Modelling the Population Distribution in Multi-objective Optimization by Generative Topographic Mapping

Under mild conditions, the Pareto set of a continuous multi-objective optimization problem exhibits certain regularity. We have recently advocated taking into consideration such regularity in designing multi-objective evolutionary algorithms. Following our previous work on using Local Principal Component Analysis for capturing the regularity, this paper presents a new approach for acquiring and using the regularity of the Pareto set in evolutionary algorithms. The approach is based on the Generative Topographic Mapping and can be regarded as an Estimation of Distribution Algorithm. It builds models of the distribution of promising solutions based on regularity patterns extracted from the previous search, and samples new solutions from the models thus built. The proposed algorithm has been compared with two other state-of-the-art algorithms, NSGA-II and SPEA2 on a set of test problems.