Motivated by Bland's linear programming (LP) generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum flow algorithm, we analyze three closely related natural augmentation rul...
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Motivated by Bland's linear programming (LP) generalization of the renowned Edmonds-Karp efficient refinement of the Ford-Fulkerson maximum flow algorithm, we analyze three closely related natural augmentation rules for LP and integer-linear programming (ILP) augmentation algorithms. For all three rules and in both contexts, LP and ILP, we bound the number of augmentations. Extending Bland's "discrete steepest-descent" augmentation rule (i.e., choosing directions with the best ratio of cost improvement per unit 1-norm length, and then making maximal augmentations in such directions) from LP to ILP, we (i) show that the number of discrete steepest-descent augmentations is bounded by the number of elements in the Graver basis of the problem matrix and (ii) give the first strongly polynomial-time algorithm for N-fold ILP. For LP, two of the rules can suffer from a "zig- zagging" phenomenon, and so in those cases we apply the rules more subtly to achieve good bounds. Our results improve on what is known for such augmentation algorithms for LP (e.g., extending the style of bounds found by Kitahara and Mizuno for the number of steps in the simplex method) and are closely related to research on the diameters of polytopes and the search for a strongly polynomial-time simplex or augmentation algorithm.
New technologies allow to carry out a change in the way we educate more focused on the student rather than the teacher. In this regard, with the support of Information and Communications Technology (TIC) is very commo...
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New technologies allow to carry out a change in the way we educate more focused on the student rather than the teacher. In this regard, with the support of Information and Communications Technology (TIC) is very common nowadays, students are increasingly using their mobile devices in the classroom, becoming the best friend student, figuratively. Based on the above drawing these guidelines, this paper presents the development of an App for calculating basic feasible solutions to transport problems to support the teaching-learning process to be used inside and outside the classroom; this app is to provide a learning environment movement to transport problems in linear programming (PL).
This paper describes a linear programming (LP) approach for solving the network utility maximization problem. The developed approach is inspired by a convex relaxation technique from non-convex polynomial optimization...
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ISBN:
(纸本)9781509013364
This paper describes a linear programming (LP) approach for solving the network utility maximization problem. The developed approach is inspired by a convex relaxation technique from non-convex polynomial optimization methods. In contrast to most of the existing results where concavity of the network's utility function is often assumed, the proposed LP approach may still be used to solve the NUM problem even in the absence of such a concavity assumption. Although the presented LP approach is originally formulated to compute upper bounds for the global optima of the NUM problem, we illustrate through simulation examples that the obtained bounds often correspond to the exact global optima.
Environmental concerns, providing a decrease in production cost and utility of products and materials constitute reverse logistics activities in recent years. One of the most important goals of the reverse logistics n...
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Environmental concerns, providing a decrease in production cost and utility of products and materials constitute reverse logistics activities in recent years. One of the most important goals of the reverse logistics network design is to minimize the costs or to maximize the profit. By the way, deciding on the number of collection centers, fabrics and distribution centers in a reverse logistics system are also very important. Uncertain factors can affect a reverse logistic network negatively. In this paper to cope with these uncertainties a fuzzy mixed integer linear programming model is developed for a reverse logistics network with a real case application on white goods sector refrigerator product group. In the proposed model customers' demand, return rate of products, unit transportation cost and repair cost are considered as uncertain parameters. The proposed model is solved by using General Algebraic Modeling System (GAMS)/CPLEX 9.0 optimization software ant it is executed for different return and repair rates to determine and compare the number of collection centers, fabrics, distribution centers and maximum profit. The obtained results are consistent with each other.
This paper deals with the problem of stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with a fixed delay by linear programming (LP) while imposing positivity in closed-loop. The sufficient conditions o...
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ISBN:
(纸本)9781467389549
This paper deals with the problem of stability and stabilization of Takagi-Sugeno (T-S) fuzzy systems with a fixed delay by linear programming (LP) while imposing positivity in closed-loop. The sufficient conditions of stabilization are derived using the single Lyapunov-Krasovskii Functional (LKF). An example of a real plant is studied, and the comparison between LMI and LP approach is presented to show the advantages of the design procedure.
We compare the computational performance of linear programming (LP) and the policy iteration algorithm (PIA) for solving discrete-time infinite-horizon Markov decision process (MDP) models with total expected discount...
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We compare the computational performance of linear programming (LP) and the policy iteration algorithm (PIA) for solving discrete-time infinite-horizon Markov decision process (MDP) models with total expected discounted reward. We use randomly generated test problems as well as a real-life health-care problem to empirically show that, unlike previously reported, barrier methods for LP provide a viable tool for optimally solving such MDPs. The dimensions of comparison include transition probability matrix structure, state and action size, and the LP solution method. (C) 2015 Elsevier Ltd. All rights reserved.
Clustering is a hierarchical method to data transmission in wireless sensor networks, which has a considerable effect on energy conservation. A balanced and efficient clustering has an important role in these networks...
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ISBN:
(纸本)9781509041404
Clustering is a hierarchical method to data transmission in wireless sensor networks, which has a considerable effect on energy conservation. A balanced and efficient clustering has an important role in these networks. This paper discusses an optimal clustering method in wireless sensor network. Firstly, by considering energy and distance parameters, we model the clustering problem using two techniques, Integer linear programming and linear programming. Then we propose a clustering algorithm based on the optimal selected cluster heads. Experimental results shown that linear programming technique has better performance in energy consumption and network lifetime in comparison to the Integer linear programming technique.
This paper addresses the problem of decentralised event detection in a large-scale wireless sensor network (WSN), where without the coordination of any fusion centre, sensor nodes autonomously make decisions through i...
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This paper addresses the problem of decentralised event detection in a large-scale wireless sensor network (WSN), where without the coordination of any fusion centre, sensor nodes autonomously make decisions through information exchange with their neighbours. We formulate the event detection problem as a linear program, and propose a heuristic decentralised linear programming (DLP) approach to solve it. Compared to the existing algorithms which solve decentralised optimisation problems, the DLP algorithm requires low communication cost per iteration and shows fast convergence. Convergence property of the DLP algorithm is theoretically analysed, and then validated through simulation results. We also implement the DLP algorithm in the structural health monitoring application and demonstrate its effectiveness in decentralised event detection.
In this paper, we study the fuzzy bilevel programming problem in which the coefficients in the objective functions and the constraints are assumed to be fuzzy numbers. In comparison with deterministic bilevel programm...
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ISBN:
(纸本)9781509048410
In this paper, we study the fuzzy bilevel programming problem in which the coefficients in the objective functions and the constraints are assumed to be fuzzy numbers. In comparison with deterministic bilevel programming, this kind of problem is usually much more difficult to solve due to fuzziness involved in the problem. To handle such a problem, we first transform it into an interval bilevel programming in terms of αlevel sets of fuzzy number. For the transformed interval bilevel problem, a new possibility degree of interval numbers is applied to convert the interval constraints into equivalent forms and the order relation of intervals is used to transform interval objective functions into crisp ones. Based on these, the equivalent deterministic bilevel programming can be obtained. Finally, a numerical example is given to demonstrate the feasibility of the proposed approach.
Post-silicon validation is the most vital parts of modern Integrated Circuits. The key challenge of silicon validation is that it has limited observability and controllability of internal signals. To improve those, a ...
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ISBN:
(纸本)9781467367264
Post-silicon validation is the most vital parts of modern Integrated Circuits. The key challenge of silicon validation is that it has limited observability and controllability of internal signals. To improve those, a profitable set of signals should be selected. An automated procedure is proposed to select those signals which are used to facilitate early malfunctions of the design. Given the input vector set to the design an error transmission matrix is generated. From that, both relatively independent and dependent flip-flops are identified for grouping the signals through Mixed-Integer linear programming. This method precisely identifies the paths which improves observability and can speed up the process.
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