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linear programming-Based Decision Support System of Solar Power Reserve Management in Pulsation Free Current Circulation (PFCC) for Agricultural Systems

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IEEE ACCESS 2025年 13卷 44510-44525页

作者： Saivineeth, M. Venkateswarlu, B. Vellore Inst Technol Sch Adv Sci Dept Math Vellore 632014 India

Sustainably powering agricultural systems including greenhouses, irrigation, and farm equipment relies on the Pulsation Free Current Circulation System's (PFCC) efficient use of solar energy reserves. Improving the distribution of solar power reserves in light of the fact that solar energy output varies over time is the primary goal of this research. Energy reserve expenses are reduced and storage battery operating life is extended using an interval linear programming technique. Power distribution that is both dependable and efficient is achieved by use of the system's models, which take into consideration factors like allocation costs, power reserve and network losses. Through the use of a two-tiered structural approach, the optimization procedure guarantees balanced dispatching and rapid responsiveness to fluctuating energy needs by managing distribution and reserve capacity in tandem. Enhancing the sustainability of solar-powered agricultural systems, the suggested technology minimizes battery deterioration and ensures energy availability during important agricultural activities. Multi-power reserve systems are also used to reduce distributed energy swings, which makes the system even more reliable and stable. According to the findings of the tests, the technology has the power to greatly improve the efficiency and longevity of solar energy in farming, with an output efficiency of 0.99(in decimal). This strategy tackles the problem of energy management and sets the stage for renewable energy solutions that can be easily scaled and adjusted for use in agriculture. This will guarantee the sustainability and effectiveness of these solutions in the long run.

关键词： Biological system modeling Water resources Optimization Wind farms Resource management Costs Load modeling Crops Wind power generation Wind forecasting Pulsation free current circulation solar power reserve linear programming farming-system solar power allocation

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linear programming formulations for the hydro production function in a water value calculation

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RENEWABLE ENERGY 2025年 243卷

作者： Guisandez, Ignacio Perez-Diaz, Juan Ignacio Univ Politecn Madrid Dept Hydraul Energy & Environm Engn 28040 Madrid Spain

The global transition toward sustainability demands improved modeling approaches for energy sources like hydroelectricity. This study compares five linear programming formulations for modeling the hydro production function: four derived from prior works (the typical method based on a single concave piecewise linear flow- power function, a new parameterization of it, the upper convex hull method, and a linear version of the logarithmic independent branching 6-stencil method) and a novel approach introduced here (the binary function method). The comparison focuses on water value calculations, and subsequent scheduling simulations, for three hypothetical hydropower plants with varying reservoir regulation capacities across three national day-ahead electricity markets, using daily and weekly stages. The results highlight the linear version of the logarithmic independent branching 6-stencil method as the most accurate. For effectiveness, this method and the binary function method excel in daily and weekly stages, respectively. The classical parameterization of the single concave piecewise linear flow-power function is the fastest, while the new parameterization proposed here offers the best trade-off between effectiveness and speed. These findings provide actionable insights for selecting the most suitable method based on the stage length and reservoir regulation capacity, aiding in the optimization of hydropower operations in increasingly competitive electricity markets.

关键词： Hydro production function linear programming Long-term hydro scheduling Problem linearization Water value

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linear programming of the Loopwise Route Representation for the Shortest Path Problems by Introducing the Reference Link Flow

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IEEE ACCESS 2025年 13卷 38856-38864页

作者： Kim, Geunu Kim, Changyeong Park, Sanghoon Kim, Jeonghun Jang, In Gwun Korea Adv Inst Sci & Technol Cho Chun Shik Grad Sch Mobil Daejeon 34051 South Korea

Loopwise route representation (LRR), which has been recently proposed as an alternative network representation, can determine the optimal path for the vehicle routing problems with a simpler optimization formulation. However, it requires a significant computing burden due to nonlinear optimization. This study proposes a novel linearization approach for the LRR by introducing the reference link flow. The proposed method consists of two stages: selecting the reference link flow in Stage 1 and formulating a linearized optimization problem in Stage 2. Through the above two stages, the proposed method does not require nonlinear functions while maintaining the unique advantages of the LRR. To validate the performance of the proposed method, numerical experiments are designed with ideal grid-type networks of various sizes. For comparison, integer linear programming (ILP) is conducted in the corresponding link-wise route representation. Numerical results demonstrate that the proposed linearization outperforms conventional ILP in terms of computing time and solution accuracy. For a 100 x 100 grid-type network, the proposed method takes 0.15 seconds, whereas conventional ILP takes 1.39 seconds. Furthermore, the proposed method provides a 0-to-1% relative error (i.e., optimal and near-optimal solutions) in 802 cases out of total 1000 cases, whereas conventional ILP provides the same level of errors only in 406 cases. With further work, the proposed linearization scheme could be applied to other vehicle routing problems such as a traveling salesman problem in order to enhance a computational efficiency.

关键词： Optimization Vehicle routing Shortest path problem Costs Mathematical models linear programming Electric vehicles Topology Routing Robot sensing systems Loop-wise route representation linear programming reference link flow shortest path problem topology optimization vehicle routing problem

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linear programming Approach to Optimal Control Problems with Unbounded State Constraint

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第2期204卷 1-23页

作者： Shvartsman, Ilya Penn State Harrisburg Middletown PA 17057 USA

This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in continuous time. It is known that these problems are related to certain infinite-dimensional linear programming problems, but to facilitate the analysis of these LP problems, it is usually assumed that all admissible trajectories remain in a compact set. In the recent paper (Shvartsman in Discrete Contin Dyn Syst Series B 29(1):110-123, 2024), a problem without the latter assumption was considered, and Alexandroff compactification was used to carry out the analysis. In this paper, we carry over and further extend the compactification approach to problems in continuous time and show applications of the obtained results to estimating Abel and Ces & agrave;ro limits of the optimal value functions.

关键词： Optimal control Infinite horizon Discounting Long-run average linear programming

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linear programming with infinite, finite, and infinitesimal values in the right-hand side

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APPLIED MATHEMATICS AND COMPUTATION 2025年 486卷

作者： Cococcioni, Marco Fiaschi, Lorenzo Univ Pisa Dept Informat Engn Largo Lucio Lazzarino 1 I-56122 Pisa Italy

The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron becomes more complex, since its vertices can be represented by non-purely finite coordinates, and so is the optimum of the problem. The introduction of such constraints enlarges the class of linear programs, where those described by finite values only become a special case. To tackle optimization problems over such polyhedra, there is a need for an ad-hoc solving routine: this work proposes a generalization of the Simplex algorithm, which is able to solve common linear programs as corner cases. Finally, the study presents three relevant applications that can benefit from the use of these novel constraints, making the use of the extended Simplex algorithm essential. For each application, an exemplifying benchmark is solved, showing the effectiveness of the proposed routine.

关键词： linear programming Scientific computing with infinite/finite/infinitesimal values Infinite/infinitesimal values in the right-hand side Grossone methodology

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linear programming complementation

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THEORETICAL COMPUTER SCIENCE 2025年 1032卷

作者： Gadouleau, Maximilien Mertzios, George B. Zamaraev, Viktor Univ Durham Dept Comp Sci Durham England Univ Liverpool Dept Comp Sci Liverpool England

In this paper we introduce a new operation for linear programming (LP), called LP complementation, which resembles many properties of LP duality. Given a maximisation (resp. minimisation) LP P, we define its complement Q as a specific minimisation (resp. maximisation) LP which has the same objective function as P. Our central result is the LP complementation theorem, that relates the optimal value OPT(P) of P and the optimal value OPT(Q) of its complement by OPT(P) + 1 1 OPT(Q) = 1. The LP complementation operation can be applied if and only if P has an optimum value greater than 1. To illustrate this, we first apply LP complementation to hypergraphs. For any hypergraph H, we review the four classical LPs, namely covering x(H), packing P(H), matching M(H), and transversal T (H). For every hypergraph H = (V, E), we call H = (V, {V \ e : e E E}) the complement of H. For each of the above four LPs, we relate the optimal values of the LP for the dual hypergraph H* to that of the complement hypergraph H (e.g. 1 1 OPT(x(H*)) + = 1). OPT(x(H)) We then apply LP complementation to fractional graph theory. We prove that the LP for the fractional in-dominating number of a digraph D is the complement of the LP for the fractional total out-dominating number of the digraph complement D of D. Furthermore we apply the hypergraph complementation theorem to matroids. We establish that the fractional matching number of a matroid coincide with its edge toughness. As our last application of LP complementation, we introduce the natural problem VERTEX COVER WITH BUDGET (VCB): for a graph G = (V, E) and a positive integer b, what is the maximum number tb of vertex covers S1, ... , Stb of G, such that every vertex v E V appears in at most b vertex covers? The integer b can be viewed as a "budget" that we can spend on each vertex and, given this budget, we aim to cover all edges for as long as possible. We relate VCB with the LP QG for the fractional chromatic number xf of a graph G. More sp

关键词： linear programming Duality Hypergraph Fractional vertex cover Fractional dominating number

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linear programming based heuristic algorithms for tunnel assignment and reconfiguration in MPLS networks

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TELECOMMUNICATION SYSTEMS 2024年第4期87卷 991-1013页

作者： Joung, Seulgi Ryu, Jaehyeon Kwon, Sun-Hyeon Shin, Jongyoon Park, Sungsoo Ajou Univ Dept Ind Engn 206 Worldcup Ro Suwon 16499 South Korea Korea Adv Inst Sci & Technol Dept Ind & Syst Engn 291 Daehak Ro Daejeon 34141 South Korea SK telecom Seongnam Si Gyeonggi Do South Korea

Multi-Protocol Label Switching (MPLS) sets up a connecting tunnel for each origin-destination pair of traffic demands to send data packets over Internet Protocol (IP) networks. We should assign each tunnel to one of the available candidate paths to achieve efficient use of the network and avoid congestion. Additionally, we need to update the bandwidths and routing of the tunnels efficiently in short periods of time to accommodate fluctuating traffic demands, which we refer to as the reconfiguration problem. In this paper, we propose formulations and linear programming-based heuristic algorithms for the tunnel assignment and reconfiguration problems arising in MPLS networks. First, we propose a formulation and algorithms for the tunnel assignment problem, considering realistic constraints such as port limitations and priority queue capacity restrictions. Our model incorporates unidirectional, bidirectional, protected, and unprotected tunnel cases altogether. Then, we present a heuristic algorithm to obtain a schedule for changing the bandwidths and routing of tunnels from the current configuration to a target configuration quickly while adhering to network capacity constraints. We report computational results using some random data from the real-life telecommunication network of the Republic of Korea.

关键词： Multi-protocol label switching Bandwidth packing problem Heuristic Integer programming linear programming

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linear programming Models for the Design of Energy-Efficient IoT Networks With Transmission Constraints

IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING

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IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING 2024年第1期8卷 391-401页

作者： Manuel, Ebin M. Pankajakshan, Vinod Mohan, Manil T. Indian Inst Technol Roorkee Dept Elect & Commun Roorkee 247664 India Indian Inst Technol Roorkee Dept Math Roorkee 247664 India

Networks consisting of sensors of multiple transmission ranges are preferred for next-generation wireless sensor networks because of their functional advantages. However, such multiple transmission ranges enforce restrictions in signal transmissions. In this work, we conduct the signal flow analysis in such networks and address the energy-efficient signal aggregation techniques that rely on linear programming techniques. We introduce a mathematical program that captures the widely different characteristics associated with the networks with sensors of multiple transmission ranges and converts it into an integer linear program which is hard to solve. To solve the scalability issues, we devise a linear program relaxation method to arrive at a solution that reduces the total signal transmissions in the network. We accommodate efficient signal compaction techniques based on compressive sensing. The simulation results demonstrate the impressive performance of the proposed method in reducing transmissions and conserving energy.

关键词： Sensors Wireless sensor networks Sensor phenomena and characterization Routing Costs linear programming Correlation IoT networks signal aggregation multiple transmission ranges LP relaxation LP rounding

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linear programming ON THE STIEFEL MANIFOLD

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SIAM JOURNAL ON OPTIMIZATION 2024年第1期34卷 718-741页

作者： Song, Mengmeng Xia, Yong Beihang Univ Sch Math Sci Beijing 100191 Peoples R China Beihang Univ Sch Math Sci Beijing 100191 Peoples R China

linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all p-tuples of orthonormal vectors in Rn satisfying k additional linear constraints. Despite the classical polynomial -time solvable case k = 0, general (LPS) is NP -hard. According to the Shapiro-Barvinok-Pataki theorem, (LPS) admits an exact semidefinite programming relaxation when p(p + 1)/2 <= n - k, which is tight when p = 1. Surprisingly, we can greatly strengthen this sufficient exactness condition to p <= n - k, which covers the classical case p <= n and k = 0. Regarding (LPS) as a smooth nonlinear programming problem, we reveal a nice property that under the linear independence constraint qualification, the standard first- and second -order local necessary optimality conditions are sufficient for global optimality when p + 1 <= n - k.

关键词： linear programming Stiefel manifold quadratically constrained quadratic optimization semidefinite programming optimality conditions

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linear programming solve-predict for tunable couplers with coupling and phase differences

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AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS 2024年 174卷

作者： Yin, Song Feng Cao, Yuan Gu, Xin Yue Lin, Bin Liaoning Tech Univ Sch Elect & Control Engn Huludao 125100 Peoples R China

The demands for high flexibility in signal phase modulation, operating frequency, and amplitude modulation in contemporary wireless communication systems present challenges for reconfigurable devices. To address this issue, two tunable couplers have been designed, which consist of two parallel microstrips couplers with oneeighth wavelength and phase-shift networks composed of two varactors and coupling lines. Adjusting the even-odd mode impedances of one-eighth wavelength parallel coupled microstrip lines has been established as a means to control the coupling. The alteration of the capacitance of the varactors allows for manipulation of the phase differences in the couplers. Considering the disparities among simulation, manufacturing, and theoretical models, to get the capacitance combinations corresponding to the specific phase differences more quickly and accurately, the linear programming solve-predict method is introduced to this design. Finally, the errors between the predicted values and the theoretical values for the actual values are compared. The relative errors of the theoretical values are not less than 31.76 %, and the maximum errors of the predicted values are not more than 12.5 %, which shows the effectiveness of the method. For demonstration, two couplers operating at 2.4 GHz with different tuning ranges were designed and fabricated, work-1 with a tuning range of 45-135 degrees and work-2 with a tuning range of 0-180 degrees degrees. Based on the standard of 10 dB return loss and 1 dB unbalanced coupling, the relative bandwidths of work-1 and work-2 are not less than 42 % and 25 %. The relative bandwidths of phase differences effective modulation (+/- 5 degrees) are 20.1-42 % and 6-25%, respectively.

关键词： Arbitrary coupling Phase tunable couplers Phase-shift networks linear programming Solved-predicted Varactors

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