NSGA-II method is used for multiobjective optimization problem Parameter estimation of Kevlar 49 / Epoxy dataset using Weibull distribution Evaluation of parameter estimation methods togetherIn the solution of the multi-objective optimization problem, there are alternative solution sets called Pareto optimal solution instead of a single optimal solution called the ideal solution. In addition to offering a broad set of solutions, there are various approaches to obtain Pareto solutions, for which there is a compromised solution for all the functions discussed. Multi-objective meta-heuristic methods are an important method in obtaining Pareto solutions as they produce many solutions, do not use derivative calculations, provide a good approach to Pareto optimal solutions, and can be easily applied to optimization problems. Besides being a multi-objective meta heuristic method, non-dominated sorting genetic algorithm II (NSGA-II) is one of the most effective methods used in obtaining the Pareto solution set.
Figure A. Pareto optimal solution setPurpose: This study, which is based on least square (LS), weighted least square (WLS) and maximum likelihood (ML) estimation methods, proposes the use of a multi-objective programming approach to estimate the parameters of the Weibull distribution. Thus, it is aimed to obtain better estimation results by evaluating the parameter estimation process of these methods together.
Theory and Methods:The NSGA-II method, which is a multi-objective heuristic approach, was used to solve the multi-objective programming estimation model. As the multi-objective estimation model, the cases of LS-WLS, LS-ML and WLS-ML were taken into consideration and these cases were compared with the classical LS, WLS and ML methods.
Results:The Kevlar 49 / Epoxy dataset was used to demonstrate the applicability of the proposed approach.According to the results, the best parameter estimation results were given in cases where the ML method was evaluated only and together, LS-ML and WLS-ML multi-objective parameter estimation models.
Conclusion:If it is desired to use a multi-objective optimization problem in estimating the parameters of a data set with Weibull distribution, a model including ML method will give better results.