الفهرس 
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Abstract
Multi-objective optimization problems give rise to a set of trade-off optimal solutions, known as Pareto-optimal solutions. In solving these problems, one popular approach has been to first find a representative set of Pareto-optimal solutions and then use higher-level information involving one or more decision-makers to choose a preferred solution from the set. Evolutionary multi-objective optimization (EMO) methodologies follow this principle of solving multi-objective optimization problems and have received extensive attention for the past two decades. Karush-Kuhn-Tucker (KKT) optimality conditions are used for checking whether a solution obtained by an optimization algorithm is truly an optimal solution or not by theoretical and applied optimization researchers. When a point is not the true optimum, a simple violation measure of KKT optimality conditions cannot indicate anything about its proximity to the optimal solution. Past few studies by researchers suggested a KKT proximity measure (KKTPM) that is able to identify relative closeness of any point from the theoretical optimum point without actually knowing the exact location of the optimum point. This Thesis consists of six chapters: In Chapter 1, provides background knowledge about the single and multi- objective optimization and Karush-Kuhn-Tucker (KKT) optimality conditions. Chapter 2 covers classical optimization methods (i.e., point-to-point algorithms) and set-based multi-objective evolutionary algorithms, such as NSGA-II and NSGA-III. This chapter explains in details the Augmented Achievement Scalarization Function (AASF) method which is wisely utilized in this thesis. Chapter 3 is devoted to extend the concept of approximate KKT proximity measure defined for single objective to multi-objective optimization using achievement scalarization function method. Some of the results established in this chapter are published in Journal IEEE transactions on evolutionary computation and Lecture Notes in Computer Science in Springer. Chapter 4 presented a several computationally fast methods for computing an approximate KKTPM value. Some of the results established in this chapter are submitted in European Journal of Operational Research. The main concern of Chapter 5 is to propose a new local search operator based on both KKTPM and Achievement Scalarization Function (ASF), with the intention of improving convergence of NSGA-III algorithm. Results established in this chapter are submitted in Journal of Global optimization C. hapter 6 contains conclusion and provides directions for further researches.