Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of rand (r, s)-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of ...
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ISBN:
(纸本)9781538679012;9781538679265
Convergence guarantees of many resilient consensus algorithms are based on the graph theoretic properties of rand (r, s)-robustness. These algorithms guarantee consensus of normally behaving agents in the presence of a bounded number of arbitrarily misbehaving agents if the values of the integers r and s are sufficiently high. However, determining the largest integer r for which an arbitrary digraph is r-robust is highly nontrivial. This paper introduces a novel method for calculating this value using mixed integer linear programming. The method only requires knowledge of the graph Laplacian matrix, and can be formulated with affine objective and constraints, except for the integer constraint. integerprogramming methods such as branch-and-bound can allow both lower and upper bounds on r to be iteratively tightened. Simulations suggest the proposed method demonstrates greater efficiency than prior algorithms.
This work proposes a mixedintegerlinear program. ming (MILP) formulation, based on a linear power flow that has recently been proposed in the literature, for the reactive power compensation of distribution networks ...
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ISBN:
(纸本)9781538622124
This work proposes a mixedintegerlinear program. ming (MILP) formulation, based on a linear power flow that has recently been proposed in the literature, for the reactive power compensation of distribution networks through the optimal selection of capacitor banks (CB) as well as the optimal tap selection of voltage regulators (VRs) and on load tap changers (OLTCs) in order to maintain the system voltages within hounds. In the proposed formulation the voltage dependent load model is taken into account and the objective is to minimize the supply energy cost on a day-long time period. In order to evaluate the proposed model, several simulations are shown for a 34-bus radial distribution system. The results are duly discussed.
Varying demands and global competition pose significant challenges in the consumer goods industry. Exploiting market opportunities often leads to the need of an extension of the production capacities of manufacturing ...
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Agile assembly systems in automotive production are predominantly characterized by decoupled and independent workstations. This raises the question how such assembly systems can be evaluated and compared against the p...
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Agile assembly systems in automotive production are predominantly characterized by decoupled and independent workstations. This raises the question how such assembly systems can be evaluated and compared against the predominantly used assembly lines. Job-shop-problems as a promising formulation do not yet offer a model that covers all the intended degrees of freedom. This research work thus presents an extended job-shop-problem and its validation while considering parallel and multifunctional workstations, sequence-dependent set-up times, routing and sequence flexibility as well as a multivariable objective function. The resulting model based on mixed integer linear programming contributes to the evaluation of agile assembly systems and supports the development of real-time capable algorithms for practical applications.
Security-constrained unit commitment (SCUC) is one of the most important daily tasks that must be accomplished in electric power market. To solve the SCUC problem efficiently, this paper proposes a mixed-integer linea...
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ISBN:
(数字)9781728191645
ISBN:
(纸本)9781728191652
Security-constrained unit commitment (SCUC) is one of the most important daily tasks that must be accomplished in electric power market. To solve the SCUC problem efficiently, this paper proposes a mixed-integerlinearprogramming (MILP) model and related constraints reduction methods. The proposed model includes both pre-and post-contingency security constraints, which are linearized by the DC power flow equation and the line outage distribution factor (LODF), respectively. The proposed constraints reduction methods reduce the security constraints of parallel branches by identifying the representative branches in each group of parallel branches, and eliminate the redundant post-contingency security constraints by analyzing the maximum possible values of post-contingency power flow. The correctness and effectiveness of the proposed model and methods are verified on 39 bus New England system and IEEE-118 test system.
We investigate the augmented Lagrangian dual (ALD) for mixed integer linear programming (MIP) problems. ALD modifies the classical Lagrangian dual by appending a nonlinear penalty function on the violation of the dual...
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We investigate the augmented Lagrangian dual (ALD) for mixed integer linear programming (MIP) problems. ALD modifies the classical Lagrangian dual by appending a nonlinear penalty function on the violation of the dualized constraints in order to reduce the duality gap. We first provide a primal characterization for ALD for MIPs and prove that ALD is able to asymptotically achieve zero duality gap when the weight on the penalty function is allowed to go to infinity. This provides an alternative characterization and proof of a recent result in Boland and Eberhard (Math Program 150(2):491-509, 2015, Proposition 3). We further show that, under some mild conditions, ALD using any norm as the augmenting function is able to close the duality gap of an MIP with a finite penalty coefficient. This generalizes the result in Boland and Eberhard (2015, Corollary 1) from pure integerprogramming problems with bounded feasible region to general MIPs. We also present an example where ALD with a quadratic augmenting function is not able to close the duality gap for any finite penalty coefficient.
The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nod...
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The Minimum Weighted Tree Reconstruction (MWTR) problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes. This problem has applications in several areas, namely, the inference of phylogenetic trees, the modeling of traffic networks and the analysis of internet infrastructures. In this paper, we investigate the MWTR problem and we present two compact mixed-integerlinearprogramming models to solve the problem. Computational results using two different sets of instances, one from the phylogenetic area and another from the telecommunications area, show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes. (C) 2016 Elsevier B.V. All rights reserved.
The bus company mainly relies on the experienced scheduling personnel to prepare the time plate of the bus line manually in advance, and then conFigure the vehicles. However, this kind of scheduling method often cause...
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ISBN:
(数字)9781728152448
ISBN:
(纸本)9781728152455
The bus company mainly relies on the experienced scheduling personnel to prepare the time plate of the bus line manually in advance, and then conFigure the vehicles. However, this kind of scheduling method often cause a waste of bus seat resources only by experience. In this paper, we propose a vehicles scheduling model called MILPS (mixed-integerlinearprogramming Model of Scheduling) to minimise the gap between the demand and supply of bus seats. In the first phase, we first analyze the historical trajectory data of taxis in Xiamen and select the two most popular stations as the starting and ending points of bus routes, then generate the service area between them by rectangle. In the second phase, we derive several criteria to build bus scheduling model based on mixed-integerlinearprogramming. Finally, we use CPLEX optimizer to solve this MILP problem. Experimental results show that the proposed scheme can effectively reduce the waste of bus seat resources (>76.8% reduction) and significantly improve the delivery ratio (>71.5%).
Modularity density maximization is a clustering method that improves some issues of the commonly used modularity maximization approach. Recently, some mixed integer linear programming (MILP) reformulations have been p...
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Modularity density maximization is a clustering method that improves some issues of the commonly used modularity maximization approach. Recently, some mixed integer linear programming (MILP) reformulations have been proposed in the literature for the modularity density maximization problem, but they require as input the solution of a set of auxiliary binary Non-linear Programs (NLPs). These can become computationally challenging when the size of the instances grows. In this paper we propose and compare some explicit MILP reformulations of these auxiliary binary NLPs, so that the modularity density maximization problem can be completely expressed as MILP. The resolution time is reduced by a factor up to two order of magnitude with respect to the one obtained with the binary NLPs. (C) 2017 Elsevier B.V. All rights reserved.
In this work, sparse regression using a penalized least absolute deviations objective function is considered. Regression model sparsity is promoted using a L-0 - pseudo norm penalty (the cardinality of the model param...
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In this work, sparse regression using a penalized least absolute deviations objective function is considered. Regression model sparsity is promoted using a L-0 - pseudo norm penalty (the cardinality of the model parameter vector). Implemented using mixed integer linear programming (MILP) it is demonstrated that the use of the L-0 norm (without approximation) enables efficient and accurate solutions to sparse regression problems of practical size. For model development with a large number of potential model parameters (or features) methods to relax the MILP are also developed;using nonlinear function approximations to the L-0- norm, penalty terms are linearized and solved using sequential linearprogramming. Experimental results (using both simulated and real data) demonstrate that these algorithms are also computationally efficient producing accurate and parsimonious model structures. Applications considered are the development of a calibration model for prediction with Near Infrared (NIR) data and the development of a model for the prediction of chemical toxicity - a quantitative structure activity relationship (QSAR).
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