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Electric Vehicle Charging Station Placement for Urban Public Bus Systems

IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2017年第1期18卷 128-139页

作者： Wang, Xiumin Yuen, Chau Hassan, Naveed Ul An, Ning Wu, Weiwei Hefei Univ Technol Sch Comp & Informat Hefei 230009 Peoples R China Singapore Univ Technol & Design Singapore 487372 Singapore Lahore Univ Management Sci Dept Elect Engn Lahore 54792 Pakistan Southeast Univ Sch Comp Sci & Engn Nanjing 210096 Jiangsu Peoples R China

Due to the low pollution and sustainable properties, using electric buses for public transportation systems has attracted considerable attention, whereas how to recharge the electric buses with long continuous service hours remains an open problem. In this paper, we consider the problem of placing electric vehicle (EV) charging stations at selected bus stops, to minimize the total installation cost of charging stations. Specifically, we study two EV charging station placement cases, with and without considering the limited battery size, which are called ECSP_ LB and ECSP problems, respectively. The solution of the ECSP problem achieves the lower bound compared with the solution of the ECSP_ LB problem, and the larger the battery size of the EV, the lower the overall cost of the charging station installation. For both cases, we prove that the placement problems under consideration are NP-hard and formulate them into integer linear programming. Specifically, for the ECSP problem we design a linear programming relaxation algorithm to get a suboptimal solution and derive an approximation ratio of the algorithm. Moreover, we derive the condition of the battery size when the ECSP problem can be applied. For the ECSP_ LB problem, we show that, for a single bus route, the problem can be optimally solved with a backtracking algorithm, whereas for multiple bus routes we propose two heuristic algorithms, namely, multiple backtracking and greedy algorithms. Finally, simulation results show the effectiveness of the proposed schemes.

关键词： Electric bus for public transportation system EV charging station placement linear programming relaxation

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Graph Isomorphism, Color Refinement, and Compactness

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COMPUTATIONAL COMPLEXITY 2017年第3期26卷 627-685页

作者： Arvind, V. Koebler, Johannes Rattan, Gaurav Verbitsky, Oleg Inst Math Sci Chennai 600113 Tamil Nadu India Humboldt Univ Inst Informat Unter Linden 6 D-10099 Berlin Germany

Color refinement is a classical technique used to show that two given graphs G and H are non-isomorphic;it is very efficient, although it does not succeed on all graphs. We call a graph G amenable to color refinement if the color refinement procedure succeeds in distinguishing G from any non-isomorphic graph H. Babai et al. (SIAM J Comput 9(3):628-635, 1980) have shown that random graphs are amenable with high probability. We determine the exact range of applicability of color refinement by showing that amenable graphs are recognizable in time , where n and m denote the number of vertices and the number of edges in the input graph. We use our characterization of amenable graphs to analyze the approach to Graph Isomorphism based on the notion of compact graphs. A graph is called compact if the polytope of its fractional automorphisms is integral. Tinhofer (Discrete Appl Math 30(2-3):253-264, 1991) noted that isomorphism testing for compact graphs can be done quite efficiently by linear programming. However, the problem of characterizing compact graphs and recognizing them in polynomial time remains an open question. Our results in this direction are summarized below: We show that all amenable graphs are compact. In other words, the applicability range for Tinhofer's linear programming approach to isomorphism testing is at least as large as for the combinatorial approach based on color refinement. Exploring the relationship between color refinement and compactness further, we study related combinatorial and algebraic graph properties introduced by Tinhofer and Godsil. We show that the corresponding classes of graphs form a hierarchy, and we prove that recognizing each of these graph classes is P-hard. In particular, this gives a first complexity lower bound for recognizing compact graphs.

关键词： Graph Isomorphism color refinement linear programming relaxation polytope of fractional automorphisms

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Relating domination, exponential domination, and porous exponential domination

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DISCRETE OPTIMIZATION 2017年 23卷 81-92页

作者： Henning, Michael A. Jaeger, Simon Rautenbach, Dieter Univ Johannesburg Dept Pure & Appl Math ZA-2006 Auckland Pk South Africa Univ Ulm Inst Optimizat & Operat Res Ulm Germany

The domination number gamma(G) of a graph G, its exponential domination number gamma e (G), and its porous exponential domination number gamma(*)(e)(G) satisfy gamma(e)*(G) <= gamma(e)(G) <= gamma(G). We contribute results about the gaps in these inequalities as well as the graphs for which some of the inequalities hold with equality. Relaxing the natural integer linear program whose optimum value is gamma(e)*(G), we are led to the definition of the fractional porous exponential domination number gamma e* f (G) of a graph G. For a subcubic tree T of order n, we show gamma(e,f)*(T) = n+2/6 and gamma e (T) <= 2 gamma(e,f)*(T). We characterize the two classes of subcubic trees T with gamma(e) (T) =gamma(e,f)* (T) and gamma(T) = gamma(e)(T), respectively. Using linear programming arguments, we establish several lower bounds on the fractional porous exponential domination number in more general settings. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Domination Exponential domination Porous exponential domination linear programming relaxation

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Load Balanced Mobile User Recruitment for Mobile Crowdsensing Systems

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IEEE COMMUNICATIONS LETTERS 2017年第11期21卷 2420-2423页

作者： An, Xin Guo, Hao Wang, Xiumin Chen, Xiaoming Hefei Univ Technol Sch Comp & Informat Hefei 230009 Anhui Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Guangdong Peoples R China Zhejiang Univ Coll Informat Sci & Elect Engn Hangzhou 310058 Zhejiang Peoples R China

In this letter, we study the mobile user recruitment problem for mobile crowdsensing systems. Instead of minimizing the overall sensing cost or user utility, this letter aims to optimize the load balancing of the mobile users, which is particularly important for the resource-constrained individual user. We refer to such a problem as the load balanced mobile user recruitment (LB-MUR) problem. Specifically, we first formulate the LB-MUR problem as a mixed integer linear programming (LP) and prove that it is NP-hard. Then an efficient polynomial-time suboptimal algorithm is proposed, which is based on LP relaxation. Furthermore, we derive the approximation ratio of the proposed algorithm. Finally, we evaluate the effectiveness of the proposed scheme through simulations.

关键词： Mobile crowdsensing load balance linear programming relaxation

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Segmented Arrival Graph based Evacuation Plan Assessment Algorithm Using linear programming 11

Segmented Arrival Graph based Evacuation Plan Assessment Alg...

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11th Annual IEEE International Systems Conference (SysCon)

作者： Min, Manki Lim, Sunho South Dakota State Univ Dept Elect Engn & Comp Sci Brookings SD 57007 USA Texas Tech Univ Dept CS TTU Wireless Mobile Networking Lab T2WISTOR Lubbock TX 79409 USA

ISBN: (纸本)9781509046232

The evacuation routing problem is NP-hard and hence no polynomial-time algorithm exists for the problem. There have been many studies on the evacuation planning heuristic algorithms but the in-depth comparison between them is not available especially in terms of the performance ratio. Without knowing the heuristic solution quality with respect to the optimal solution, we cannot accurately determine each heuristic algorithm's strengths and weaknesses that can lead to a better combination of heuristic algorithms. In this paper we present a linear programming (LP) based iterative algorithm to assess the evacuation planning algorithms in terms of the evacuation time. The proposed algorithm takes the paths that are found and/or used in a heuristic algorithm as the input and finds the minimum evacuation time using only those paths. To get the optimal solution, our algorithm repeatedly solves relaxed LP formulations formed from the concept of segmented arrival graphs. We segment the arrival graphs of paths based on the edge-sharing and construct the LP formulations along the segmented edges on the graphs. The computational experiment shows that the proposed algorithm computes the solution using time that is comparable to that of the heuristic algorithms as long as the number of paths is adequately maintained. Using the algorithm we perform the comparison between the existing heuristic algorithms, CCRP++, SMP, EET, and FBSP.

关键词： Segmented Arrival Graphs Evacuation Routing Assessment linear programming relaxation

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Iterative learning for optimal residential load scheduling in smart grid

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AD HOC NETWORKS 2016年第May期41卷 99-111页

作者： Chai, Bo Yang, Zaiyue Gao, Kunlun Zhao, Ting State Grid Smart Grid Res Inst Beijing 102211 Peoples R China Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Zhejiang Peoples R China

In this paper, as a fundamental problem in smart grid, the residential load scheduling is studied in a comprehensive way. The main contributions lie in threefold. First, three indices, i.e., the power consumption expense, the robustness of schedule subject to uncertain electricity price and the satisfaction of customer, are taken into full consideration. We propose to optimize simultaneously the three indices via convex optimization. Second, iterative learning is utilized to setting parameters in the objective function, and keeps a proper tradeoff between the consumption expense and the satisfaction index. Third, in order to fully characterize the operation states of appliances, both binary and continuous variables are used, which results in a hybrid mixed-integer quadratic optimization problem. The relaxation technique is utilized to tackle the hybrid optimization problem. Theoretical analysis of the performance gap based on the proposed approach is provided as well. The performance of the proposed approach is illustrated by simulations. The parameter settings reflect actual preference and consumption manner of the consumer. In addition, both peak-to-average ratio of power load and variation of power load are reduced. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Smart grid Residential load scheduling Iterative learning Real time price Price uncertainty linear programming relaxation

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MATHEMATICS OF OPERATIONS RESEARCH 2016年第3期41卷 851-864页

作者： Skutella, Martin Sviridenko, Maxim Uetz, Marc Tech Univ Berlin Inst Math D-10623 Berlin Germany Yahoo Labs New York NY 10018 USA Univ Twente Dept Appl Math NL-7500 AE Enschede Netherlands

Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. By means of a novel time-indexed linear programming relaxation, we show how to compute in polynomial time a scheduling policy with provable performance guarantee for the stochastic version of the unrelated parallel machine scheduling problem with the weighted sum of completion times objective. Our performance guarantee depends on the squared coefficient of variation of the processing times and we show that this dependence is tight. Currently best-known bounds for deterministic scheduling problems are contained as special cases.

关键词： stochastic scheduling approximation algorithm linear programming relaxation

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Rounding-based Moves for Semi-Metric Labeling

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年第1期17卷 3121-3162页

作者： Kumar, M. Pawan Dokania, Puneet K. Univ Oxford Dept Engn Sci Parks Rd Oxford OX1 3PJ England Cent Supelec Ctr Visual Comp F-92295 Chatenay Malabry France

Semi-metric labeling is a special case of energy minimization for pairwise Markov random fields. The energy function consists of arbitrary unary potentials, and pairwise potentials that are proportional to a given semi-metric distance function over the label set. Popular methods for solving semi-metric labeling include (i) move-making algorithms, which iteratively solve a minimum st-cut problem;and (ii) the linear programming (LP) relaxation based approach. In order to convert the fractional solution of the LP relaxation to an integer solution, several randomized rounding procedures have been developed in the literature. We consider a large class of parallel rounding procedures, and design move-making algorithms that closely mimic them. We prove that the multiplicative bound of a move-making algorithm exactly matches the approximation factor of the corresponding rounding procedure for any arbitrary distance function. Our analysis includes all known results for move-making algorithms as special cases.

关键词： semi-metric labeling move-making algorithms linear programming relaxation multiplicative bounds

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On linearization techniques for budget-constrained binary quadratic programming problems

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OPERATIONS RESEARCH LETTERS 2016年第6期44卷 702-705页

作者： Yang, Mei-Jia Xia, Yong Zou, Hui-Min Beihang Univ Sch Math & Syst Sci Minist Educ State Key Lab Software Dev EnvironmLMIB Beijing 100191 Peoples R China Beijing Polytech Beijing 100176 Peoples R China

Glover's linearization technique is revisited for solving the binary quadratic programming problem with a budget constraint (BBQP). When compared with the recent two linearizations for (BBQP), it not only provides a tighter relaxation at the root node, but also has a much better computational performance for globally solving (BBQP). (C) 2016 Elsevier B.V. All rights reserved.

关键词： Binary quadratic programming Budget constraint linearization linear programming relaxation

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Robust Optimization of Sums of Piecewise linear Functions with Application to Inventory Problems

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OPERATIONS RESEARCH 2016年第2期64卷 474-494页

作者： Ardestani-Jaafari, Amir Delage, Erick HEC Montreal Dept Decis Sci Montreal PQ H3T 2A7 Canada

Robust optimization is a methodology that has gained a lot of attention in the recent years. This is mainly due to the simplicity of the modeling process and ease of resolution even for large scale models. Unfortunately, the second property is usually lost when the cost function that needs to be "robustified" is not concave (or linear) with respect to the perturbing parameters. In this paper we study robust optimization of sums of piecewise linear functions over polyhedral uncertainty set. Given that these problems are known to be intractable, we propose a new scheme for constructing conservative approximations based on the relaxation of an embedded mixed-integer linear program and relate this scheme to methods that are based on exploiting affine decision rules. Our new scheme gives rise to two tractable models that, respectively, take the shape of a linear program and a semidefinite program, with the latter having the potential to provide solutions of better quality than the former at the price of heavier computations. We present conditions under which our approximation models are exact. In particular, we are able to propose the first exact reformulations for a robust (and distributionally robust) multi-item newsvendor problem with budgeted uncertainty set and a reformulation for robust multiperiod inventory problems that is exact whether the uncertainty region reduces to a L-1-norm ball or to a box. An extensive set of empirical results will illustrate the quality of the approximate solutions that are obtained using these two models on randomly generated instances of the latter problem.

关键词： optimization piecewise linear linear programming relaxation semidefinite program tractable approximations newsvendor problem inventory problem

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