This paper report the proposed of an optimization process of power dispatch in a DC microgrid using principles of linear programming. The microgrid used has as microsources: a wind turbine, a solar PV plant, a battery...
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ISBN:
(纸本)9781728199047
This paper report the proposed of an optimization process of power dispatch in a DC microgrid using principles of linear programming. The microgrid used has as microsources: a wind turbine, a solar PV plant, a battery bank, an electric load and an electrical interconnection point with utility network. The microgrid only allows the energy input from utility network. Additionally, every component is configured to offer/request a fixed nominal power of production/demand during periods of five minutes of duration;this is a new operating strategy: a constant power generation and consumption is defined in each microsources, loads and storages. To optimization process search the minimum cost of production, distributing adequate the demand between microsources and utility network under the proposed operating strategy. In this paper has been assumed that costs vary randomly in every period by each microsource and utility network. The optimization process has been development, implemented and compared with its equivalent in Matlab.
Deciding upon which algorithm would be the most efficient for a given set of linear programming problems is a significant step in linear programming solvers. CPLEX Optimizer supports primal and dual variants of the si...
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ISBN:
(纸本)9783030386290;9783030386283
Deciding upon which algorithm would be the most efficient for a given set of linear programming problems is a significant step in linear programming solvers. CPLEX Optimizer supports primal and dual variants of the simplex algorithm and the interior point method. In this paper, we examine a prediction model using artificial neural networks for the performance of CPLEX's interior point method on a set of benchmark linear programming problems (netlib, kennington, M ' esz ' aros, Mittelmann). Our study consists of the measurement of the execution time needed for the solution of 295 linear programming problems. Specific characteristics of the linear programming problems are examined, such as the number of constraints and variables, the nonzero elements of the constraint matrix and the right-hand side, and the rank of the constraint matrix of the linear programming problems. The purpose of our study is to identify a model, which could be used for prediction of the algorithm's efficiency on linear programming problems of similar structure. This model can be used prior to the execution of the interior point method in order to estimate its execution time. Experimental results show a good fit of our model both on the training and test set, with the coefficient of determination value at 78% and 72%, respectively.
In this paper, we are interested in the performance of the logarithmic barrier type of interior point method to solve a linear programming problem. We present a new alternative allowing to easily compute the step of d...
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In this paper, we are interested in the performance of the logarithmic barrier type of interior point method to solve a linear programming problem. We present a new alternative allowing to easily compute the step of displacement and without line search. This purpose is confirmed by numerical tests showing the efficiency of this approach versus classical line search methods.
Mismatch filters are generally used to reduce the range sidelobes when phase coded waveforms are used. It is shown that such mismatch filters can be designed with linear programming techniques. This particular formula...
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ISBN:
(纸本)9781728168135
Mismatch filters are generally used to reduce the range sidelobes when phase coded waveforms are used. It is shown that such mismatch filters can be designed with linear programming techniques. This particular formulation allows a trade between the degree of sidelobe suppression and the loss to the main peak sensitivity.
Following the breakthrough work of Tardos (Oper. Res. '86) in the bit-complexity model, Vavasis and Ye (Math. Prog. '96) gave the first exact algorithm for linear programming in the real model of computation w...
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ISBN:
(纸本)9781450369794
Following the breakthrough work of Tardos (Oper. Res. '86) in the bit-complexity model, Vavasis and Ye (Math. Prog. '96) gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For solving a linear program (LP) max c(T)x, Ax = b, x >= 0, A is an element of R-mxn, Vavasis and Ye developed a primal-dual interior point method using a 'layered least squares' (LLS) step, and showed that O(n(3.5) log((chi) over bar (A) + n)) iterations suffice to solve (LP) exactly, where (chi) over bar (A)* is a condition measure controlling the size of solutions to linear systems related to A. Monteiro and Tsuchiya (SIAM J. Optim. '03), noting that the central path is invariant under rescalings of the columns of A and c, asked whether there exists an LP algorithm depending instead on the measure (chi) over bar (A)*, defined as the minimum (chi) over bar (AD) value achievable by a column rescaling AD of A, and gave strong evidence that this should be the case. We resolve this open question affirmatively. Our first main contribution is an O(m(2)n(2) + n(3)) time algorithm which works on the linear matroid of A to compute a nearly optimal diagonal rescaling D satisfying (chi) over bar (AD) <= n((chi) over bar*)(3). This algorithm also allows us to approximate the value of (chi)over bar>(A) up to a factor n((chi) over bar*)(2). This result is in (surprising) contrast to that of Tuncel (Math. Prog. '99), who showed NP -hardness for approximating (chi) over bar (A) to within 2(poly(rank(A))). The key insight for our algorithm is to work with ratios g(i)/g(j) of circuits of A-i.e., minimal linear dependencies Ag = 0 which allow us to approximate the value of (chi) over bar (A)* by a maximum geometric mean cycle computation in what we call the 'circuit ratio digraph' of A. While this resolves Monteiro and Tsuchiya's question by appropriate preprocessing, it falls short of providing either a truly scaling i
In the framework of free flight, there can be no intersection between the protected areas of two planes. The traditional conflict resolution methods allow generally the aircraft to change the speed alone or to change ...
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ISBN:
(纸本)9781728158556
In the framework of free flight, there can be no intersection between the protected areas of two planes. The traditional conflict resolution methods allow generally the aircraft to change the speed alone or to change angle alone. Starting from the method of linear programming and based on solving some special problems, this article presents a method that can change the speed and angle of aircraft in the same time. Finally, some tests verify the feasibility of the method.
In this study, we consider a particular version of the hybrid flexible flow shop (HFFS) scheduling problem, inspired from a real-life application in a printing industry. The considered problem is a variation of the cl...
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In this study, we consider a particular version of the hybrid flexible flow shop (HFFS) scheduling problem, inspired from a real-life application in a printing industry. The considered problem is a variation of the classical Flow shop problem, in which specific constraints are jointly considered, such as non-identical parallel machines, sequence-dependent setups on machines, machine eligibility, and precedence constraints among jobs, in order to minimize the total tardiness time. After a problem description, a mathematical model, in form of mixed integer linear programming (MILP) model, that incorporates these aspects is developed and evaluated using ILOG Cplex software.
The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one consid...
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The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.
When solving a linear programming model, the coefficients should be fixed at specific values in advance. In practice, however, data overwhelmingly lack precision and this affects the model's optimal solution. Amon...
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When solving a linear programming model, the coefficients should be fixed at specific values in advance. In practice, however, data overwhelmingly lack precision and this affects the model's optimal solution. Among other theories including fuzzy set and intuitionistic fuzzy set theories, the neutrosophic set theory is considered a generalization of the two theories mentioned and is shown to be very powerful in assimilating inaccurate, vague, and maladjusted data. In this study, we deal with neutrosophic linear programming models where all coefficients are represented by triangular neutrosophic numbers. Maximization, minimization, and all types of constraints are considered. A novel parametric-based approach is introduced to solve this type of model and a few numerical examples are provided. Results show that the presented approach yields more realistic solutions. Finally, we conclude that the proposed approach is efficient, flexible, and capable of solving neutrosophic linear programming models.
A common situation when each academic period starts in academic institutions is the challenge of assign classrooms for the different courses in each faculty. This article shows an integer binary linear programming mod...
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ISBN:
(纸本)9783030395124;9783030395117
A common situation when each academic period starts in academic institutions is the challenge of assign classrooms for the different courses in each faculty. This article shows an integer binary linear programming model (objective function, constraints and the relationship between decision variables) which, on a daily basis, performs a classroom assignment based on the hourly scheduling and the capacity of each classroom;the model considers two assumptions: (1) the assignment of each subject in a certain time period is already carried out optimally, and (2) the availability of teachers is not a restrictive element of the model. The test and analysis of the proposed model was carried out at the Faculty of Science and Technology of the University of Azuay (Cuenca, Ecuador). The result of the proposed model, which can be solved with any linear programming algorithm, allows an efficient assignment of the different classrooms, considering the constraints mentioned above. It is considered that under the proposed approach the model can be extended considering additional aspects and conditions, however this would increase the complexity which can be managed through a phased approach (fragmented problems).
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