Minimizing Expected Deviation in Upper-level Outcomes Due to Lower-level Decision-making in Hierarchical Multi-objective Optimization Problems

—Many societal and industrial problem solving tasks involving search, optimization, design and management, are conveniently decomposed into hierarchical sub- problems. While the process allows a systematic procedure to have a multi-stakeholder solution, an independent decision- making process for the lower-level problem causes a deviation in expected outcome at the upper-level problem. In this paper, we provide a new and computationally efficient evolutionary approach for the upper-level decision-makers to analyze vagaries of lower-level decision-making for choosing a preferred solution with the minimum deviation from their expectations. The concept is novel and pragmatic. We demonstrate the concept through a search for optimistic-pessimistic trade-off solutions found by an evolutionary multi-objective optimization approach first on two difficult test problems, followed by a watershed management problem, and a telecommunication management problem. The approach is generic and can be applied to other similar hierarchical management problems for achieving minimum deviation with a more predictive and reliable outcome. The proposed solution procedure is found to choose an optimistic solution causing about 31% to 65% reduced deviation compared to another optimistic solution chosen at random in test problems and about 85% to 95% in two practical problems, making such a study worthy for practical hierarchical problems.