Improved Sampling of Decision Space for Pareto Estimation

Pareto Estimation (PE) is a novel method for increasing the density of Pareto optimal solutions across the entire Pareto Front or in a specific region of interest. PE identifies the inverse mapping of Pareto optimal solutions, namely, from objective space to decision space. This identification can be performed using a number of modeling techniques, how- ever, for the sake of simplicity in this work we use a radial basis neural network. In any modeling method, the quality of the resulting model depends heavily on the training samples used. The original version of PE uses the result- ing set of Pareto optimal solutions from any multi-objective optimization algorithm and then utilizes this set to identify the aforementioned mapping. However, we argue that this selection may not always be the best possible and propose an alternative scheme to improve the resulting set of Pareto optimal solutions in order to produce higher quality samples for the identification scheme in PE. The proposed approach is integrated with MAEA-gD, and the resulting solutions are used with PE. The results show that the proposed method shows promise, in that there is measurable improvement in the quality of the estimated PE in terms of the coverage and density.