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A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

Applied Mathematics 2017年第2期8卷 154-163页

作者： el-desouky rahmo Marcin Studniarski Department of Mathematics Faculty of Science Taif University Khurma Kingdom of Saudi Arabia Mathematics Department Faculty of Science Mansoura University Mansoura Egypt Faculty of Mathematics and Computer Science University of Lód&eacute Lód&eacute Poland

We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.

关键词： Multiobjective Optimization Scalarization Function Generalized Jacobian Vector Critical Point

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Generating Epsilon-Efficient Solutions in Multiobjective Optimization by Genetic Algorithm

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Applied Mathematics 2017年第3期8卷 395-409页

作者： el-desouky rahmo Marcin Studniarski Department of Mathematics Faculty of Science Taif University Khurma KSA Mathematics Department Faculty of Science Mansoura University Mansoura Egypt Faculty of Mathematics and Computer Science University of &#573 ódź ódź Poland

We develop a new evolutionary method of generating epsilon-efficient solutions of a continuous multiobjective programming problem. This is achieved by discretizing the problem and then using a genetic algorithm with some derived probabilistic stopping criteria to obtain all minimal solutions for the discretized problem. We prove that these minimal solutions are the epsilon-optimal solutions to the original problem. We also present some computational examples illustrating the efficiency of our method.

关键词： Vector Optimization Approximate Solutions Genetic Algorithm Stopping Criteria

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The Numerical Solution of the MRLW Equation Using the Multigrid Method

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Applied Mathematics 2014年第21期5卷 3328-3334页

作者： Yasser Mohamed Abo Essa Ibrahim Abouefarag el-desouky rahmo Mathematics Department Faculty of Education and Science (AL-Khurmah Branch) Taif University Taif KSA Mathematics Department Faculty of Science Al-Azhar University Nasr City Cairo Egypt Mathematics Department Faculty of Science Suez Canal University Ismailia Egypt Mathematics Department Faculty of Science Mansoura University Mansoura Egypt

In this paper, we obtained the numerical solutions of the modified regularized long-wave (MRLW) equation, by using the multigrid method and finite difference method. The solitary wave motion, interaction of two and three solitary waves, and development of the Maxwellian initial condition into solitary waves are studied using the proposed method. The numerical solutions are compared with the known analytical solutions. Usingerror norms and conservative properties of mass, momentum and energy, accuracy and efficiency of the mentioned method will be established through comparison with other techniques.

关键词： Multigrid Method Finite Difference Method MRLW Equation

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