Regularity Evolution for Multiobjective Optimization

Recent years have witnessed the repaid progress in developing and applying multiobjective evolutionary algorithms (MOEAs). However, as a major component of an MOEA, the offspring generator has been largely overlooked, lacking a principle to design generators. This article addresses this issue by introducing an offspring generation paradigm, called regularity evolution (RE), for MOEAs. RE assumes that a solution consists of two parts: 1) a structure vector and 2) a perturbation vector. The former represents the manifold structure learned from the population, in accordance with the regularity property of multiobjective optimization problems, while the latter represents the noise or uncertainty that can be embedded in the learned manifold structure. With the RE paradigm, we can explain and improve some existing generation operators, e.g., the regularity model-based generators, and furthermore, design new generators by proposing alternative ways to construct structure or perturbation vectors. The systematic studies with comparisons on popular generation operators and newly developed MOEAs indicate that the RE paradigm has significant superiority in offspring generation for multiobjective optimization.