K. Nowruzi - Ph.D. Student, Shiraz University, Shiraz, Iran
G.R. Rakhshandehroo - Associate Prof. Shiraz University, Shiraz, Iran
P. Monadjemi - Assistant Prof. Shiraz University, Shiraz, Iran

Finding the Pareto front has become the goal of multiobjective optimization methods. Nondominated Sorting Algorithm (NSA) is mostly used by researchers to find the Pareto front. Although NSA has been used increasingly in recent years, one of its main drawbacks has been its omputational efficiency. The Algorithm’s computational cost has a cubic dependency to the number of individuals being searched for the Pareto front. For small data sets, the algorithm performs Pareto front discovery within a reasonable time. For larger data sets, however, the number of comparisons grow enormously, and hence, the time and effort that goes to Pareto front discovery increases very rapidly. In this paper, the topological ordering of Self Organizing Maps (SOM) was utilized to enhance nondominated sorting efficiency for Pareto Front discovery in large data sets. The method utilizes extracted clusters from application of SOM as a close approximation of the topology of the input data. Then, nondominated sorting is applied to the clusters which have a smaller population size. In other words, the proposed hybrid method eliminates the unnecessary comparison of individuals most likely to be a Pareto front member with individuals that are far from the front. As a case study, the method was applied to an inventory of about 7500 solutions of a benchmark water distribution optimization problem. Different population sizes were tried to demonstrate efficiency of the proposed method. It is verified that the method increased optimization efficiency considerably. Even in the data sets that were biased toward the Pareto front, the proposed method increased efficiency of nondominated sorting and reduced the computational effort by four folds.

Pareto Front, Nondominated Sorting, Self Organizing Map, Water Distribution Networks, Optimization