A Clustering Method Based on Dynamic Self Organizing Trees for Post-Pareto Optimality Analysis

Multiple objective optimization involves the simultaneous optimization of several objective functions. Solving this type of problem involves two stages; the optimization stage and the post-Pareto analysis stage. The first stage focuses in obtaining a set of nondominated solutions while the second one involves the selection of one solution from the Pareto set. Most of the work found in the literature focuses in the first stage. However, the decision making stage is as important as obtaining the set of nondominated solutions. Selecting one solution over others, or reducing the number of alternatives to choose from is not a simple task since the Pareto-optimal set can potentially contain a very large number of solutions. This paper introduces the dynamic self organizing tree algorithm as a method to perform post-Pareto analysis. This algorithm offers two main advantages: there is no need to provide an initial number of clusters, and at each hierarchical level, the algorithm optimizes the number of clusters, and can reassign data from previous hierarchical levels in order to rearrange misclustered data. The proposed method is tested in a well-known multiple objective optimization problem in order to show the performance of the algorithm.