Analysis and Improvements of the Pareto Optimal Solution Visualization Method Using the Self-Organizing Maps

Abstract

: 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.

Bio-inspired multiobjective clustering optimization: A survey and a proposal

“…[36] This is important to a more clear understanding of the tradeoff among the potential solutions. [37] A very promising approach, based on Self Organizing Maps, for visualizing the Pareto front has been studied by several authors. [36][37][38][39] The robustness and population-based nature of swarm intelligence (SI) algorithms are important and attractive features for MOO problems.…”

“…[37] A very promising approach, based on Self Organizing Maps, for visualizing the Pareto front has been studied by several authors. [36][37][38][39] The robustness and population-based nature of swarm intelligence (SI) algorithms are important and attractive features for MOO problems. [46] In the literature, different multiobjective clustering algorithms based on SI are presented.…”

“…where N is the total number of objects [37] and C is the set of all clusters. S(C) ∈ [−1, 1], where 1 represents better clusters.…”

“…• Two objective functions: The modified Silhouette [36,37] combined with the Dev(C); [11] and the modified Silhouette combined with the number of clusters.…”

“…Concerning neural networks, the self organizing maps have been addressed as useful tools for visualizing and analyzing the Pareto front. [36][37][38][39] In Santos et al, [32] it was presented an algorithm, called multi ant colony clustering algorithm (MACC), which works with two artificial colonies, each one with k bees working in parallel, to cluster a dataset taking account two different objectives: compactness and connectedness. Experiments were performed with the Iris dataset from UCI to assess the quality of the ant clustering algorithm for multiobjective problems, and the results were compared with other results present in the literature.…”