Linear search mechanism for multi- and many-objective optimisation

Abstract

This article proposes a search mechanism based on linear combinations of population members to increase the solution quality of multi-objective and many-objective optimisation algorithms. Our approach makes use of the inherent knowledge in the solution population at a given time step, and forms new solutions through linear combinations of the existing ones. A population of coefficient vectors is formed and optimised by a metaheuristic to explore and exploit promising areas of the search space. In addition, our proposed method provides a reduction of dimensionality for large search spaces. The concept is formally introduced and implemented into a generic algorithm structure to be used in arbitrary metaheuristics. The experimental evaluation uses four multi- and many-objective algorithms (NSGA-II, GDE3, NSGA-III and RVEA) and is performed on a total of 60 test instances from three benchmark families with 2 to 5 objective functions and 30 to 514 decision variables. The results indicate that the performance of existing methods can be significantly improved by the proposed search strategy, especially in high-dimensional search spaces and for many-objective problems.