Post Pareto-optimal ranking algorithm for multi-objective optimization using extended angle dominance

Abstract

Abstract This paper presents a solution ranking algorithm to find the outstanding solutions in given set of non-dominated solutions of multi-objective optimization problems, which are the results from either Multi-Objective Evolutionary Algorithms (MOEAs) or exact methods. The algorithm enables the decision makers to identify outstanding solutions without a deep understanding of the problem. The algorithm provides a ranking for all solutions so that they can obtain any top K ranked solutions to implement. This novel parameter-free solution ranking approach is based on two concepts: an extended angle-based dominance technique from the algorithm called ADaptive angle-based pruning Algorithm (ADA) for discovering the knee solutions and the inverse-square law of light for enhancing the diversity of solutions. We evaluate the performance of the approach on several well-known test problems against well-known knee finding algorithms as well as on a practical system design and optimization problem to demonstrate the usefulness of the algorithm.