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 th...
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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.
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 complemen...
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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
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 f...
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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.
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-dimen...
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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.
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. ...
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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.
Based on the sequential linear programming approach for the data-driven computational mechanics considering uncertainty, a novel approach for truss optimization with displacement and stress constraints is introduced. ...
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Based on the sequential linear programming approach for the data-driven computational mechanics considering uncertainty, a novel approach for truss optimization with displacement and stress constraints is introduced. The proposed approach still capitalizes on the merits of data-driven computational mechanics, enabling optimization across various constitutive relationships by a mere replacement of the dataset. Moreover, in order to obtain the singular global optimal solution, the approach integrates the Simultaneous Analysis and Design framework, incorporating displacement as a design variable and establishing conservation law and kinematic relationship as equality constraints. In actuality, the data-driven approach is not only applicable to handling constitutive models but can also be employed to transform complex nonlinear relationships into linear combinations of data points. Consequently, the original nonlinear problem is transformed into a sequential linear programming problem. Numerical examples demonstrate that for stress-constrained truss optimization problem with the lower bound of cross-sectional area as 0, the proposed algorithm can directly yield a global optimum solution rather than a local optimal solution. In scenarios featuring linear constitutive behavior and incorporating stress and displacement constraints, both the results and efficiency yielded by this methodology closely align with traditional algorithms. Additionally, within the realm of a nonlinear constitutive model, the computational time is close to that of the linear constitutive model. In a word, the aforementioned results thoroughly demonstrate the effectiveness of the data-driven approach, providing a novel approach to solve nonlinear problems by sequential linear programming.
We consider two-stage robust linear programs with uncertain righthand side. We develop a General Polyhedral Approximation (GPA), in which the uncertainty set U is substituted by a finite set of polytopes derived from ...
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We consider two-stage robust linear programs with uncertain righthand side. We develop a General Polyhedral Approximation (GPA), in which the uncertainty set U is substituted by a finite set of polytopes derived from the vertex set of an arbitrary polytope that dominates U. The union of the polytopes need not contain U. We analyze and computationally test the performance of GPA for the frequently used budgeted uncertainty set U (with m rows). For budgeted uncertainty affine policies are known to be best possible approximations (if coefficients in the constraints are nonnegative for the second-stage decision). In practice calculating affine policies typically requires inhibitive running times. Therefore an approximation of U by a single simplex has been proposed in the literature. GPA maintains the low practical running times of the simplex based approach while improving the quality of approximation by a constant factor. The generality of our method allows to use any polytope dominating U (including the simplex). We provide a family of polytopes that allows for a trade-off between running time and approximation factor. The previous simplex based approach reaches a threshold at Gamma>root m after which it is not better than a quasi nominal solution. Before this threshold, GPA significantly improves the approximation factor. After the threshold, it is the first fast method to outperform the quasi nominal solution. We exemplify the superiority of our method by a fundamental logistics problem, namely, the Transportation Location Problem, for which we also specifically adapt the method and show stronger results.
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