A high generation of solar panels and wind turbines is able to increase voltage magnitudes of electricity grids, whereas uncoordinated procedures of recharging several plug-in electric vehicles (PEV) have capability t...
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A high generation of solar panels and wind turbines is able to increase voltage magnitudes of electricity grids, whereas uncoordinated procedures of recharging several plug-in electric vehicles (PEV) have capability to decrease them. Accordingly, this paper proposes a novel decentralized algorithm of power management to reschedule charging and discharging events of PEV over appropriate time slots of energy generation and consumption to maintain voltage profiles within their limits. A linear programming model of optimization is utilized to coordinate bi-directional power flows of charging and discharging PEV batteries, while considering solar panels and wind turbines in smart grids. Simulation results of 7 scenarios show that the proposed strategy is able to maintain voltage profiles of power grids within their margins by charging and discharging PEV batteries over specific hours of energy generation and consumption. The proposed algorithm of power management prevents PEV batteries from being overcharged or deeply discharged by keeping their state of charge between upper and lower boundaries. Therefore, the proposed technique has capability to increase PEV hosting capacity of distribution networks without significant upgrading requirements.
This paper investigates the fault detection filter and consensus control of positive multi-Agent systems with disturbances and faults. First, a kind of positive fault detection filter is designed by virtue of the posi...
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After the 1950s, operations research (OR) moved from military applications of scientific methods to a distinct academic discipline, applying mainly mathematical models to complex systems in the public and private sect...
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After the 1950s, operations research (OR) moved from military applications of scientific methods to a distinct academic discipline, applying mainly mathematical models to complex systems in the public and private sectors. linear programming (LP) with its simplex algorithm, developed by George Dantzig in 1949, is the first method that marked OR as a new academic discipline. The purpose of this article is to examine the evolution of OR through linear programming, its leading methodology, and some of its derivatives, concentrating on one of them-data envelopment analysis (DEA)-developed by Charnes, Cooper, and Rhodes in 1978. We focus on DEA and its derivatives, as this article is the most cited in a search performed using the main OR journals. Although we found LP to be mentioned much more than DEA in our search of Google Scholar and beyond, DEA is still well represented in the OR literature. Fur-thermore, based on insights gained from examining DEA vis-a-vis LP and the "secret" of their spread, we conclude with suggestions to further enhance OR's visibility, implementing ideas from OR founders and others over the years. Thus, future directions include combining hard and soft OR, involving interdisci-plinary teams, consulting of OR academic researchers, and more.(c) 2022 Elsevier B.V. All rights reserved.
A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the propos...
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A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the proposed solution are that it uses economic value added (EVA), a comprehensive performance index commonly used in business management, instead of regulation to a set point or to a interval of stock values;it does not require knowledge or prediction of the demand distribution;it achieves good efficiency with respect to a globally optimal value, defined in this paper, and no significant bullwhip effect, while being robust to demand and lead time variations. The proposed one step ahead optimal controller is compared with the classical (s, S) controller, as well as with a representative of the inventory and order-based production controller family. In order to make a fair comparison, this paper also proposes a tuning method for the latter two controllers. Numerical experiments based on average performance of the three controllers for a set of normally distributed demands show the superiority of the proposed one step ahead optimal controller, in terms of EVA as well as in terms of other measures proposed in the paper.
One of the oldest results in scheduling theory is that the Shortest Processing Time (SPT) rule finds an optimal solution to the problem of scheduling jobs on identical parallel machines to minimize average job complet...
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One of the oldest results in scheduling theory is that the Shortest Processing Time (SPT) rule finds an optimal solution to the problem of scheduling jobs on identical parallel machines to minimize average job completion times. We present a new proof of correctness of SPT based on linear programming (LP). Our proof relies on a generalization of a single-machine result that yields an equivalence between two scheduling problems. We first identify and solve an appropriate variant of our problem, then map its solutions to solutions for our original problem to establish SPT optimality. Geometric insights used therein may find further uses;we demonstrate two applications of the same principle in generalized settings. (c) 2022 Elsevier B.V. All rights reserved.
The problem of localizing a set of nodes from relative pairwise measurements appears in different fields, such as computer vision, sensor networks, and robotics. In practice, the measurements might be contaminated by ...
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The problem of localizing a set of nodes from relative pairwise measurements appears in different fields, such as computer vision, sensor networks, and robotics. In practice, the measurements might be contaminated by noise and outliers that lead to erroneous localization. Previous work has empirically shown that robust algorithms can, in some situations, almost completely cancel the effect of outliers. However, there is a theoretical gap in answering the following question: Under what conditions on the number, magnitude, and arrangement of the outlier measurements can we guarantee that a robust algorithm will recover the ground truth locations from the relative measurements alone? We denote this concept as verifiability, and answer the question for the case of an l(1)-norm robust optimization formulation, with translation measurements that are affected only by large-magnitude outliers and no small-magnitude noise. We prove that verifiability depends only on the topology of the graph, the location of the edges affected by the outliers, and the sign of the outliers, while it is independent of the (a priori unknown) true location of the nodes, and the magnitude of the outliers. We present an algorithm based on the dual simplex algorithm that checks the verifiability of a problem, and, if not verifiable, completely characterizes the space of equivalent solutions that are consistent with the given pairwise measurements. Our theory and algorithms can be used to compute the a priori probability of recovering a solution congruent or equivalent to the ground truth, without having access to the true locations.
In the lobster processing industry, savvy decision-makers call for robust, fast, and cheap decision support systems to simulate scenarios in hard-to-predict market conditions for planning sales and operations of the n...
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In the lobster processing industry, savvy decision-makers call for robust, fast, and cheap decision support systems to simulate scenarios in hard-to-predict market conditions for planning sales and operations of the next season. For optimizing the planning of simulated scenarios, linear programming models are customized to the constraints of each business case, and to data readily available from past seasons. For illustration, two significantly different cases are presented with results. Considerations regarding cross training and cell operations is discussed to resolve shifting bottlenecks and consequently improve financial performance. Depending on cases, direct margins could be improved by up to two-digit rates.
Currently, the simplex method and the interior point method are indisputably the most popular algo-rithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require...
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Currently, the simplex method and the interior point method are indisputably the most popular algo-rithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in order to establish strong duality. Hence strict feasibility is seldom a concern, even though strict feasibility is equivalent to stability and a compact dual optimal set. This lack of concern is also true for other types of degeneracy of basic feasible solutions in LP. In this paper we discuss that the specific degeneracy that arises from lack of strict feasibility necessarily causes difficul-ties in both simplex and interior point methods. In particular, we show that the lack of strict feasibility implies that every basic feasible solution, BFS, is degenerate;thus conversely, the existence of a nonde-generate BFS implies that strict feasibility (regularity) holds. We prove the results using facial reduction and simple linear algebra. In particular, the facially reduced system reveals the implicit non-surjectivity of the linear map of the equality constraint system. As a consequence, we emphasize that facial reduction involves two steps where, the first guarantees strict feasibility, and the second recovers full row rank of the constraint matrix. This illustrates the implicit singularity of problems where strict feasibility fails, and also helps in obtaining new efficient techniques for preproccessing. We include an efficient preprocessing method that can be performed as an extension of phase-I of the two-phase simplex method. We show that this can be used to avoid the loss of precision for many well known problem sets in the literature, e.g., the NETLIB problem set. (c) 2023 Elsevier B.V. All rights reserved.
Finding the optimal solution to a linear programming (LP) problem is a long-standing computational problem in Operations Research. This paper proposes a deep learning approach in the form of feed -forward neural netwo...
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Finding the optimal solution to a linear programming (LP) problem is a long-standing computational problem in Operations Research. This paper proposes a deep learning approach in the form of feed -forward neural networks to solve the LP problem. The latter is first modeled by an ordinary differential equations (ODE) system, the state solution of which globally converges to the optimal solution of the LP problem. A neural network model is constructed as an approximate state solution to the ODE system, such that the neural network model contains the prediction of the LP problem. Furthermore, we extend the capability of the neural network by taking the parameter of LP problems as an input variable so that one neural network can solve multiple LP instances in a one-shot manner. Finally, we validate the pro-posed method through a collection of specific LP examples and show concretely how the proposed method solves the example.(c) 2022 Elsevier B.V. All rights reserved.
We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transforma...
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We present a full-Newton step feasible interior-point algorithm for linear optimization based on a new search direction. We apply a vector-valued function generated by a univariate function on a new type of transformation on the centering equations of the system which characterizes the central path. For this, we consider a new function psi(t) = t7\4 psi(t) =t74$ \psi (t)\enspace ={t}<^>{\frac{7}{4}}$. Furthermore, we show that the algorithm finds the epsilon-optimal solution of the underlying problem in polynomial time, namely O(root nlog(n+3\7 root 2))On logn+327 epsilon$ O\left(\sqrt{n}\enspace \mathrm{log}\frac{\left(n+\frac{3}{\sqrt[7]{2}}\right)}{\epsilon }\right)$ iterations. Finally, a comparative numerical study is reported in order to analyze the efficiency of the proposed algorithm.
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