An inverse model-guided two-stage evolutionary algorithm for multi-objective optimization

The estimation of distribution algorithm (EDA) is a kind of distinctive evolutionary algorithm that generates candidate solutions by directly sampling on distribution models. In this paper, we propose a distribution model-guided two-stage evolutionary algorithm for better solving multi-objective optimization problems (MOPs). To enhance modeling efficiency, the clustering method is employed to divide the population into multiple subpopulations. Then multivariate inverse models mapping from the objective space to the decision space are constructed by using a single decision variable and two objectives from each subpopulation. Then offspring are generated by randomly sampling the global and local objective space using the constructed inverse models. Moreover, a two-stage framework is proposed for better quality, i.e., convergence and diversity, of the solution set. In the first stage, exploration is mainly considered, during which the population converge rapidly. And exploitation is emphasized in the second stage, where the solution set is tuned by a replacement strategy. Experimental studies with several peer competitors on a set of widely-used benchmark MOPs as well as an engineering design MOP verify the competitiveness of the proposed method.