Data-Driven Evolutionary Multi-Objective Optimization Based on Multiple-Gradient Descent for Disconnected Pareto Fronts

TL;DR

This paper introduces a novel data-driven evolutionary multi-objective optimization algorithm based on multiple-gradient descent, effectively handling disconnected Pareto fronts and improving surrogate model utilization for expensive problems.

Contribution

It proposes a new EMO algorithm that leverages surrogate models and multiple-gradient descent to better optimize disconnected Pareto fronts with convergence guarantees.

Findings

Outperforms four peer algorithms on 33 benchmark problems with disconnected PFs.

Effectively explores disconnected Pareto fronts with improved distribution.

Provides convergence guarantees for the proposed method.

Abstract

Data-driven evolutionary multi-objective optimization (EMO) has been recognized as an effective approach for multi-objective optimization problems with expensive objective functions. The current research is mainly developed for problems with a 'regular' triangle-like Pareto-optimal front (PF), whereas the performance can significantly deteriorate when the PF consists of disconnected segments. Furthermore, the offspring reproduction in the current data-driven EMO does not fully leverage the latent information of the surrogate model. Bearing these considerations in mind, this paper proposes a data-driven EMO algorithm based on multiple-gradient descent. By leveraging the regularity information provided by the up-to-date surrogate model, it is able to progressively probe a set of well distributed candidate solutions with a convergence guarantee. In addition, its infill criterion recommends a batch of promising candidate solutions to conduct expensive objective function evaluations. Experiments on $33$ benchmark test problem instances with disconnected PFs fully demonstrate the effectiveness of our proposed method against four selected peer algorithms.