Post-Pareto Optimality Analysis to Efficiently Identify Promising Solutions for Multi-Objective Problems

Post-Pareto Optimality Analysis to Efficiently Identify Promising Solutions for Multi-Objective Problems Heidi A. Taboada and David W. Coit Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Rd. Piscataway, NJ 08854, USA ABSTRACT: Techniques have been developed and demonstrated to efficiently identify particularly promising solutions from among a Pareto-optimal set or sub-set. Multi-objective optimization problems can be solved by combining the objectives into a single objective, using utility theory, etc., or by determination of a Pareto-optimal set. This paper focuses on the second general approach. Pareto-optimal sets or representative sub-sets can be found by using a multiobjective evolutionary algorithm (MOEA) or by other means. Then, in practice, the decisionmaker ultimately has to select one solution from this set for system implementation. However, the Pareto-optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially if the number of objectives is large. Our research is focused on the post-Pareto analysis phase, and two methods are presented to intelligently filter or reduce the size of the Pareto-optimal set. The first method is pruning using non-numerical objective function ranking preferences. It is a pseudo-ranking scheme that assists the decision maker to select solutions that reflect his/her preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Paretooptimal set. The clustered data allows the decision maker to have just k general solutions to choose from, without using any objective function preference information. To demonstrate these methods, two multi-objective problems were analyzed, (1) the reservoir operating rules, and (2) the scheduling of the bottleneck operation of a Printed Wiring Board (PWB) manufacturing line.