Towards Evaluation of the Adaptive-Epsilon-R-NSGA-II algorithm (AE-R-NSGA-II) on industrial optimization problems

Abstract: Simulation-based optimization methodologies are widely applied in real world optimization problems. In developing these methodologies, beside simulation models, algorithms play a critical role. One example is an evolutionary multi objective optimization algorithm known as Reference point-based Non-dominated Sorting Genetic Algorithm-II (R-NSGA-II), which has shown to have some promising results in this regard. Its successor, R-NSGA-II-adaptive diversity control (hereafter Adaptive Epsilon-R-NSGA-II (AE-R-NSGA-II) algorithm) is one of the latest proposed extensions of the R-NSGA-II algorithm and in the early stages of its development. So far, little research exists on its applicability and usefulness, especially in real world optimization problems. This thesis evaluates behavior and performance of AE-R-NSGA-II, and to the best of our knowledge is one of its kind. To this aim, we have investigated the algorithm in two experiments, using two benchmark functions, 10 performance measures, and a behavioral characteristics analysis method. The experiments are designed to (i) assess behavior and performance of AE-R-NSGA-II, (ii) and facilitate efficient use of the algorithm in real world optimization problems. This is achieved through the algorithm parameter configuration (parametric study) according to the problem characteristics. The behavior and performance of the algorithm in terms of diversity of the solutions obtained, and their convergence to the optimal Pareto front is studied in the first experiment through manipulating a parameter of the algorithm referred to as Adaptive epsilon coefficient value (C), and in the second experiment through manipulating the Reference point (R) according to the distance between the reference point and the global Pareto front. Therefore, as one contribution of this study two new diversity performance measures (called Modified spread, and Population diversity), and the behavioral characteristics analysis method called R-NSGA-II adaptive epsilon value have been introduced and applied. They can be modified and applied for the evaluation of any reference point based algorithm such as the AE-R-NSGA-II. Additionally, this project contributed to improving the Benchmark software, for instance by identifying new features that can facilitate future research in this area. Some of the findings of the study are as follows: (i) systematic changes of C and R parameters influence the diversity and convergence of the obtained solutions (to the optimal Pareto front and to the reference point), (ii) there is a tradeoff between the diversity and convergence speed, according to the systematic changes in the settings, (iii) the proposed diversity measures and the method are applicable and useful in combination with other performance measures. Moreover, we realized that because of the unexpected abnormal behaviors of the algorithm, in some cases the results are conflicting, therefore, impossible to interpret. This shows that still further research is required to verify the applicability and usefulness of AE-R-NSGA-II in practice. The knowledge gained in this study helps improving the algorithm.