Visualization of Pareto optimal solutions using MIGSOM

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 study 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. However, this method has shortcomings in its solution representation capability. This study proposes a new Pareto optimal solution visualization method using MIGSOM. The MIGSOM is one of the self-organizing algorithms inspired by the neuronal migration. In the MIGSOM algorithm, all input data directly migrate in the projection map space so as to form a suitable map. This direct migration is expected to contribute to the improvements of the solution representation capability. Three improvements are introduced for the application of MIGSOM to the visualization. The effectiveness of the proposed method is confirmed through comparisons to the visualization method using conventional MIGSOM.