It is an NP-complete problem to find several figures from a given set of figures and make their sum equal to a designated figure. In this paper, the linear programming model is used to model it, and its Excel solution...
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In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate ...
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In the process of determination of breakpoints for overcurrent relays (OCR), different sets with equal number of OCRs can be selected as minimum breakpoint set (MBPS). Therefore, determination of the most appropriate MBPS is an issue which must be considered. This paper proposes a prioritization between different MBPSs based on the sum of operating times of OCRs. In this case, a set which results the minimum sum of operating times is selected as the appropriate MBPS. For this purpose, the proposed method combines two problems: determination of MBPS and coordination of OCRs, and is expressed in mixed-integer linear programming (MILP) form. Also, a modified depth-first search (DFS) algorithm is applied to determine the OCRs contained loops of studied networks. It is shown that the proposed method has the capability to be combined with previous defined expert rules in this field in order to consider the network conditions in the process of determination of optimal breakpoint set (OBPS). The proposed method has been implemented on various size networks, and the results show the effectiveness of proposed method in determining breakpoint set with the least number in first priority and minimum operating times of relays in second priority.
This paper presents models and optimization algorithms to compute the fuel-optimal energy management strategies for a parallel hybrid electric powertrain on a given driving cycle. Specifically, we first identify a mix...
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This paper presents models and optimization algorithms to compute the fuel-optimal energy management strategies for a parallel hybrid electric powertrain on a given driving cycle. Specifically, we first identify a mixed-integer model of the system, including the engine on/off signal and the gear-shift commands. Thereafter, by carefully relaxing the fuel-optimal control problem to a linear program, we devise an iterative algorithm to rapidly compute the minimum-fuel energy management strategies including the optimal gear-shift trajectory. We validate our approach by comparing its solution with the globally optimal one obtained solving the mixed-integer linear program and with the one resulting from the implementation of the optimal strategies in a high-fidelity nonlinear simulator. We showcase the effectiveness of the presented algorithm by assessing the impact of different powertrain configurations and electric motor size on the achievable fuel consumption. Our numerical results show that the proposed algorithm can assess fuel-optimal control strategies with low computational burden, and that powertrain design choices significantly affect the achievable fuel consumption of the vehicle.
Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our rob...
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Sensitivity analysis is applied to the robust linear programming problem in this paper. The coefficients of the linear program are assumed to be perturbed in three perturbation manners within ellipsoidal sets. Our robust sensitivity analysis is to calculate the maximal radii of the perturbation sets to keep some properties of the robust feasible set. Mathematical models are formulated for the robust sensitivity analysis problems and all models are either reformulated into linear programs or convex quadratic programs except for the bi-convex programs where more than one row of the constraint matrix is perturbed. For the bi-convex programs, we develop a binary search algorithm.
This study focuses on the problem of event-triggered control for positive switched systems without/with input saturation in both continuous-time and discrete-time contexts. First, a 1-norm based event-triggering mecha...
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This study focuses on the problem of event-triggered control for positive switched systems without/with input saturation in both continuous-time and discrete-time contexts. First, a 1-norm based event-triggering mechanism is established for continuous-time positive switched systems. By means of the matrix decomposition technique, an event-triggered controller for the systems is designed by decomposing controller gain matrix into non-positive and non-negative components. Under the designed controller, the resulting closed-loop systems are positive and stable. For the systems with input saturation, the saturation term is transformed into interval form under the event-triggering condition. Then, an event-triggered controller gain matrix and a cone domain of attraction gain matrix are designed for the corresponding interval systems in terms of linear programming, respectively. Furthermore, the presented approaches are extend to discrete-time positive switched systems without/with input saturation. Compared with existing results on positive switched systems, the designed event-triggered controller can reduce sampling frequency and save resources. Finally, two numerical examples are provided to verify the effectiveness of the obtained results.
As urban traffic congestion is on the increase worldwide, many cities are increasingly looking to inexpensive public transit options such as light rail that operate at street-level and require coordination with conven...
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As urban traffic congestion is on the increase worldwide, many cities are increasingly looking to inexpensive public transit options such as light rail that operate at street-level and require coordination with conventional traffic networks and signal control. A major concern in light rail installation is whether enough commuters will switch to it to offset the additional constraints it places on traffic signal control and the resulting decrease in conventional vehicle traffic capacity. In this study, the authors study this problem and ways to mitigate it through a novel model of optimised traffic signal control subject to light rail schedule constraints solved in a mixed-integer linear programming (MILP) framework. The authors' key results show that while this MILP approach provides a novel way to optimise fixed-time control schedules subject to light rail constraints, it also enables a novel optimised adaptive signal control method that virtually nullifies the impact of the light rail presence, reducing average delay times in microsimulations by up to 58.7% versus optimal fixed-time control.
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over prime fields, i.e., the finite fields F-p of size p where p is a prime, when used over a p-ary input memoryless channel. In par...
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In this work, we consider adaptive linear programming (ALP) decoding of linear codes over prime fields, i.e., the finite fields F-p of size p where p is a prime, when used over a p-ary input memoryless channel. In particular, we provide a general construction of valid inequalities (using no auxiliary variables) for the codeword polytope (or the convex hull) of the so-called constant-weight embedding of a single parity-check (SPC) code over any prime field. The construction is based on sets of vectors, called building block classes, that are assembled to form the left-hand side of an inequality according to several rules. In the case of almost doubly-symmetric valid classes we prove that the resulting inequalities are all facet-defining, while we conjecture this to be true if and only if the class is valid and symmetric. Valid symmetric classes impose certain symmetry conditions on the elements of the vectors from the class, while valid doubly-symmetric classes impose further technical symmetry conditions. For p=3, there is only a single valid symmetric class and we prove that the resulting inequalities together with the so-called simplex constraints give a complete and irredundant description of the codeword polytope of the embedded SPC code. For p>5, we show that there are additional facets beyond those from the proposed construction. As an example, for p=7, we provide additional inequalities that all define facets of the embedded codeword polytope. The resulting overall set of linear (in)equalities is conjectured to be irredundant and complete. Such sets of linear (in)equalities have not appeared in the literature before, have a strong theoretical interest, and we use them to develop an efficient (relaxed) ALP decoder for general (non-SPC) linear codes over prime fields. The key ingredient is an efficient separation algorithm based on the principle of dynamic programming. Furthermore, we construct a decoder for linear codes over arbitrary fields F-q with q=p(m) an
We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavio...
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We consider a system of nonlinear ordinary differential equations for the solution of linear programming (LP) problems that was first proposed in the mathematical biology literature as a model for the foraging behavior of acellular slime mold Physarum polycephalum, and more recently considered as a method to solve LP instances. We study the convergence time of the continuous Physarum dynamics in the context of the linear programming problem, and derive a new time bound to approximate optimality that depends on the relative entropy between projected versions of the optimal point and of the initial point. The bound scales logarithmically with the LP cost coefficients and linearly with the inverse of the relative accuracy, establishing the efficiency of the dynamics for arbitrary LP instances with positive costs.
Data Warehouse (DW) and OLAP systems are first citizens of Business Intelligence tools. They are widely used in the academic and industrial communities for numerous different fields of application. Despite the maturit...
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Data Warehouse (DW) and OLAP systems are first citizens of Business Intelligence tools. They are widely used in the academic and industrial communities for numerous different fields of application. Despite the maturity of DW and OLAP systems, with the advent of Big Data, more and more sources of data are available, and warehousing this data can lead to important quality issues. In this work, we focus on missing numerical and categorical in presence of aggregated facts. Motivated by the lack of a formal approach for the imputation of this kind of data taking into account all type of aggregation functions (distributive, algebraic and holistic), we propose an new methodology based on linear programming. Our methodology allows dealing with the relaxed constraints over classical SQL aggregation functions. The proposed approach is tested on two well-known datasets. Experiments show the effectiveness of the proposed approach.
Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places where ther...
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Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in places where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems;therefore, in this paper, we have studied such problems. For this purpose, at first, the motivation of this paper is explained;then, types of hesitant fuzzy linear programming models are introduced. Since it is not easy to examine all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.
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