A linear programming method for fault restoration is proposed, which considering the dynamic island partition and balanced node. Firstly, the analytical expression of the mapping between the network topology matrix an...
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(纸本)9798350339345
A linear programming method for fault restoration is proposed, which considering the dynamic island partition and balanced node. Firstly, the analytical expression of the mapping between the network topology matrix and the island partition is expressed, while the balanced node selection strategy is proposed. From this, the dynamic fault restoration model for distribution network is established. Secondly, the linearization of island partition map is realized based on Koopman theory, and the mixed integer linear programming form of fault dynamic restoration model is established by combining the big M method. The effectiveness of this method is tested by a 43-node system. The results show that the proposed method can achieve the coordination of network topology and distributed generations(DGs), and effectively improve the resilience of the distribution network.
BackgroundAdequate nutrition is crucial for optimal child growth and development, especially for children under five. Over the years, the linear programming (LP) approach has been used to develop food-based recommenda...
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BackgroundAdequate nutrition is crucial for optimal child growth and development, especially for children under five. Over the years, the linear programming (LP) approach has been used to develop food-based recommendations (FBRs) for children under *** scoping review aims to (i) summarize the use of LP in diet optimization to improve nutrient adequacy, (ii) evaluate nutrient requirements by using modelling techniques when the use of local foods is optimized, and (iii) identify and compare the problem nutrient(s).MethodsThis scoping review was performed by searching PubMed and Wiley databases from 2012 to 2025, and also screened the reference lists of included publications to identify potentially eligible articles. Forward and backward citation searches were also performed to supplement the structured searches in the *** studies were included after a systematic literature search. The objective functions and the final set of FBRs of the included studies were summarized. Moreover, the nutrient intakes in the optimized diets and the problem nutrients of the included studies were compared and discussed. When optimizing diets using the LP approach, most of the nutrient requirements can be achieved, except for iron and zinc and, in some studies, thiamine, niacin, folate, and calcium. Iron was identified as the problem nutrient in all studies involving infants aged 6 to 11 months old, followed by calcium and zinc. In children aged 12 to 23 months, iron and calcium were identified as the problem nutrients in almost all studies, followed by zinc and folate. In children aged 1 to 3 years, fat, calcium, iron, and zinc were recognized as the absolute problem nutrients, while fat, calcium, and zinc were the absolute problem nutrients for children aged 4 to 5 years. Findings on dietary inadequacy of nutrient intakes were remarkably consistent across studies conducted in different geographic and socioeconomic *** diets in
This letter presents a novel coordinate-wise event-triggered control mechanism for stabilizing and ensuring positivity of continuous-time linear systems with time delay. By explicitly comparing each state coordinate a...
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This letter presents a novel coordinate-wise event-triggered control mechanism for stabilizing and ensuring positivity of continuous-time linear systems with time delay. By explicitly comparing each state coordinate against individual thresholds, we achieve a more accurate determination of when the event-triggered condition is violated. This approach ensures positivity, since each coordinate is treated independently within the triggering condition, and effectively handles the destabilizing influence of delay. We formulate the stability and positivity criteria as solvable linear programming constraints. Additionally, we prove that the proposed mechanism excludes Zeno behavior by guaranteeing a positive lower bound on inter-event times. Numerical examples illustrate that our method balances system performance and reduced triggering frequency far more effectively than time-triggered strategies.
The Cohn-Elkies linear program for sphere packing, which was used to solve the 8 and 24 dimensional cases, is conjectured to not be sharp in any other dimension d > 2. By mapping feasible points of this infinite-di...
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The Cohn-Elkies linear program for sphere packing, which was used to solve the 8 and 24 dimensional cases, is conjectured to not be sharp in any other dimension d > 2. By mapping feasible points of this infinite-dimensional linear program into a finite-dimensional problem via discrete reduction, we provide a general method to obtain dual bounds on the Cohn-Elkies linear program. This reduces the number of variables to be finite, enabling computer optimization techniques to be applied. Using this method, we prove that the Cohn-Elkies bound cannot come close to the best packing densities known in dimensions 3 <= d <= 13 except for the solved case d = 8. In particular, our dual bounds show the Cohn-Elkies bound is unable to solve the 3, 4, and 5 dimensional sphere packing problems. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar
In this paper, a new method to address the scheduling problem of a renewable energy community while considering network constraints and users' privacy preservation is proposed. The method decouples the optimizatio...
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In this paper, a new method to address the scheduling problem of a renewable energy community while considering network constraints and users' privacy preservation is proposed. The method decouples the optimization solution into two interacting procedures: conic projection(CP) and linear programming(LP) optimization. A new optimal CP method is proposed based on local computations and on the calculation of the roots of a fourth-order polynomial for which a closed-form solution is known. Computational tests conducted on both 14-bus and 84-bus distribution networks demonstrate the effectiveness of the proposed method in obtaining the same quality of solutions compared with that by a centralized solver. The proposed method is scalable and has features that can be implemented on microcontrollers since both LP and CP procedures require only simple matrix-vector multiplications.
In estimating the average treatment effect in observational studies, the influence of confounders should be appropriately addressed. To this end, the propensity score is widely used. If the propensity scores are known...
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In estimating the average treatment effect in observational studies, the influence of confounders should be appropriately addressed. To this end, the propensity score is widely used. If the propensity scores are known for all the subjects, bias due to confounders can be adjusted by using the inverse probability weighting (IPW) by the propensity score. Since the propensity score is unknown in general, it is usually estimated by the parametric logistic regression model with unknown parameters estimated by solving the score equation under the strongly ignorable treatment assignment (SITA) assumption. Violation of the SITA assumption and/or misspecification of the propensity score model can cause serious bias in estimating the average treatment effect (ATE). To relax the SITA assumption, the IPW estimator based on the outcome-dependent propensity score has been successfully introduced. However, it still depends on the correctly specified parametric model and its identification. In this paper, we propose a simple sensitivity analysis method for unmeasured confounders. In the standard practice, the estimating equation is used to estimate the unknown parameters in the parametric propensity score model. Our idea is to make inferences on the (ATE) by removing restrictive parametric model assumptions while still utilizing the estimating equation. Using estimating equations as constraints, which the true propensity scores asymptotically satisfy, we construct the worst-case bounds for the ATE with linear programming. Differently from the existing sensitivity analysis methods, we construct the worst-case bounds with minimal assumptions. We illustrate our proposal by simulation studies and a real-world example.
This study uses linear programming to develop a methodology for selecting the best raw material mix in an ASCOM cement plant in Egypt. In cement factories, this type adheres to Egyptian chemical composition criteria f...
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This study uses linear programming to develop a methodology for selecting the best raw material mix in an ASCOM cement plant in Egypt. In cement factories, this type adheres to Egyptian chemical composition criteria for raw feed (e.g. 82.5% calcium carbonate, 14.08% silica, 2.5% alumina and 0.92% iron oxide). Furthermore, the model is bound by industry-specific characteristics (e.g. lime saturation factor, silica modulus, alumina modulus and loss of ignition). The results reveal that the model is able to accurately reproduce the mixing of high-quality feed with varying constituent percentages. It is also capable of determining the combining limitations of each ingredient. Furthermore, it demonstrates optimality for additive sourcing short-term planning and capping limestone quality to meet changeable component combinations. Additionally, improving the raw mix reduces limestone feed quality from 51 to 50.6%, resulting in the inclusion of extra limestone reserves.
This letter presents an enhanced Trust Region Method (TRM) for Sequential linear programming (SLP) designed to improve the initial feasible solution to a constrained nonlinear programming problem while maintaining the...
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This letter presents an enhanced Trust Region Method (TRM) for Sequential linear programming (SLP) designed to improve the initial feasible solution to a constrained nonlinear programming problem while maintaining the interim solutions feasibility throughout the SLP iterations. The method employs a polytopic sub-approximation of the feasible region, defined around the interim solution as a level set based on variable limits for the linearization error. This polytopic feasible region is established by using a trust region that ensures that maximum limits of the linearization errors are respected. The method adaptively adjusts the size of the feasible region during iterations to achieve convergence to a local optimum by employing variable linearization error limits. Local convergence is attained by reducing the size of the trust radius. A case study illustrates the effectiveness of the proposed method, which is compared to the benchmark TRM that uses heuristic limits on the permissible changes in manipulated variables.
linear programming has had a tremendous impact in the modeling and solution of a great diversity of applied problems, especially in the efficient allocation of resources. As a result, this methodology forms the backbo...
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linear programming has had a tremendous impact in the modeling and solution of a great diversity of applied problems, especially in the efficient allocation of resources. As a result, this methodology forms the backbone of introductory courses in operations research. What students, and others, may not appreciate is that linear programming transcends its linear nomenclature and can be applied to an even wider range of important practical problems. The objective of this article is to present a selection, and just a selection, from this range of problems that at first blush do not seem amenable to linear programming formulation. The exposition focuses on the most basic models in these selected applications, with pointers to more elaborate formulations and extensions. Thus, our intent is to expand the modeling awareness of those first encountering linear programming. In addition, we hope this article will be of interest to those who teach linear programming and to seasoned academics and practitioners, alike.
This article recalls the recent work on a linear programming for-mulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then appl...
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This article recalls the recent work on a linear programming for-mulation of infinite horizon risk-sensitive control via its equivalence with a single controller game, using a classic work of Vrieze. This is then applied to a constrained risk-sensitive control problem with a risk-sensitive cost and risk-sensitive constraint. This facilitates a Lagrange multiplier based resolu-tion thereof. In the process, this leads to an unconstrained linear program and its dual, parametrized by a parameter that is a surrogate for Lagrange multiplier. This also opens up the possibility of a primal -dual type numeri-cal scheme wherein the linear program is a subroutine within the subgradient ascent based update rule for the Lagrange multiplier. This equivalent uncon-strained risk-sensitive control formulation does not seem obvious without the linear programming equivalents as intermediaries. We also discuss briefly other related algorithmic possibilities for future research.
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