A generalized varying-domain optimization method for fuzzy goal programming with priorities based on a genetic algorithm

This paper proposes a generalized domain optimization method for fuzzy goal programming with different priorities. According to the three possible styles of the objective function, the domain optimization method and its generalization are correspondingly proposed. This method can generate the results consistent with the decision-maker's priority expectations, according to which the goal with higher priority may have higher level of satisfaction. However, the reformulated optimization problem may be nonconvex for the reason of the nature of the original problem and the introduction of the varying-domain optimization method. It is possible to obtain a local optimal solution for nonconvex programming by the SQP algorithm. In order to get the global solution of the new programming problem, the co-evolutionary genetic algorithm, called GENOCOP III, is used instead of the SQP method. In this way the decision-maker can get. the optimum of the optimization problem. We demonstrate the power of this proposed method based on genetic algorithm by illustrative examples.