Analysis and Improvements of the Pareto Optimal Solution Visualization Method Using the Self-Organizing Maps
Atsushi Hironaka, Takashi Okamoto, Seiichi Koakutsu, Hironori Hirata · SICE Journal of Control Measurement and System Integration · 2015
In the multi-objective optimization problem that appears naturally in the decision making process for the complex system, the visualization of the innumerable solutions called Pareto optimal solutions is important issue. This paper focuses on the Pareto optimal solution visualization method using the self-organizing maps which is one of promising visualization methods. The method has advantages in grasping the overall structure of the solutions and comparing the objective functions simultaneously. This method has been applied to some real problems, but its solution representation capability has not been studied well. This paper investigates the solution representation capability of the Pareto optimal solution visualization method using the SOM and points out its shortcomings. Then, two improvements are introduced to the visualization method. The effectiveness of the proposed method is confirmed via comparing it to the conventional visualization method using three indices evaluating the solution representation capability.