulated annealing. Science. 1983, vol. 220, núm. 4598, pp. 671-680.
LEI, G. Adaptive random search in Quasi-Monte Carlo methods for global optimization. Computers & Mathematics with Applications. 2002, vol. 43, núms. 6-7, pp. 747-754.
PARDALOS, P. M. y RESENDE, M. G. C. (eds.). Handbook of applied optimization. New York: Oxford University Press, 2002.
PATEL, N. R.; SMITH, R. L. y ZABINSKY, Z. B. Pure adaptive search in Monte Carlo optimization. Mathematical Programming. 1988, vol. 43, pp. 317-328.
PIERRE, D. A. Optimization theory with application. New York: Dover, 1986.
RAO, S. Engineering optimization, theory and practice. London: Wiley, 1996.
REN, Y.; DING, Y. y LIANG, F. Adaptive evolutionary Monte Carlo algorithm for optimization with applications to sensor placement problems. Statistics and Computing. 2008, vol. 18, núm. 4, pp. 375-390.
RIABOV, G. A.; RIABOV, V. G. y TVERSKOY, M. G. Application of Monte-Carlo method for design and optimization of beam lines. Nuclear Instruments and Methods in Physics Research. 2006, vol. 558, núm. 1, pp. 44-46.
RINNOOY KAN, A. H. G. y TIMMER, G. T. Stochastic methods for global optimization. American Journal of Mathematical and Management Sciences. 1984, vol. 4, pp. 7-39.
TÖRN, A. y ZILINSKAS, A. Global optimization. Lecture Notes in Computer Science. 1989, vol. 350, pp. 1-255.
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