The Importance of Diversity in the Variable Space in the Design of Multi-Objective Evolutionary Algorithms

Most current Multi-Objective Evolutionary Algorithms (mOEAs) do not directly manage the population's diversity in the variable space. Usually, these kind of mechanisms are only considered in Evolutionary Multimodal Multi-Objective Algorithms (EmmAs) which aim to obtain a complete representation of the set of - locally or globally - optimal solutions in variable space. This is a remarkable difference with respect to single-objective optimizers, where maintaining diverse solutions is considered favorable to better explore the search space. The contribution of this research is to show that the quality of current mOEAs in terms of objective space metrics can be enhanced by integrating mechanisms to explicitly manage the diversity in the variable space. The key is to consider the stopping criterion and elapsed period in order to dynamically alter the importance granted to the diversity in the variable space and to the quality and diversity in the objective space, which is an important difference with respect to EmmAs. Specifically, more importance is given to the variable space in the initial phases and, decisions are progressively more biased by the information of the objective space as the evolution progresses. This paper presents a novel mOEA based on decomposition (Avsd-mOEA/d) that relies on these principles by means of a novel replacement phase. Extensive experimentation shows the clear benefits provided by the proposed design principle.(c) 2023 Elsevier B.V. All rights reserved.