Machine Learning-Based Prediction of New Pareto-Optimal Solutions From Pseudo-Weights
Anirudh Suresh, Kalyanmoy Deb
Abstract
Owing to the stochasticity of Evolutionary Multi-objective Optimization (EMO) Algorithms and an application with a limited budget of solution evaluations, a perfectly converged and uniformly distributed Pareto-optimal (PO) front cannot be always guaranteed. Thus, a subsequent decision-making step or a curiosity on the part of the optimization researcher may demand solutions at regions not well-represented by the obtained PO front. In this study, we propose to train Machine Learning (ML) models to capture the mapping between unique identifiers of PO solutions – pseudo-weight vectors, computed from the existing PO front data, and their corresponding decision variable vectors. These learned models can then be used to predict PO decision variables for any new desired pseudo-weight vector. We evaluate the proposed approach with two different ML methods on a variety of multi-and many-objective test and real-world problems. This procedure can also be incorporated into an EMO algorithm to find a better converged set of PO solutions, attempt to fill apparent gaps, and find more non-dominated solutions at preferred regions of the PO front, facilitating a number of key advances for multi-objective optimization and decision-making tasks.