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.

[1]  Kaisa Miettinen,et al.  Visualizing the Pareto Frontier , 2008, Multiobjective Optimization.

[2]  Hisao Ishibuchi,et al.  Many-objective and many-variable test problems for visual examination of multiobjective search , 2013, 2013 IEEE Congress on Evolutionary Computation.

[3]  Takashi Okamoto,et al.  Optimal Design of Buffer Material in the Geological Disposal of Radioactive Wastes Using the Satisficing Trade‐off Method and a Self‐Organizing Map , 2014 .

[4]  Christian Fonteix,et al.  Multicriteria optimization using a genetic algorithm for determining a Pareto set , 1996, Int. J. Syst. Sci..

[5]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[6]  Xavier Gandibleux,et al.  Metaheuristics for Multiobjective Optimisation , 2004, Lecture Notes in Economics and Mathematical Systems.

[7]  Xavier Blasco Ferragud,et al.  A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization , 2008, Inf. Sci..

[8]  Olga Kurasova,et al.  Visualization of Pareto Front Points when Solving Multi-objective Optimization Problems , 2013, Inf. Technol. Control..

[9]  Teuvo Kohonen,et al.  Self-organized formation of topologically correct feature maps , 2004, Biological Cybernetics.

[10]  Yutaka Matsuo,et al.  A self organizing document map algorithm for large scale hyperlinked data inspired by neuronal migration , 2011, WWW.

[11]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[12]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[13]  Miguel J. Bagajewicz,et al.  Pareto Optimal Solutions Visualization Techniques for Multiobjective Design and Upgrade of Instrumentation Networks , 2003 .

[14]  Takashi Okamoto,et al.  Analysis and Improvements of the Pareto Optimal Solution Visualization Method Using the Self-Organizing Maps , 2015 .

[15]  Daisuke Sasaki,et al.  Visualization and Data Mining of Pareto Solutions Using Self-Organizing Map , 2003, EMO.

[16]  Ofer M. Shir,et al.  Self-organizing maps for multi-objective pareto frontiers , 2013, 2013 IEEE Pacific Visualization Symposium (PacificVis).