A genetic algorithm approach for fuzzy goal programming formulation of chance constrained problems using stochastic simulation

Abstract

This paper presents how the stochastic simulation based genetic algorithm (GA) can be used to the fuzzy goal programming (FGP) formulation of a chance constrained multiobjective decision making (MODM) problem. In the proposed approach, a stochastic simulation to the chance constraints having the continuous random parameters is introduced first to determine the candidate solutions in the decision making context. Then, in the model formulation, the fuzzy goal descriptions of the objective are defined by employing the proposed GA method. In the solution process, achievement of the membership goals of the defined fuzzy goals to the highest membership value (unity) by minimizing the associated under-deviational variables to the extent possible by using the GA scheme is taken into consideration. A numerical example is solved and a comparison of the model solution with the conventional fuzzy programming (FP) approach is made to illustrate the potential use of the approach.