An interactive multistage ε-inequality constraint method for multiple objectives decision making

Multiple objectives decision making (MODM) in engineering design refers to obtaining a preferred optimal solution in the context of conflicting design objectives. Problems with multiple objectives do not have a unique optimal solution but a set of Pareto optimal solutions. This paper presents a new interactive multistage MODM method which captures a decision maker's preference structure in order to obtain a preferred Pareto solution even for non-convex problems. Representative subsets of an entire Pareto optimal set are generated and expanded based on the decision maker's preference. The epsilon-constraint method is used to constrain the multiple objectives problem based on the decision maker's feedback. In addition, ideas from an interactive weighted Tchebycheff approach are applied to reduce the feasible region at each stage, ensuring that the process eventually converges to a preferred solution. The method is demonstrated with two examples: (i) a simple two-bar truss design, and (ii) a more complicated problem in power electronic module design.