RegEMO: Sacrificing Pareto-Optimality for Regularity in Multi-objective Problem-Solving

Abstract

Multi-objective optimization problems give rise to a set of Pareto-optimal (PO) solutions, each of which makes a certain trade-off among objectives. When multiple PO solutions are to be considered for different scenarios as platform-based solutions, a common structure in them, if available, is highly desired for easier understanding, standardization, and management purposes. In this paper, we propose a modified optimization methodology to avoid converging to theoretical PO solutions having no common structure and converging to a set of near-Pareto solutions having simplistic common principles with regularity where the common principles are extracted from the PO solutions in an automated fashion. After proposing the methodology, we first demonstrate its working principle on a number of constrained and unconstrained multi-objective test problems. Thereafter, we demonstrate the practical significance of the proposed approach to a number of popular engineering design problems. Searching for a set of solutions with regularity-based principles for different platforms is a practically important task. This paper should encourage more similar algorithmic developments in the near future.