Is Selection All You Need in Differential Evolution?

TL;DR

This paper introduces Unbounded Differential Evolution (UDE), a novel approach that retains all candidates without discarding any, simplifying the algorithm and potentially enhancing search capabilities in black-box optimization.

Contribution

The paper proposes UDE, a new DE framework that eliminates population replacement and archive management, focusing solely on selection for improved simplicity and effectiveness.

Findings

UDE removes the need for population replacement and archive management.

UDE simplifies DE while maintaining or improving performance.

Experimental results show UDE's competitive or superior optimization capabilities.

Abstract

Differential Evolution (DE) is a widely used evolutionary algorithm for black-box optimization problems. However, in modern DE implementations, a major challenge lies in the limited population diversity caused by the fixed population size enforced by the generational replacement. Population size is a critical control parameter that significantly affects DE performance. Larger populations inherently contain a more diverse set of individuals, thereby facilitating broader exploration of the search space. Conversely, when the maximum evaluation budgets is constrained, smaller populations focusing on a limited number of promising candidates may be more suitable. Many state-of-the-art DE variants incorporate an archive mechanism, in which a subset of discarded individuals is preserved in an archive during generation replacement and reused in mutation operations. However, maintaining what is essentially a secondary population via an archive introduces additional design considerations, such as policies for insertion, deletion, and appropriate sizing. To address these limitations, we propose a novel DE framework called Unbounded Differential Evolution (UDE), which adds all generated candidates to the population without discarding any individual based on fitness. Unlike conventional DE, which removes inferior individuals during generational replacement, UDE eliminates replacement altogether, along with the associated complexities of archive management and dynamic population sizing. UDE represents a fundamentally new approach to DE, relying solely on selection mechanisms and enabling a more straightforward yet powerful search algorithm.