This paper aims to present a new linearization approach to finding the optimal protective relay settings in power systems. The traditional protective relay coordination problem (CP) involving directional overcurrent r...
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This paper aims to present a new linearization approach to finding the optimal protective relay settings in power systems. The traditional protective relay coordination problem (CP) involving directional overcurrent relays (OcRs) is a nonconvex, nonlinear constrained optimization problem that is widely addressed in the literature. In linear programming (LP) based solution methods, the current plug settings (CPS) are fixed, and the time dial settings (TDS) are found, which though reasonably adequate but do not fetch the global solution. In nonlinear programming (NLP), both TDS and CPS are deemed to be decision variables, but NLP requires a proper initial-point to get the best optimal solution. In this paper, the nonconvexity in CP formulation is convexified using bilinear relaxations, and global optimum is obtained. It is done by writing each bilinear term in CP formulation as a set of four linear inequalities using McCormick envelopes, and the error generated due to the linear approximations is reduced iteratively by updating the variable bounds. The proposed approach is programmed in MATLAB coding platform, and theoretical validation has been performed. The proposed approach has the advantages of being independent of initial-point and attain the global optimum without the help of global optimization solvers.
Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this paper, we present an application of this approach to a famous class of algorithms for linear pr...
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Tropical geometry has been recently used to obtain new complexity results in convex optimization and game theory. In this paper, we present an application of this approach to a famous class of algorithms for linear programming, i.e., log-barrier interior point methods. We show that these methods are not strongly polynomial by constructing a family of linear programs with 3r + 1 inequalities in dimension 2r for which the number of iterations performed is in Omega(2(r)). The total curvature of the central path of these linear programs is also exponential in r, disproving a continuous analogue of the Hirsch conjecture proposed by Deza, Terlaky, and Zinchenko. These results are obtained by analyzing the tropical central path, which is the piecewise linear limit of the central paths of parameterized families of classical linear programs viewed through "logarithmic glasses."" This allows us to provide combinatorial lower bounds for the number of iterations and the total curvature in a general setting.
This paper studies the energy efficiency optimization problem for coordinated multipoint (CoMP)-enabled and backhaul-constrained ultra-dense small-cell networks (UDNs). Energy efficiency is an eternal topic for future...
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This paper studies the energy efficiency optimization problem for coordinated multipoint (CoMP)-enabled and backhaul-constrained ultra-dense small-cell networks (UDNs). Energy efficiency is an eternal topic for future wireless communication networks;however, taking actual bottleneck of the backhaul link and the coordinated network architecture into consideration, it is difficult to find an effective way to improve the energy efficiency of the network. Aiming at this problem, we propose to combine cell association, subchannel allocation, backhaul resource allocation, and sleep/on of the cells together to develop an optimization algorithm for energy efficiency in UDN and then solve the formulated energy efficiency optimization problem by means of improved modified particle swarm optimization (IMPSO) and linear programming in mathematics. Simulation results indicate that nearly 13% energy cost saving and 21% energy efficiency improvement can be obtained by combining IMPSO with linear programming, and the backhaul link data rate can be improved by 30% as the number of small cells increases. From the results, it can be found that by combining IMPSO with linear programming, the proposed algorithm can improve the network energy efficiency effectively at the expense of limited complexity.
An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unk...
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An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unknown controls, the state variables of plant, and possibly the constraints imposed on the controls and state variables. The solution of this LP provides the control to be applied to the plant. The main advantages of the proposed method are: simplicity of applying to multi-input multi-output systems, taking into account the actuator saturation and constraints on states, and robustness to uncertainties in the model. Two numerical examples are presented to verify the effectiveness of the proposed method. These are output voltage regulation of a two-input two-output dc-dc boost converter with actuator saturation and position control of a magnetic levitation system with a constraint on the speed of ball.
Given a graph, we wish to find a maximum number of vertex-disjoint paths of length 2. We propose a series of local improvement algorithms for this problem, and present a linear-programming based method for analyzing t...
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Given a graph, we wish to find a maximum number of vertex-disjoint paths of length 2. We propose a series of local improvement algorithms for this problem, and present a linear-programming based method for analyzing their performance. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional...
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Stability and performance of hybrid integrator-gain systems (HIGS) are mostly analyzed using linear matrix inequalities (LMIs) to construct continuous piecewise quadratic (CPQ) Lyapunov functions. To create additional methods for the analysis of HIGS and other conewise linear systems, a method based on linear programming (LP) for constructing continuous piecewise affine (CPA) Lyapunov functions is investigated. In this paper, it is shown how linear programming can be used to prove input-to-state stability and calculate upper bounds on the L 1 -gain and H 1 -norm. The numerical efficiency of this CPA (LP) method will be compared to that of the CPQ (LMI) method on a numerical example involving HIGS.
In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions is additionally int...
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In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions is additionally introduced in the diagnosis function, leading to a more informative and precise diagnosis result. An integer linear programming (ILP) problem is built according to an observed word. By specifying different objective functions to the ILP problem, the diagnosis result is obtained without enumerating all observable transition sequences consistent with the observed word, which is more efficient in comparison with the existing ILP-based approaches.
Facility layout problems (FLPs) in hospitals are typically to arrange facilities or rooms along both sides of a corridor to minimize some objectives. In a hospital, very often there are center-islands to decrease the ...
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Facility layout problems (FLPs) in hospitals are typically to arrange facilities or rooms along both sides of a corridor to minimize some objectives. In a hospital, very often there are center-islands to decrease the flow cost among facilities or rooms. However, these islands have not been considered before. In this article, we propose an FLP with center-islands that involves two parallel rows and center-islands. A mixed-integer program formulation is established for modeling it. A methodology for combining a multiobjective evolutionary algorithm based on decomposition (MOEA/D) and linear program is proposed to solve this problem. MOEA/D optimizes the sequence of facilities on two rows and center-islands while the linear program is embedded into MOEA/D to optimize the exact locations of center-islands. A tabu search with a local search is also integrated into MOEA/D to enhance its search capability. Experiments show that our proposed methodology can effectively solve the problem.
In real world problems, the parameters of the solid transportation (ST) problems (supply, demand and capacity of vehicles) are not always accurate. Therefore, in dealing with these problems due to the existence of unc...
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Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that ...
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Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations is considered through a bit-complexity analysis. Yet in practice, implementations typically use limited-precision arithmetic. In this paper we introduce the idea of a limited-precision LP oracle and study how such an oracle could be used within a larger framework to compute exact precision solutions to LPs. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. This work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.
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