Mohamed Abouhawwash

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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 it’s proximity to(More)
Recent studies have used Karush-Kuhn-Tucker (KKT) optimality conditions to develop a KKT ProximityMeasure (KKTPM) for terminating amulti-objective optimization simulation run based on theoretical convergence of solutions. In addition to determining a suitable termination condition and due to their ability to provide a single measure for convergence to(More)
Set-based multi-objective optimization methods, such as evolutionary multi-objective optimization (EMO) methods, attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms from their convergence to the efficient set, the current performance metrics require the knowledge of the true Pareto-optimal(More)
In EMO diversity of the obtained solutions is an important factor, particularly for decision makers. NSGA-III is a recently proposed reference direction based algorithm that was shown to be successful up to as many as 15 objectives. In this study, we propose a diversity enhanced version of NSGA-III. Our algorithm augments NSGA-III with two types of local(More)
A measure for estimating the convergence characteristics of a set of non-dominated points obtained by a multi-objective optimization algorithm was developed recently. The idea of the measure was developed based on the Karush-Kuhn-Tucker (KKT) optimality conditions which require the gradients of objective and constraint functions. In this paper, we extend(More)
A previous study suggested a Karush–Kuhn–Tucker 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. However, the drawback of the KKTPM metric is that it requires a new optimization problem to be solved for each(More)
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