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 Proximity Measure (KKTPM) for terminating a multi-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)
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