Hybridizing Hypervolume-Based Evolutionary Algorithms and Gradient Descent by Dynamic Resource Allocation

Abstract

Evolutionary algorithms (EAs) are well-known to be well suited for multi-objective (MO) optimization. However, especially in the case of real-valued variables, classic domination-based approaches are known to lose selection pressure when approaching the Pareto set. Indicator-based approaches, such as optimizing the uncrowded hypervolume (UHV), can overcome this issue and ensure that individual solutions converge to the Pareto set. Recently, a gradient-based UHV algorithm, known as UHV-ADAM, was shown to be more efficient than (UHV-based) EAs if few local optima are present. Combining the two techniques could exploit synergies, i.e., the EA could be leveraged to avoid local optima while the efficiency of gradient algorithms could speed up convergence to the Pareto set. It is a priori however not clear what would be the best way to make such a combination. In this work, therefore, we study the use of a dynamic resource allocation scheme to create hybrid UHV-based algorithms. On several bi-objective benchmarks, we find that the hybrid algorithms produce similar or better results than the EA or gradient-based algorithm alone, even when finite differences are used to approximate gradients. The implementation of the hybrid algorithm is available at https://github.com/damyha/uncrowded-hypervolume.