A novel model-based multi-objective evolutionary algorithm

Abstract

In multi-objective evolutionary algorithm (MOEA), modelling method is a crucial part. Moreover, variable linkages enable the modelling process more complex for multi-objective optimisation problems. The Karush-Kulm-Tucker condition shows that the Pareto set of a continuous MOP with m objectives is a piecewise continuous (m-1)-dimensional manifold. How to use this regularity property to model continuous MOP with variable linkages has been the research focus. In this paper, a model-based multi-objective evolutionary algorithm based on regression analysis (MMEA-RA) for continuous multi-objective optimisation problems with variable linkages is put forward. In the algorithm, the optimisation problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m-1)-dimensional piecewise continuous manifold. The least squares algorithm is used to build such a model. Systematic experiments have shown that, compared with two state-of-the-art algorithms, MMEA-RA performs excellent on a set of test instances with variable linkages.