Interactive co-evolutionary multiple objective optimization algorithms for finding consensus solutions for a group of Decision Makers

Abstract

We introduce interactive algorithms for identifying consensus solutions to multiple objective optimization problems. They learn the Decision Makers’ (DMs’) preferences from indirect judgments and represent the recognized aspirations using scalar optimization goals. Their role is to set guidelines for the evolution and discovery of consensuses. The novelty of our proposals lies in co-evolving two populations: primary and supportive. The former’s role is to discover solutions relevant to the committee. The latter approximates the entire Pareto front, revealing a variety of trade-offs between objectives. The method improves the potential of conducting more informative interactions with the DMs and prevents the evolution from stagnation. Furthermore, it improves the evolutionary pace by dynamically removing no longer worthwhile goals from the supportive population in favor of increasing the primary population size. We confirm the importance of using co-evolution and dynamic resource allocation in extensive experiments. Also, we prove the competitiveness of our proposals by comparing them with the state-of-the-art methods on the WFG benchmarks. Finally, we demonstrate their practical usefulness when applied to the real-world problem of designing an environmentally friendly supply chain.