الفهرس 
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Abstract
Almost every real-world problems involve more than one (often conflicting) objective functions. This class of problems are known as Multi-objective Optimization Problems (MOPs). For over twenty years, researchers have been developing Evolutionary Multi-objective Optimization (EMO) algorithms which attempt to find a set of well-converged and well-distributed set of trade-off solutions for MOPs. 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. The purpose of this thesis is to contribute scientifically and propose the B-KKTPM metric, which is able to identify relative closeness for any solution from a corresponding Pareto-optimal solution without any knowledge about the true optimum solution. The thesis also aims to evaluate the performance of EMOs.
Thesis content:
Content of the thesis is in (6) chapters as follow:
Chapter one presents the essential background and the basic concepts of multi-objective optimization problems.
Chapter two provides a number of classical and evolutionary methods that related to this thesis.
Chapter three proposes a Benson’s KKT-based proximity measure (B-KKTPM) to multi-objective optimization. One of the important outcomes is that the proposed metric can be used to terminate an EMO run as an indicator of overall convergence behavior (and their proximity) of non-dominated points to the true Pareto-optimal solutions.
Chapter four presents several computationally fast methods for computing an approximate B-KKTPM value.
Chapter five discusses some special cases to know the merits of KKTPM metric and to confirm that this metric is an essential measure for convergence.
Chapter six presents conclusions, which will wrap up this thesis and propose possible future works.