MCDM, EMO and Hybrid Approaches: Tutorial and Review

Most of the practical applications that require optimization often involve multiple objectives. These objectives, when conflicting in nature, pose both optimization as well as decision-making challenges. An optimization procedure for such a multi-objective problem requires computing (computer-based search) and decision making to identify the most preferred solution. Researchers and practitioners working in various domains have integrated computing and decision-making tasks in several ways, giving rise to a variety of algorithms to handle multi-objective optimization problems. For instance, an a priori approach requires formulating (or eliciting) a decision maker’s value function and then performing a one-shot optimization of the value function, whereas an a posteriori decision-making approach requires a large number of diverse Pareto-optimal solutions to be available before a final decision is made. Alternatively, an interactive approach involves interactions with the decision maker to guide the search towards better solutions (or the most preferred solution). In our tutorial and survey paper, we first review the fundamental concepts of multi-objective optimization. Second, we discuss the classic interactive approaches from the field of Multi-Criteria Decision Making (MCDM), followed by the underlying idea and methods in the field of Evolutionary Multi-Objective Optimization (EMO). Third, we consider several promising MCDM and EMO hybrid approaches that aim to capitalize on the strengths of the two domains. We conclude with discussions on important behavioral considerations related to the use of such approaches and future work.