An Interactive Fuzzy Satisficing Method for Multiobjective Stochastic Integer Programming Problems through a Probability Maximization Model

In this paper, we deal with multiobjective integer programming problems involving random variable coefficients in objective functions and/or constraints. After reformulation of them on the basis of a probability maximization model for the chance constrained programming, incorporating fuzzy goals of the decision maker for the objective functions, we propose an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker using genetic algorithms as a fusion of the stochastic programming and the fuzzy one.

[1]  I. M. Stancu-Minasian,et al.  Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions , 1990 .

[2]  Masatoshi Sakawa,et al.  Genetic Algorithms and Fuzzy Multiobjective Optimization , 2001 .

[3]  J. Teghem,et al.  STRANGE: an interactive method for multi-objective linear programming under uncertainty , 1986 .

[4]  C. Mohan,et al.  An interactive satisficing method for solving multiobjective mixed fuzzy-stochastic programming problems , 2001, Fuzzy Sets Syst..

[5]  Masatoshi Sakawa,et al.  An Interactive Satisficing Method through the Variance Minimization Model for Fuzzy Random Multiobjective Linear Programming Problems , 2003 .

[6]  H. Zimmermann.  Fuzzy programming and linear programming with several objective functions , 1978 .

[7]  Masahiro Inuiguchi,et al.  Fuzzy multiobjective combinatorial optimization through revised genetic algorithms , 1994 .

[8]  Zbigniew Michalewicz,et al.  Genetic algorithms + data structures = evolution programs (3rd ed.) , 1996 .

[9]  坂和 正敏.  Fuzzy sets and interactive multiobjective optimization , 1993 .

[10]  坂和 正敏.  Genetic algorithms and fuzzy multiobjective optimization , 2002 .

[11]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[12]  David E. Goldberg,et al.  Alleles, loci and the traveling salesman problem , 1985 .

[13]  Richard Bellman,et al.  Decision-making in fuzzy environment , 2012 .

[14]  J. Leclercq.  Stochastic programming: An interactive multicriteria approach , 1982 .

[15]  Sam Kwong,et al.  Genetic algorithms and their applications , 1996, IEEE Signal Process. Mag..

[16]  John J. Grefenstette,et al.  Genetic Algorithms for the Traveling Salesman Problem , 1985, ICGA.

[17]  I. Nishizaki,et al.  An interactive fuzzy satisficing method for multiobjective stochastic linear programs through simple recourse model , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[18]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[19]  M. Sakawa,et al.  Fuzzy programming for multiobjective 0–1 programming problems through revised genetic algorithms , 1997 .