A Pareto optimal solution visualization method using SOM-NG with learning parameter optimization

Abstract

The visualization of the Pareto optimal solution set is one of important issues of the decision-making process on the multi-objective optimization problem. The Pareto optimal solution visualization method using the self-organizing maps (SOM) is one of promising visualization methods. This method has two shortcomings in the Pareto optimal solution representation capability. One is that the maps have incorrect points that represent non-Pareto optimal solutions. The other is that the coverage of the maps for the edge region of the Pareto optimal solution set is not good. This study proposes a Pareto optimal solution visualization method using SOM-NG. In SOM, winner nodes affect neighbor nodes on the map space irrespective of similarity on the input data space. This causes the above-mentioned shortcomings. SOM-NG can form maps with considering similarity on the input space; hence, the shortcomings are expected to be overcome. In addition, in the proposed method, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed on the incorrectness and the coverage of maps through numerical experiments.