الفهرس 
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Abstract
Optimization algorithms play a pivotal role in various fields, including economics, engineering, operations research, and others. These algorithms can significantly contribute to decision-making processes by identifying the best possible solutions, thereby enhancing efficiency and achieving optimal results within available resources. One prominent category of optimization algorithms is the evolutionary algorithm, widely recognized for its efficacy in solving different optimization problems.
Despite the widespread application of evolutionary algorithms, evaluating their performance demands reliable and effective metrics. In the literature on evolutionary algorithms, there are various metrics that evaluate the convergence ability of these algorithms. However, many of them require prior knowledge of the true Pareto-optimal front. This requirement poses a challenge as it is often impractical or unattainable to obtain the optimal solutions beforehand in real-world engineering problems. As a result, these metrics have limited applicability. Recently, two versions of Karush-Kuhn-Tucker Proximity Metrics (KKTPMs) have been introduced to measure convergence without requiring prior knowledge of the true Pareto-optimal front. However, these metrics face some challenges, the most important of which is that they require appropriate parameters and reference points. Furthermore, the metrics need complex calculations with a high computational cost. These challenges limit their effectiveness in reliably evaluating evolutionary algorithms. This thesis introduces a novel version of KKT-based proximity metric. This proposed metric is designed specifically for single- and multi-objective optimization problems. The new metric addresses difficulties in previous versions of KKTPMs with a low computational cost. The use of this metric facilities in evaluating the convergence behavior of optimization algorithms effectively and reliably Additionally, a simplified version of KKTPMs (S-KKTPM) is introduce to improve and develop preference-based evolutionary algorithms. This thesis presents a new version of reference point-based Non-dominated Sorting Genetic Algorithm II (R-NSGA-II) called RS-KKTPM. By incorporating the S-KKTPM metric into R-NSGA-II, we enhance the performance and effectiveness of R-NSGA-II that consider user preferences during optimization Moreover, the present study shows that the RS-KKTPM can efficiently treat some disadvantages of the original algorithm (R-NSGA-II). Finally, this thesis introduces two versions of multi-objective optimization algorithms, namely, Multi-Objective Nutcracker Optimization Algorithm (MONOA) and Multi-objective Mantis Search Algorithm (MOMSA). The recent single-objective algorithms, called Nutcracker Optimization algorithm and Mantis search algorithm, have been developed to be applicable to multi-objective optimization problems. The effectiveness of these developed algorithms has been confirmed in solving multi-objective real-world engineering problems.