Comparison of NSGA-II and MODE performances by using MCDM methods for multi-response experimental data

Multi-response experimental data, composed with more than one response variable, can be examined in three stages: modeling, optimization and decision making. In this study, these three stages were considered sequentially. Model parameters were estimated through Seemingly Unrelated Regression (SUR) method due to linear correlation between responses during the modeling stage. In the optimization stage, simultaneous optimization of predicted multiple responses were considered as a multi-objective optimization (MOO) problem. For this purpose, Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Multi Objective Differential Evolution (MODE), were applied to obtain Pareto solution sets. In the decision making stage, compromise solution was chosen from the Pareto sets through various multi-criteria decision making (MCDM) methods. This study aims to compare performances of the NSGA-II and the MODE via various MCDM methods using three real data sets taken from different fields. The novelty of this paper is applying the MCDM methods to the Pareto solution set to choose a compromise solution by taking into account the Entropy weights of responses primarily. Afterwards, closeness of the compromise solution to the ideal solution using the mean absolute error (MAE) and the root mean square error (RMSE) metrics is calculated for decision making on the performance of the MOO methods. The results showed that compromise solution of the MODE is closer to the ideal solution than the NSGA-II according to the MAE and RMSE metrics. As a result, the MODE outperforms the NSGA-II.