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.

[1]  Yacov Y. Haimes,et al.  Multiobjective optimization in water resources systems : the surrogate worth trade-off method , 1975 .

[2]  J. Cohon Multiobjective optimization in water resources systems , 1976 .

[3]  Norio Baba ∊-Optimal nonlinear reinforcement scheme under a nonstationary muititeacher environment , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Bernard P. Zeigler,et al.  Modelling and simulation methodology in the artificial intelligence era. , 1986 .

[5]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[6]  Manfred Grauer,et al.  Interactive Decision Analysis , 1984 .

[7]  E. A. Nurminskii Convergence conditions of stochastic programming algorithms , 1973 .

[8]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[9]  Arthur M. Geoffrion,et al.  An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department , 1972 .

[10]  N. Baba New Topics in Learning Automata Theory and Applications , 1985 .

[11]  M. T. Wasan Stochastic Approximation , 1969 .

[12]  Y. Ermoliev Stochastic quasigradient methods and their application to system optimization , 1983 .

[13]  Hirotaka Nakayama,et al.  Satisficing Trade-off Method for Multiobjective Programming , 1984 .

[14]  Kumpati S. Narendra,et al.  Learning Automata - A Survey , 1974, IEEE Trans. Syst. Man Cybern..

[15]  Harold J. Kushner,et al.  wchastic. approximation methods for constrained and unconstrained systems , 1978 .

[16]  A. Dvoretzky On Stochastic Approximation , 1956 .