New approaches on Pareto based for solving multi-objective optimization problems

In the design of real-world problems, it is desired that every objective be flawless; for instance, while the cost of a designed vehicle is expected to be low, its speed and safety are also desired to be high. Nevertheless, it is important to acknowledge the inherent limitations imposed by finite resources. Such inherent contradictions can be observed in nearly all engineering problems. To address and surmount these challenges, multi objective problem-solving approaches have been developed, enabling the simultaneous optimization of two or more objectives. Furthermore, regardless of the efficacy of an algorithm, the pursuit of new problem-solving approaches remains imperative, as no algorithm can guarantee flawless outcomes for every problem. The thesis study focused on the examination of two distinct problems, with the formulation of hypotheses aimed at resolving these issues. Subsequently, multi-objective solution approaches were developed based on these hypotheses. In both studies, Pareto-based algorithms, renowned as one of the most established multi-objective solution approaches, were employed. Additionally, a distinct system was utilized in lieu of the objective function for both problems. In essence, a hybrid system was implemented, combining the multi-objective algorithm with another system to work in tandem and achieve multiple objectives effectively. The hybrid approaches prove particularly beneficial for problems in which deriving a single objective function is challenging or impractical. In the initial study, the focus was on hyperparameter optimization of a system developed based on CNN, which is a commonly used artificial neural network architecture in the field of deep learning. In this study, one of the primary challenges lies in the fact that optimization-based solution approaches primarily rely on trial and error and incorporate an element of randomness. These types of problems can fall into classes of problems that cannot be solved in polynomial time. Consequently, a substantial number of iterations, often reaching hundreds of thousands, are required to achieve satisfactory results. Conversely, one of the major obstacles encountered in deep learning is the significant time cost associated with the training and inference processes. The objective of the research is to devise an algorithm capable of yielding satisfactory outcomes with a reduced number of trials for the given problem. This approach is pursued to mitigate the substantial increase in time costs that would ensue if both methods were employed simultaneously. In light of this objective, a fast convergence algorithm called F-MODE was proposed. This algorithm was subsequently compared with several established algorithms in the literature using test functions. Afterwards, it has been utilized for hyperparameter optimization of the CNN-based system. As a result, data points that are close to the Pareto-optimal set of hyperparameters have been identified. In the second study, a distinct algorithm called D-MOGA was developed specifically to optimize the ratios of asphalt mixtures. This algorithm aimed to find optimal combinations of asphalt mixture ratios considering multiple objectives. This study utilized forty-two asphalt mixture experiments conducted in a laboratory environment, which were originally conducted as part of another research investigation. These experimental data served as the basis for the analysis and optimization process in the current study. Each of these experiments comprises data characterized by five input variables and three corresponding output variables. Initially, a rule-based fuzzy logic system was developed utilizing the available data. This system enabled the generation of output results for various input combinations without the necessity of conducting real experiments. Subsequently, a balanced and competitive algorithm called D-MOGA was developed, specifically tailored for the optimization of asphalt mixture ratios. This algorithm was subject to rigorous comparisons with established and successful algorithms found in the literature, employing various statistical tests. Lastly, the fuzzy logic system developed earlier was employed as an objective function and seamlessly integrated into the D-MOGA algorithm. By utilizing this integrated approach, optimal Pareto solutions for the asphalt mixture problem were determined, providing a range of ideal solutions that balance multiple objectives effectively. In the final part of the study, a comparative analysis was conducted between F-MODE and D-MOGA algorithms using test functions. Initially, the test functions were evaluated based on the conditions specific to the first algorithm (F-MODE). Subsequently, the same test functions were examined considering the conditions specific to the second algorithm (D-MOGA). This comparative analysis aimed to assess the performance and effectiveness of each algorithm under different scenarios and conditions. As a result, two distinct problems have been addressed within the scope of multi-objective optimization problem, and approaches have been developed to solve these problems.