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Papers by Alkailany Mohammed
In this research, a new algorithm of conjugation algorithms was developed to solve nonlinear opti... more In this research, a new algorithm of conjugation algorithms was developed to solve nonlinear optimization problems. This algorithm depend on a new search direction(í µí² í µí² = −í µí±¯ í µí² −í µí¿ í µí² í µí² + í µí²í µí² í µí²). Numerical results proved the efficiency of the proposed algorithm compared to other algorithms
Traveling Salesman Problem (TSP) is special case from assignment problem (AP) except there is a c... more Traveling Salesman Problem (TSP) is special case from assignment problem (AP) except there is a conditional restriction, Cij=∞ , if i=j. Traveling Salesman Problem has to visit n cities. In this paper we present new revised ones assignment method to solve TSP, We obtain an optimal solution for Traveling Salesman Problem by New Revised Ones Assignment Method, the results of the tests show that New Revised ones assignment is superior to some other methods such as ones assignment method, Revised Ones Assignment method. Keyword: Traveling Salesman Problem (TSP), ones assignment method, Linear integer programming.
Heuristic optimization techniques have became very general techniques and have diffuse know areas... more Heuristic optimization techniques have became very general techniques and have diffuse know areas. Main purpose of these techniques is to achieve good performance on problem. One of these techniques is Bat Algorithm (BA). BA is an optimization algorithm based on echolocation usually of bats and promoted by simulate of bats' behavior. In this study, exploration and exploitation mechanisms of bat algorithm are improved by Using descent directions(Powell). Performance of proposed and standard version of algorithm is compared on eight basic criterion test problems. Results indicate that proposed version is preferable than standard version in terms of standard deviation and other parameters.
In this paper base on the Lagrange Multiplier and sequential unconstrained minimization technical... more In this paper base on the Lagrange Multiplier and sequential unconstrained minimization technical (SUMT). we investigated a new algorithm of Augmented Lagrange-method to solve nonlinear programming. The Result of new proposed method satisfied global convergence. Conclusion the new proposed (NMALM) is too effective when compared with other established algorithm(SALM, PHRALM) to solve standard nonlinear programming. INTRODICTION The nonlinear programming (NLP) is the process of solving an optimization problem divided by constrained and unconstrained optimization, The class of the general constrained optimization problems seeks the solution by replacing the original constrained problem with a sequence of unconstrained sub-problems in which the objective function is formed by the original objective function of the constrained optimization plus additional 'penalty' terms. The 'penalty' terms are made up of constraint functions multiplied by a positive coefficient. By making this coefficient larger and larger along the optimization of the sequential unconstrained sub problems, we force the Minimization of the objective function closer and closer to the feasible region of the original constrained problem. However, as the penalty coefficient grows to be too large, the objective function of the unconstrained optimization sub-problem may become ill conditioned, thus, making the optimization of the sub-problem dilute. This issue is avoided, after the proof of convergence, by the so-called ' Augmented Lagrangian Method' (ALM) in which an explicit estimate of the Lagrange multipliers is included in the objective function. Hence, the objective function becomes optimality condition in the above method in order to improve its sufficiency and Reliability. The above technique is based on solid theoretical considerations, and the methods commonly recommended for the initial choice of Lagrange multipliers. (ALBayati, and Hamed, 2013) A general constrained nonlinear programming problem (NLP) the following form (3) 0 h(x) (2) 0 g(x) subject to 1) (f(x) minimize where f(x) is an objective function that we want to minimize. h(x) =[ h 1 (x); _ _ _ ; h m (x)] t is a set of m equality constraints, and g(x) = [g 1 (x); _ _ _ ; g k (x) ] t is a set of k inequality constraints. All f(x), h(x), and g(x) are either linear or nonlinear.(Wang, 2001) Augmented lagrange multiplier method : We now discussion approach known as the method of multipliers or the augmented Lagrangian method. This algorithm is related to the quadratic penalty algorithm, but it reduces the possibility of ill conditioning of the sub problems that are generated in this approach by introducing explicit Lagrange multiplier estimates at each step into the function to be minimized, which is known as the augmented Lagrangian function. In contrast to the penalty functions, the augmented Lagrangian function largely preserves smoothness, and implementations
Drafts by Alkailany Mohammed
The theory of optimal control is considered one of the modern and developed subjects, especially ... more The theory of optimal control is considered one of the modern and developed subjects, especially which can be represented in a dynamic setting. One of the modern applications of the optimal control theory is the field two-sided networks, as the model of optimal control was applied in this study and which was suggested by the scientists (Sun & TSE) in 2007 and has been applied as a case study on Mosul University internet Center. The optimal upload and download quantities of the subscribers during one month ,has been calculated through the application of the optimal control model. Aim: The aim of this study is to resolve the optimal control model proposed by the researchers (Sun& Tse) as they did not discuss how to resolve these two models. Finding the optimal values for each state variable is by solving the equations of the solution resulting from applying the terms of the maximization principle on these two models using the Runge-kutta method.
In this research, a new algorithm of conjugation algorithms was developed to solve nonlinear opti... more In this research, a new algorithm of conjugation algorithms was developed to solve nonlinear optimization problems. This algorithm depend on a new search direction(í µí² í µí² = −í µí±¯ í µí² −í µí¿ í µí² í µí² + í µí²í µí² í µí²). Numerical results proved the efficiency of the proposed algorithm compared to other algorithms
Traveling Salesman Problem (TSP) is special case from assignment problem (AP) except there is a c... more Traveling Salesman Problem (TSP) is special case from assignment problem (AP) except there is a conditional restriction, Cij=∞ , if i=j. Traveling Salesman Problem has to visit n cities. In this paper we present new revised ones assignment method to solve TSP, We obtain an optimal solution for Traveling Salesman Problem by New Revised Ones Assignment Method, the results of the tests show that New Revised ones assignment is superior to some other methods such as ones assignment method, Revised Ones Assignment method. Keyword: Traveling Salesman Problem (TSP), ones assignment method, Linear integer programming.
Heuristic optimization techniques have became very general techniques and have diffuse know areas... more Heuristic optimization techniques have became very general techniques and have diffuse know areas. Main purpose of these techniques is to achieve good performance on problem. One of these techniques is Bat Algorithm (BA). BA is an optimization algorithm based on echolocation usually of bats and promoted by simulate of bats' behavior. In this study, exploration and exploitation mechanisms of bat algorithm are improved by Using descent directions(Powell). Performance of proposed and standard version of algorithm is compared on eight basic criterion test problems. Results indicate that proposed version is preferable than standard version in terms of standard deviation and other parameters.
In this paper base on the Lagrange Multiplier and sequential unconstrained minimization technical... more In this paper base on the Lagrange Multiplier and sequential unconstrained minimization technical (SUMT). we investigated a new algorithm of Augmented Lagrange-method to solve nonlinear programming. The Result of new proposed method satisfied global convergence. Conclusion the new proposed (NMALM) is too effective when compared with other established algorithm(SALM, PHRALM) to solve standard nonlinear programming. INTRODICTION The nonlinear programming (NLP) is the process of solving an optimization problem divided by constrained and unconstrained optimization, The class of the general constrained optimization problems seeks the solution by replacing the original constrained problem with a sequence of unconstrained sub-problems in which the objective function is formed by the original objective function of the constrained optimization plus additional 'penalty' terms. The 'penalty' terms are made up of constraint functions multiplied by a positive coefficient. By making this coefficient larger and larger along the optimization of the sequential unconstrained sub problems, we force the Minimization of the objective function closer and closer to the feasible region of the original constrained problem. However, as the penalty coefficient grows to be too large, the objective function of the unconstrained optimization sub-problem may become ill conditioned, thus, making the optimization of the sub-problem dilute. This issue is avoided, after the proof of convergence, by the so-called ' Augmented Lagrangian Method' (ALM) in which an explicit estimate of the Lagrange multipliers is included in the objective function. Hence, the objective function becomes optimality condition in the above method in order to improve its sufficiency and Reliability. The above technique is based on solid theoretical considerations, and the methods commonly recommended for the initial choice of Lagrange multipliers. (ALBayati, and Hamed, 2013) A general constrained nonlinear programming problem (NLP) the following form (3) 0 h(x) (2) 0 g(x) subject to 1) (f(x) minimize where f(x) is an objective function that we want to minimize. h(x) =[ h 1 (x); _ _ _ ; h m (x)] t is a set of m equality constraints, and g(x) = [g 1 (x); _ _ _ ; g k (x) ] t is a set of k inequality constraints. All f(x), h(x), and g(x) are either linear or nonlinear.(Wang, 2001) Augmented lagrange multiplier method : We now discussion approach known as the method of multipliers or the augmented Lagrangian method. This algorithm is related to the quadratic penalty algorithm, but it reduces the possibility of ill conditioning of the sub problems that are generated in this approach by introducing explicit Lagrange multiplier estimates at each step into the function to be minimized, which is known as the augmented Lagrangian function. In contrast to the penalty functions, the augmented Lagrangian function largely preserves smoothness, and implementations
The theory of optimal control is considered one of the modern and developed subjects, especially ... more The theory of optimal control is considered one of the modern and developed subjects, especially which can be represented in a dynamic setting. One of the modern applications of the optimal control theory is the field two-sided networks, as the model of optimal control was applied in this study and which was suggested by the scientists (Sun & TSE) in 2007 and has been applied as a case study on Mosul University internet Center. The optimal upload and download quantities of the subscribers during one month ,has been calculated through the application of the optimal control model. Aim: The aim of this study is to resolve the optimal control model proposed by the researchers (Sun& Tse) as they did not discuss how to resolve these two models. Finding the optimal values for each state variable is by solving the equations of the solution resulting from applying the terms of the maximization principle on these two models using the Runge-kutta method.