Learning Regularity for Evolutionary Multiobjective Search: A Generative Model-Based Approach

The prior domain knowledge, i.e., the regularity property of continuous multiobjective optimization problems (MOPs), could be learned to guide the search for evolutionary multiobjective optimization. This paper proposes a learning-to-guide strategy (LGS) for assisting the search for multiobjective optimization algorithms in dealing with MOPs. The main idea behind LGS is to capture the regularity via learning techniques to guide the evolutionary search to generate promising offspring solutions. To achieve this, a generative model called the generative topographic mapping (GTM) is adopted to capture the manifold distribution of a population. A set of regular grid points in the latent space are mapped into the decision space within some manifold structures to guide the search for mating with some parents for offspring generation. Following this idea, three alternative LGS-based generation operators are developed and investigated, which combine the local and global information in the offspring generation. To learn the regularity more efficiently in an algorithm, the proposed LGS is embedded in an efficient evolutionary algorithm (called LGSEA). The LGSEA includes an incremental training procedure aimed at reducing the computational cost of GTM training by reusing the built GTM model. The developed algorithm is compared with some newly developed or classical learning-based algorithms on several benchmark problems. The results demonstrate the advantages of LGSEA over other approaches, showcasing its potential for solving complex MOPs.