Title: Decomposition gradient descent method for bi-objective optimisation

Authors: Jingjing Chen; Genghui Li; Xi Lin

Addresses: Department of Computer Science, City University of Hong Kong, Hong Kong, China ' School of System Design and Intelligent Manufacturing, Southern University of Science and Technology, Shenzhen, 518055, China ' Department of Computer Science, City University of Hong Kong, Hong Kong, China

Abstract: Population-based decomposition methods decompose a multi-objective optimisation problem (MOP) into a set of single-objective subproblems (SOPs) and then solve them collaboratively to produce a set of Pareto optimal solutions. Most of these methods use heuristics such as genetic algorithms as their search engines. As a result, these methods are not very efficient. This paper investigates how to do a gradient search in multi-objective decomposition methods. We use the NBI-style Tchebycheff method to decompose a MOP since it is not sensitive to the scales of objectives. However, since the objectives of the resultant SOPs are non-differentiable, they cannot be directly optimised by the classical gradient methods. We propose a new gradient descent method, decomposition gradient descent (DGD), to optimise them. We study its convergence property and conduct numerical experiments to show its efficiency.

Keywords: multi-objective optimisation; decomposition strategy; NBI-style Tchebycheff method; gradient descent method.

DOI: 10.1504/IJBIC.2024.136218

International Journal of Bio-Inspired Computation, 2024 Vol.23 No.1, pp.28 - 38

Received: 17 Nov 2022
Accepted: 06 Jan 2023
Published online: 22 Jan 2024 *