A regularity augmented evolutionary algorithm with dual-space search for multiobjective optimization

Abstract

The well-known regularity property allows the Pareto optimal solutions of a multiobjective optimization problem (MOP) to be embedded in some latent spaces by the manifold structure of the Pareto optimal set. This paper proposes an efficient regularity augmented evolutionary algorithm (RAEA) for multiobjective optimization, which aims to adopt such latent spaces for use with offspring generations. In this algorithm, a singular value decomposition method is adopted at each iteration to extract such latent space from the population with the regularity property. The enhancements of regularity in RAEA include: (1) an acceleration of convergence by incrementally projecting the dominated solutions into the latent space built with elite solutions (i.e., the non-dominated solutions); and (2) a novel dual-space search strategy (DSS) is developed for the generation of promising offspring solutions by searching in both latent and decision space. The developed algorithm was empirically compared with five well-known multiobjective evolutionary algorithms on several complicated MOP test suites. Experimental results suggest that RAEA outperforms the compared algorithms on these test instances in terms of two commonly-used indicators. Both the effectiveness of the convergence acceleration scheme and the developed dual-space searching strategy are also empirically validated.