Global Descent Method for Non-convex Multi-objective Optimization Problems

TL;DR

This paper introduces a global descent method for non-convex multi-objective optimization that can generate the entire Pareto front without relying on predefined scalarizations, demonstrated through extensive numerical experiments.

Contribution

It extends single-objective global descent techniques to multi-objective problems, enabling systematic convergence to the global Pareto front without prior scalarization or ordering.

Findings

Method successfully generates the global Pareto front.

Demonstrates robustness and scalability on benchmark problems.

Effective in finding multiple local Pareto fronts.

Abstract

In this paper, we develop a global descent method for non-convex multi-objective optimization problems. The proposed approach builds upon foundational concepts from single-objective global descent techniques while removing the need for predefined scalars or ordering information of objective functions. Initially, the proposed method identifies a local weak efficient solution using any suitable descent algorithm, then applies an auxiliary function termed the multi-objective global descent function to systematically transition toward improved local weak efficient solutions. It is justified that this method can generate a global Pareto front for non-convex problems, which has many different local Pareto fronts. Finally, comprehensive numerical experiments on benchmark non-convex multi-objective optimization problems have been done to demonstrate the method's robustness, scalability and effectiveness of the proposed method.