Optimization and Decision Making Stages for Multiple Responses: An Application of NSGA-II and FCM Clustering Algorithm

Abstract

In multi-response studies, optimization and decision making are two crucial stages for obtaining a satisfactory solution. Generally, multiple responses are aggregated in a single objective function and the optimization result is considered as a compromise solution for all the responses. However, this approach does not meet required targets of all the responses simultaneously. In this study, Non-dominated Sorting Genetic Algorithm-II (NSGA-II), a well-known posterior preference articulation approach, is adapted with penalty function approach to optimize multiple responses with constraints. Then, the obtained non-dominated solutions are evaluated to make decision for the best satisfactory solution. In order to achieve the decision making stage, a fuzzy clustering based algorithm, fuzzy c-means (FCM), and a mostly used multi criteria decision making (MCDM) method, technique for order preference by similarity to an ideal solution (TOPSIS), are preferred. The selected combination of the NSGA-II with FCM and TOPSIS are performed on a real world data set given in the literature and results are discussed. The results show the applicability of the FCM for decision making in multiple responses. It can be said that the FCM makes easier the selection of a compromise solution in the non-dominated solution set by using membership degrees of each solution to the clusters without removing any non-dominated solution.

Keywords

• Multi-response optimization (MRO), NSGA-II, non-dominated solutions, FCM, TOPSIS

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