Sharif Digital Repository

In this thesis, we want to present methods that are able to solve the assignment tasks problem in a heterogeneous computing system. These methods are two hybrid methods that are constructed by composing Hopefield Neural Networks with Genetic Algorithms and the Simulated Annealing. First, we solve the relaxed problem by applying Genetic Algorithms and the Simulated Annealing and we compare the results of these ways with other traditional methods. Then, we solve the constrained problem with mentioned hybrid methods. The definition of the problem is as following: Consider a distributed computing system which is comprised of set of processors with different speeds but the same structure. We want... 

We discuss conjugate gradient methods for which both the gradient and func-tion values are considered in computing the conjugate gradient parameter. We pro-pose new conjugate gradient methods as members of Dai-Liao’s family of conjugate gradient methods and Andrei’s family of hybrid conjugate gradient methods. For computing the conjugate gradient parameter in our methods, three modified secant equations proposed by Zhang, Deng and Chen, Li and Fukushima, and Yuan are used. It is shown that under proper conditions, three of the proposed methods are globally convergent for uniformly convex functions and two other methods are glob-ally convergent for general functions. It is also shown that... 

Decision making is the most important and popular aspect of applying mathematical methods in various fields of human activity. Decisions are nearly always made on the basis of information obtained in conditions of uncertainty. In this thesis, the transportation planning decision (TPD) problem is defined with fuzzy parameters. Our purpose is to simultaneously minimize the total production and transportation costs and the total delivery time with reference to budget constraints and available supply, machine capacities at each source, as well as forecast demand and warehouse space constraints at each destination, and achieve an expected efficient solution for the decision maker according to the... 

Linear and nonlinear problems on integer and real numbers constitute very important optimization problems. Recently, methods have been developed using pumps to solve this type of problem. Feasibility pumps usually produce random perturbations. In this method,the generated random perturbations are replaced by a penalty framework and feasibility pumps are introduced as methods of displacement. Feasibility pump algorithms on 0-1 are used to solve these problems and the alternating direction methods are used. A convergence theorem is presented for the alternate direction method based on the penalty.New changes to the feasibility pumps and existing algorithms for solving linear and nonlinear... 

Here, the properties of separability of linkages are studied. In general, a linkage is a simple polygonal chain embedded in 3-space with disjoint, straight-line edges, which are fixed-length bars. The internal vertices are called joints. If the two end points are connected then the linkage is a closed linkage, otherwise it is an open linkage. By imposing restrictions on the way the bars in joints can move, three kinds of linkages as rigid, revolute and flexible can be introduced. A motion in a linkage is the motion of its vertices that preserves the length of the bars, and adheres the restrictions on joints. A collection of linkages are said to be separatable if for any distance d, there is... 

By increasing complexity of systems, soft computing including fuzzy computing, evolutionary computing and intelligent computing, have been developing in recent years. Here, we focus on two subjects making use of soft computing. Firstly, we study fuzzy LR linear systems.
We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares model. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the optimal value of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding... 

We explain a new trust-region method for solving unconstrained optimization problems recently introduced in the literature, where the radius update is computed using the information at the current iterate rather than at the preceeding one. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at the last iterate. Global convergence to first- and second-order critical ponits is proved under classical assumptions. Preliminary numerical expriments on CUTEr problems with MATLAB7.7 indicate that the new method is very competitive  

Wireless Mesh Network (WMN) is a new technology for developing wireless networks. In a wireless communication system, a transmitter communicates with a receiver by magnetic waves. Channel is the medium used to convey information from a sender to a receiver. Interference exists between two links if they are within interference range and are assigned to the same channel. Channel assignment is all about mapping available channels to the network interfaces in order to achieve optimal network performance. A good channel assignment algorithm minimizes the total network interference. Here, we propose a modified artificial bee colony (ABC) algorithm for the fixed channel assignment (FCA) problem in... 

We describe an interior method for solving bound-constrained systems of equations , recently introduced by S. Bellavia, M. Macconi and B. Morini in the literature. The method makes use of ideas from the classical trust-region Newton method for unconstrained nonlinear equations and the recent interior affine scaling approach for constrained optimization problems. The iterates are generated to be feasible and the bounds are handled implicitly. The method reduces to a standard trust-region method for unconstrained problems when there are no upper or lower bounds on the variables. Global and local fast convergence properties are ... 

In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. Later, Raydan derived an interesting relationship between a gradient method and the shifted power method. This relationship allows one to establish the convergence of the Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function. With this point of view, he explained the remarkable improvement obtained by using this new choice of steplength. For some special cases, he presented some very interesting convergence rate results.... 

We explain a new trust region algorithm for solving unconstrained optimization problems where the redius update is computed using the model information at the current iterate rather than at the preceding one, recently proposed by Bastin, Malmedy, Mouffe, Toint and Tomanos. Then we discuss a modification mixing the concepts of nonmonotone trust region, line search and internal doubling. We use line search to finds a point that satisfies the Wolfe conditions. After that, we explain a new trust region algorithm for solving unconstrained optimization problems where simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian... 

We explain a new penalty method recently introduced in the literature for solv-ing constrained optimization problems. In this method, the penalty parameter is adjusted dynamically at every iteration to ensure su?cient progress in linear feasi-bility. A trust region is used to assist in the determination of the penalty parameter, but not in the step computation. It is shown that the algorithm has global conver-gence. We implement the algorithm and test the program on a number of di?cult optimization problems. The numerical results con?rm the e?ectiveness of the algo-rithm  

Due to the special structure of the Hessian matrix in nonlinear least squares problems,use of effective structured updating schemes for approximating the Hessian matrix in solving such problems has been considered. Mahdavi-Amiri and Bartels used a structured BFGS method for approximating the projected Hessian matrix in solving constrained nonlinear least squares (CNLLS) problems. Recently, Mahdavi-Amiri and Ansari applied other structured DFP and BFGS methods for approximating the projected Hessian matrix in solving CNLLS problems and proved both global and asymptotic two-step superlinearconvergence of the algorithms. Here, we present other methods for approximating the structured projected... 

Recently, the primal-dual interior point methods for nonlinear programming has attracted considerable attention. Here, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. This is a convex optimization problem which is equivalent to a nonlinear convex optimization problem having linear equality and inequality and quadratic inequality constraints. This problem is reduced to a convex optimization problem of lower dimension with only inequality constraints. Finally, the problem is solved... 

In this thesis, we exmine a group of optimization methods called trust region methods for solving semidefinite programming problems. Nowadays, many application problems can be cast as semidefinite programming and problems with very large size are encountered every year. So, having a powerful method for solving such problems is very important. Trust region approach present a new scheme for constructing efficient algorithms to solve semidefinite programming problems.When using interior point methods for solving semidefinite programs (SDPs), one needs to solve a system of linear equations at every iteration. For large problems, solving the system of linear equations can be very expensive. In... 

Several types of large-sized 0-1 Knapsack Problems (KPs) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. To avoid this, it has been suggested to solve the so-called core of the problem, knapsack problem defined on a small subset of the variables. The exact core cannot, however, be identified before KP is solved to optimality and, thus previously available algorithms had to rely on approximate core sizes. Here, we describe an algorithm for KP recently proposed in the litereture, where the enumerated core size is minimal, and the computational effort for sorting and reduction is also limited in accordance with a hierarchy. The... 

We study the Personal Research Space (PRS), that is, the collection of documents a researcher gathers for her research project in order to fnd solutions for a common problem in academic research. During the orientation phase, before the academic research team makes fnal decisions on the course of its studies, abrupt change of directions of studies are common. Ideally, documents in this process are arranged in such a way that time spent in a topic saves a good portion of the time required for research studies in another. We propose an optimization model that provides solutions to parallel this ideal arrangement. PRS as an integral part of the global research system, a highly complex and...