Visualization of Pareto Optimal Solution Sets Using the Growing Hierarchical Self-Organizing Maps

2016 ◽  
Vol 100 (1) ◽  
pp. 3-17
Author(s):  
NAOTO SUZUKI ◽  
TAKASHI OKAMOTO ◽  
SEIICHI KOAKUTSU
Keyword(s):  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Self Organizing Maps ◽  
Solution Sets ◽  
Self Organizing

A Pareto Optimal Solution Visualization Method Using an Improved Growing Hierarchical Self-Organizing Maps Based on the Batch Learning

2016 ◽  
Vol 20 (5) ◽  
pp. 691-704
Author(s):  
Naoto Suzuki ◽  
◽  
Takashi Okamoto ◽  
Seiichi Koakutsu
Keyword(s):  
Learning Algorithm ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Visualization Method ◽  
Self Organizing Maps ◽  
Optimal Solution Set ◽  
Batch Learning ◽  
Solution Representation ◽  
Self Organizing

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 an important issue. This paper focuses on the Pareto optimal solution visualization method using the growing hierarchical self-organizing maps (GHSOM) which is one of promising visualization methods. This method has a superior Pareto optimal solution representation capability, compared to the visualization method using the self-organizing maps. However, this method has some shortcomings. This paper proposes a new Pareto optimal solution visualization method using an improved GHSOM based on the batch learning. In the proposed method, the batch learning algorithm is introduced to the GHSOM to obtain a consistent visualization maps for a Pareto optimal solution set. Then, the symmetric transformation of maps is introduced in the growing process in the batch learning GHSOM algorithm to improve readability of the maps. Furthermore, the learning parameter optimization is introduced. The effectiveness of the proposed method is confirmed through numerical experiments with comparing the proposed method to the conventional methods on the Pareto optimal solution representation capability and the readability of the visualization maps.

Multi-Objective Optimization Algorithm Design and Implementation of Mobile Base Station Site Selection

2010 ◽  
Vol 29-32 ◽  
pp. 2496-2502
Author(s):  
Min Wang ◽  
Jun Tang
Keyword(s):  
Site Selection ◽  
Engineering Application ◽  
Optimal Solution ◽  
Base Station ◽  
Pareto Optimal Solution ◽  
Antibody Concentration ◽  
Pareto Optimal ◽  
Memory Cells ◽  
Multi Objective Optimization ◽  
Multi Objective

The number of base station location impact the network quality of service. A new method is proposed based on immune genetic algorithm for site selection. The mathematical model of multi-objective optimization problem for base station selection and the realization of the process were given. The use of antibody concentration selection ensures the diversity of the antibody and avoiding the premature convergence, and the use of memory cells to store Pareto optimal solution of each generation. A exclusion algorithm of neighboring memory cells on the updating and deleting to ensure that the Pareto optimal solution set of the distribution. The experiments results show that the algorithm can effectively find a number of possible base station and provide a solution for the practical engineering application.

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