One-parameter Filled Function Method for Non-convex Multi-objective Optimization Problems

TL;DR

This paper introduces a novel one-parameter filled function method for nonlinear multi-objective optimization that efficiently approximates the global Pareto front without scalarization or preference assumptions.

Contribution

It adapts the filled function concept from single-objective optimization to multi-objective problems, enabling global Pareto front approximation in non-convex cases.

Findings

Effective in approximating the global Pareto front.

Avoids scalarization weights and preference ordering.

Demonstrated superior performance on test problems.

Abstract

In this paper, a new one-parameter filled function approach is developed for nonlinear multi-objective optimization. Inspired by key filled function ideas from single-objective optimization, the proposed method is adapted to the multi-objective setting. It avoids scalarization weights and does not impose any prior preference ordering among objectives. A descent-based procedure is first applied to obtain a local weak efficient solution. An associated filled function is then constructed and used to derive another local weak efficient solution that improves upon the current one. Repeating these phases drives the search toward global weak efficiency and yields an approximation of the global Pareto front, including in non-convex problems where multiple local Pareto fronts may exist. Numerical experiments on a set of test problems demonstrate the effectiveness of the proposed approach relative to existing methods.