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Visualization of Pareto Optimal Solution Sets Using the Growing Hierarchical Self‐Organizing Maps
Author(s) -
SUZUKI NAOTO,
OKAMOTO TAKASHI,
KOAKUTSU SEIICHI
Publication year - 2017
Publication title -
electronics and communications in japan
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.131
H-Index - 13
eISSN - 1942-9541
pISSN - 1942-9533
DOI - 10.1002/ecj.11915
Subject(s) - visualization , computer science , set (abstract data type) , pareto optimal , pareto principle , self organizing map , transformation (genetics) , multi objective optimization , mathematical optimization , algorithm , data mining , mathematics , artificial intelligence , machine learning , artificial neural network , biochemistry , chemistry , gene , programming language
SUMMARY The visualization of the Pareto optimal solution set is one of important issues of the multiobjective optimization. The Pareto optimal solution visualization method using the self‐organizing maps is one of promising visualization methods. This method has two shortcomings. One is that the map size has to be determined in advance. The other is that infeasible solutions can appear in the learnt maps. This paper proposes a new visualization technique using the growing hierarchical SOM (GHSOM), which is expected to solve foregoing shortcomings. This paper also proposes to introduce a symmetric transformation of maps into the learning algorithm in order to obtain easily viewable unified map. The effectiveness of the proposed method is confirmed through several numerical experiments.