Feasibility reduction approach for hierarchical decision making with multiple objectives

Several decision making problems with multiple decision makers in a hierarchical decision making scenario can be best described using multilevel optimization problem. Different organizational structure adapt a hierarchical decision making system where each decision maker controls parts of the decision variables and is affected by the decision of other decision makers. Recently, inspired by natural adaptation, a metaheuristic based algorithm is proposed for these problems. The algorithm works by using an initial solution generated by solving the leader's problem, where the leader is the decision maker in the upper level. That solution will go through each level by adjusting and evolving its components. Even though the approach is tested to be promising, the final solution can be very different from the initial one given by the leader. Furthermore, no cooperation mechanism between the decision makers is given. In addition, the decision makers may have multiple and conflicting objectives. In this paper a cooperation mechanism where fuzzy membership function is used to link the cooperation between the decision makers is used. That means once the solution received by the lower level decision makers, a cooperative feasible region will be determined which is a subset of the relaxed feasible region. To deal with the multiobjective optimization problem, preference free method called ideal point method will be used. Bi-level numerical examples are also given to demonstrate how the algorithm works.