Three Approaches for Solving the Stochastic Multiobjective Programming Problem
In this paper, we consider the multiobjective optimization problem in which each objective function is disturbed by noise. Three approaches using learning automata, random optimization method, and stochastic approximation method are proposed to solve this problem. It is shown that these three approaches are able to find appropriate solutions of this problem. Several computer simulation results also confirm our theoretical study.
KeywordsStochastic Approximation Aspiration Level Multiobjective Optimization Problem Multiobjective Program Learning Automaton
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- Y.Y. Haimes, W.A. Hall, and H.F. Friedmann, Multiobjective Optimization in Water Resources Systems, The Surrogate Worth Trade-off Method, Elsevier Scientific, 1975.Google Scholar
- A.P. Wierzbicki, “The Use of Reference Objectives in Multiobjective Optimization. Theoretical Implications and Practical Experiences”, WP-79–66, IIASA, 1979.Google Scholar
- H. Nakayama and Y. Sawaragi, “Satisficing Trade-off Method for Multiobjective Programming”, Interactive Decision Analysis, Edited by A.P. Wierzbicki, pp.113–122, Springer-Verlag, 1984.Google Scholar
- J. Matyas, “Random Optimization”, Automation and Remote Control, Vol.28, pp.246–253, 1965.Google Scholar
- N. Baba, “Recent Developments in Learning Automata Theory and Their Applications”, Modelling and Simulation Methodology in the Artificial Intelligence Era, Edited by M.S. Elzas et al, North-Holland, 1986.Google Scholar
- N. Baba, “ε-optimal Nonlinear Reinforcement Scheme Under a Nonstationary Multiteacher Environment”, IEEE Trans. Systems, Man, and Cybernetics, Vol. 14, No.3, pp. 538–541, 1984.Google Scholar
- M.T. Wasan, Stochastic Approximations, Cambridge University Press, 1969.Google Scholar
- H.J. Kushner and D.S. Clark, Stochastic Approximation Methods for Constrained and Unconstrained Systems, Springer-Verlag, 1978.Google Scholar
- R.L. Kashyap, “Application of Stochastic Approximation”, in Adaptive Learning and Pattern Recognition Systems, J.M. Mendel and K.S. Fu, Editors, Academic Press, 1970.Google Scholar
- E.A. Nurminskii, “Convergence Conditions of Stochastic Programming Algorithms”, Cybernetics, No. 3, pp.464–468, 1973.Google Scholar
- A. Dvoretsky, “On Stochastic Approximation”, Proc. 3rd Berkeley Symp. on Math. Stat. and Probability I, pp.39–55, 1956.Google Scholar