Improved Front Steepest Descent for Multi-objective Optimization

TL;DR

This paper enhances the Front Steepest Descent algorithm for multi-objective optimization by introducing modifications that improve Pareto front coverage while maintaining convergence, demonstrated through theoretical proofs and numerical experiments.

Contribution

The paper proposes modifications to the existing algorithm to better span the Pareto front without losing convergence properties.

Findings

Modified algorithm covers larger Pareto front regions

The new method preserves asymptotic convergence

Numerical results show significant performance improvement

Abstract

In this paper, we deal with the Front Steepest Descent algorithm for multi-objective optimization. We point out that the algorithm from the literature is often incapable, by design, of spanning large portions of the Pareto front. We thus introduce some modifications within the algorithm aimed to overcome this significant limitation. We prove that the asymptotic convergence properties of the algorithm are preserved and numerically show that the proposed method significantly outperforms the original one.