Sharif Digital Repository

It is possible to define multiresolution by reversing the process of subdivision. One approach to reverse a subdivision scheme appropriates pure numerical algebraic relations for subdivision using the interaction of diagrams (Bartels and Samavati, 2011; Samavati and Bartels, 2006). However, certain assumptions carried through the available work, two of which we wish to challenge: (1) the construction of multiresolutions for irregular meshes are reconsidered in the presence of any extraordinary vertex rather than being prepared beforehand as simple available relations and (2) the connectivity graph of the coarse mesh would have to be a subgraph of the connectivity graph of the fine mesh. 3... 

In recent decades, multistate two-terminal reliability problem has attracted several researchers, and accordingly many exact and approximation approaches have been proposed in the literature in terms of minimal cuts (MCs) or minimal paths (MPs) to address this problem. Here, an MP-based approximation approach is developed based on exact algorithms. With all the MPs at hand, the approach rearranges the MPs ascendingly with respect to their lengths and then sets the flow on some MPs to be zero which turns to reduce the computing cost in solving the problem. We provide the complexity results, and by employing some benchmarks and one thousand randomly generated networks illustrate that not only... 

In a stochastic-flow network, a (d, T, b, P1, P2)-MP is a system state vector for which d units of flow can be transmitted through two separate minimal paths (SMPs) P1 and P2 simultaneously from a source node to a sink node satisfying time and budget limitations T and b, respectively. Problem of determining all the (d, T, b, P1, P2)-MPs, termed as the (d, T, b, P1, P2)-MP problem, has been attractive in reliability theory. Here, some new results are established for the problem. Using these results, a new algorithm is developed to find all the (d, T, b, P1, P2)-MPs, and its correctness is established. The algorithm is compared with a recently proposed one to show the practical efficiency of... 

We consider a multi-objective linear programming model with type-2 fuzzy objectives. The considered model has the flexibility for the user to specify the more general membership functions for objectives to reflect the inherent fuzziness, while being simple and practical. We develop two solution strategies with reasonable computing costs. The additional cost, as compared to the type-1 fuzzy model, is indeed insignificant. These two algorithms compute Pareto optimal solutions of the type-2 problems, one being based on a maxmin approach and the other on aggregating the objectives. Finally, applying the proposed algorithms, we work out two illustrative examples  

We first establish some necessary and sufficient conditions for solvability of fuzzy LR linear systems. We then propose a concept for an approximate solution when a fuzzy LR linear system lacks a solution. Recently, we have proposed an approximate solution for a fuzzy LR linear system under the condition that a corresponding crisp linear system was solvable. Here, we remove this condition by presenting a more general concept of an approximate solution based on a least squares model. We also develop the conditions for the uniqueness of the approximate solution. To compute an approximate solution, we propose an algorithm based on a quadratic programming model with bound constraints on some... 

A full Nesterov-Todd (NT) step infeasible interior-point algorithm is proposed for solving monotone linear complementarity problems over symmetric cones by using Euclidean Jordan algebra. Two types of full NT-steps are used, feasibility steps and centering steps The algorithm starts from strictly feasible iterates of a perturbed problem, and, using the central path and feasibility steps, finds strictly feasible iterates for the next perturbed problem. By using centering steps for the new perturbed problem, strictly feasible iterates are obtained to be close enough to the central path of the new perturbed problem. The starting point depends on two positive numbers ρp and ρd. The algorithm... 

We present a superlinearly convergent exact penalty method for solving constrained nonlinear least squares problems, in which the projected exact penalty Hessian is approximated by using a structured secant updating scheme. We give general conditions for the two-step superlinear convergence of the algorithm and prove that the projected structured Broyden-Fletcher-Goldfarb-Shanno (BFGS), Powell-symmetric-Broyden (PSB), and Davidon-Fletcher-Powell (DFP) update formulas satisfy these conditions. Then we extend the results to the projected structured convex Broyden family update formulas. Extensive testing results obtained by an implementation of our algorithms, as compared to the results... 

A full Nesterov-Todd step infeasible interior-point algorithm is proposed for solving linear programming problems over symmetric cones by using the Euclidean Jordan algebra. Using a new approach, we also provide a search direction and show that the iteration bound coincides with the best known bound for infeasible interior-point methods  

We present a new primal-dual path-following interior-point algorithm for linear complementarity problem over symmetric cones. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the search directions, the complexity bound of the algorithm with the small update approach is the best available  

We propose an approach for finding an optimal path in a flexible jobshop manufacturing system considering two criteria of time and cost. With rise in demands, advancement in technology and increase in production capacity, the need for more shops persists. Therefore, a flexible jobshop system has more than one shop with the same duty. The difference among shops with the same duty is in their machines with various specifications. A network is configured in which the nodes are considered to be the shops with arcs representing the paths among the shops. An automated guided vehicle functions as a material handling device through the manufacturing network. To account for uncertainty, we consider... 

Bus terminal assignment with the objective of maximizing public transportation service is known as bus terminal location problem (BTLP). We formulate the BTLP, a problem of concern in transportation industry, as a p-uncapacitated facility location problem (p-UFLP) with distance constraint. The p-UFLP being NP-hard (Krarup and Pruzan, 1990), we propose evolutionary algorithms for its solution. According to the No Free Lunch theorem and the good efficiency of the distinctive preserve recombination (DPX) operator, we design a new recombination operator for solving a BTLP by new evolutionary and memetic algorithms namely, genetic local search algorithms (GLS). We also define the potential... 

Here, an approach for finding an optimal path in a flexible jobshop manufacturing system considering two criteria of time and cost is proposed. A network is configured in which the nodes are considered to be the shops with arcs representing the paths among the shops. An automated guided vehicle functions as a material handling device through the manufacturing network. To account for uncertainty, time is considered to be a triangular fuzzy number and apply an expert system to infer the cost. The expert system based on fuzzy rule backpropagation network to configure the rules for estimating the cost under uncertainty is proposed. A multiple linear regression model is applied to analyze the... 

We present a modified examplar-based inpainting method in the framework of patch sparsity. In the examplar-based algorithms, the unknown blocks of target region are inpainted by the most similar blocks extracted from the source region, with the available information. Defining a priority term to decide the filling order of missing pixels ensures the connectivity of object boundaries. In the exemplar-based patch sparsity approaches, a sparse representation of missing pixels was considered to define a new priority term. Here, we modify this representation of the priority term and take measures to compute the similarities between fill-front and candidate patches. Comparative reconstructed test... 

We propose a cost estimation model based on a fuzzy rule backpropagation network, configuring the rules to estimate the cost under uncertainty. A multiple linear regression analysis is applied to analyze the rules and identify the effective rules for cost estimation. Then, using a dynamic programming approach, we determine the optimal path of the manufacturing network. Finally, an application of this model is illustrated through a numerical example showing the effectiveness of the proposed model for solving the cost estimation problem under uncertainty  

We present a non-monotone trust region algorithm for unconstrained optimization. Using the filter technique of Fletcher and Leyffer, we introduce a new filter acceptance criterion and use it to define reference iterations dynamically. In contrast with the early filter criteria, the new criterion ensures that the size of the filter is finite. We also show a correlation between problem dimension and the filter size. We prove the global convergence of the proposed algorithm to first- and second-order critical points under suitable assumptions. It is significant that the global convergence analysis does not require the common assumption of monotonicity of the sequence of objective function... 

We present a new filter trust-region approach for solving unconstrained nonlinear optimization problems making use of the filter technique introduced by Fletcher and Leyffer to generate non-monotone iterations. We also use the concept of a multidimensional filter used by Gould et al. (SIAM J. Optim. 15(1):17-38, 2004) and introduce a new filter criterion showing good properties. Moreover, we introduce a new technique for reducing the size of the filter. For the algorithm, we present two different convergence analyses. First, we show that at least one of the limit points of the sequence of the iterates is first-order critical. Second, we prove the stronger property that all the limit points... 

Recently, we described a generalization of Rosser's algorithm for a single linear Diophantine equation to an algorithm for solving systems of linear Diophantine equations. Here, we make use of the new formulation to present a new algorithm for solving rank one perturbed linear Diophantine systems, based on using Rosser's approach. Finally, we compare the efficiency and effectiveness of our proposed algorithm with the algorithm proposed by Amini and Mahdavi-Amiri (Optim Methods Softw 21:819-831, 2006)  

We present an exact penalty approach for solving constrained non-linear least-squares problems, when the projected structured Hessian is approximated by a projected version of the structured BFGS formula and prove its local two-step Q-superlinear convergence. The numerical results obtained in an extensive comparative testing experiment confirm the approach to be reliable and efficient  

We propose a way to use the Markowitz pivot selection criterion for choosing the parameters of the extended ABS class of algorithms to present an effective algorithm for generating sparse null space bases. We explain in detail an efficient implementation of the algorithm, making use of the special MATLAB 7. 0 functions for sparse matrix operations and the inherent efficiency of the ANSI C programming language. We then compare our proposed algorithm with an implementation of an efficient algorithm proposed by Coleman and Pothen with respect to the computing time and the accuracy and the sparsity of the generated null space bases. Our extensive numerical results, using coefficient matrices of... 

In the earlier version, each iteration consisted of one so-called feasibility step and a few -at most three-centering steps. Here, each iteration consists of only a feasibility step. Thus, the new algorithm demands less work in each iteration and admits a simple analysis of complexity bound. The complexity result coincides with the best-known iteration bound for infeasible interior-point methods