An algorithm for solving multi-stage decision making model with multiple fuzzy goals based on genetic algorithms

In this paper, we introduce a goal programming (GP) procedure for solving problems with multiple fuzzy goal programming (FGP) using dynamic programming (DP) based on genetic algorithm (GA). Also this paper describe how the preemptive priority based GP can be used to solve a class of fuzzy programming (FP) problems with the characteristics of DP. In this proposed algorithm, the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first. Then, under the framework of preemptive priority based GP a multi - stage DP model of the problem, can be solved by GA, for achievement of the highest degree (unity) of each of the membership functions is developed. The main advantage of using GA to solve a preemptive priority multi - stage DP model is to overcome the curse of dimensionality in DP problem by increasing state space variables and the system of constraints. In the decision process, the goal satisficing philosophy of GP is used recursively (bases on GA) to arrive at the most satisfactory solution. A real - coded GAs is proposed to deal with the solution procedure in this paper. Finally, an illustrative numerical examples are provided to clarify the main results in this paper.