Minimizing a function of order p using a genetic algorithm
Keywords:
Genetic algorithms, nonlinear programming, order value optimizationAbstract
In this work we consider the problem OVO (order value optimization), where m given continuous functions f1; :::; fm, defined on a domain 2 Rn and an integer p 2 f1; :::;mg, the function of order p with p m, is given by f(x) = fip(x)(x), for all x 2 , where ip(x) is a function satisfying fi1(x)(x) fi2(x)(x) ::: fip(x)(x) ::: fim(x)(x): The problem we address is to minimize f with x 2 by a genetic algorithm that by its very nature has the advantage over existing continuous optimization methods, to find global minimizers. We illustrate the application of this algorithm on examples considered showing its efectiveness in solving them.
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Andreani R., Dunder C. y Martíinez J. M., Order-Value Optimization: formulation and solution by means of a primal Cauchy Method, Mathematical Methods of Operation research 58, , (2003), pp. 387{ 399.
Andreani R., Martínez J. M., Martínez L. y Yano F., Low the Order- Value Optimization and aplications, Technical Report, Institute of Mathematics, University of Campinas, Brasil, (2007).
Andreani R., Martínez J. M., Salvatierra M. y Yano F., Quasi-Newton Methods for Order-Value Optimization and Value-at-Ristk, Pacic Journal of Optimization 2, pp. 11-33, (2006).
Andreani R., Martínez J. M., Martínez L. y Yano F. S, Low Order- Value Optimization and new applications. Journal of Global Optimization 43, pp. 1-10 (2009).
Bertsekas D., Nonlinear Programming: 2da Edition, Athena Scientic, (1999).
Birgin E. G., Bueno L. F., Krejic N. y Martínez J. M., Low Order- Value Approach for Solving VaR-Constrained Optimization Problems, Journal of Global Optimization 51, pp. 715-742, (2011).
Christian D. von Lucken M., Msc.Thesis. Algoritmos Evolutivos para Optimización Multiobjetivo. Universidad de la Asunción. Paraguay. (2003).
Coello C., Introducción a la computación Evolutiva. IEEE Computational Intelligence, vol. 1, No. 1, pp 28-36, (2006).
Deb K. Multi-objetive Optimization Using Evolutionary Algorithms. John Wiley & Sons, Inc., New York, NY.(2001).
Goldberg, D.E. , Genetic Algorithms in Search, Optimization and Ma- chine Learning. Addison-Wesley Longman Publishing Co. Inc., Boston, MA, USA. (1989).
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