Minimizing Expected Deviation in Upper Level Outcomes Due to Lower Level Decision Making in Hierarchical Multiobjective Problems

Many societal and industrial problem-solving tasks involving search, optimization, design, and management are conveniently decomposed into hierarchical subproblems. While this process allows a systematic procedure to have a multistakeholder solution, the independent decision-making process for the lower level problem causes a deviation in the expected outcome of the upper level problem. In this article, we provide a new and computationally efficient evolutionary approach allowing upper level decision makers to analyze the vagaries of lower level decision making when choosing a preferred solution with the minimum deviation from their expectations. This concept is novel and pragmatic. We demonstrate the concept through a search for optimistic–pessimistic tradeoff solutions found by an evolutionary multiobjective optimization approach first on two difficult test problems, then on a watershed management problem and a telecommunication management problem. The approach is generic and can be applied to similar hierarchical management problems to achieve minimum deviation with a more predictive and reliable outcome. The proposed solution procedure is found to choose an optimistic solution that has approximately 31%–65% reduced deviation compared to another optimistic solution chosen at random in the test problems and approximately 85%–95% reduced deviation in the two practical problems, making the method of this study applicable to practical hierarchical problems.