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Joint Subcarrier and Power Allocation in OFDMA Systems for Outage Minimization

IEEE COMMUNICATIONS LETTERS 2016年第10期20卷 2007-2010页

作者： Basaran, Semiha Tedik Kurt, Gunes Karabulut Istanbul Tech Univ Dept Elect & Commun Engn TR-34469 Istanbul Turkey

The joint assignment of subcarriers and limited transmission power is addressed as a combinatorial optimization problem in orthogonal frequency division multiple access networks. To ensure fairness among users while jointly minimizing the total transmit power, the minimization of the number of outage subcarriers is considered as the objective function. The proposed scheme enables distinct rate requirement for each user. Optimal and reduced complexity algorithms, based on the application of Hungarian method to randomly weighted complete bipartite graphs, that reduce the outage probability according to the benchmark works while providing considerable power savings are proposed.

关键词： OFDMA joint subcarrier and power allocation linear sum assignment problem generalized assignment problem

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Approximations for Monotone and Nonmonotone Submodular Maximization with Knapsack Constraints

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MATHEMATICS OF OPERATIONS RESEARCH 2013年第4期38卷 729-739页

作者： Kulik, Ariel Shachnai, Hadas Tamir, Tami Technion Israel Inst Technol Dept Comp Sci IL-32000 Haifa Israel Interdisciplinary Ctr IDC Sch Comp Sci Herzliyya Israel

Submodular maximization generalizes many fundamental problems in discrete optimization, including Max-Cut in directed/undirected graphs, maximum coverage, maximum facility location, and marketing over social networks. In this paper we consider the problem of maximizing any submodular function subject to d knapsack constraints, where d is a fixed constant. We establish a strong relation between the discrete problem and its continuous relaxation, obtained through extension by expectation of the submodular function. Formally, we show that, for any nonnegative submodular function, an alpha-approximation algorithm for the continuous relaxation implies a randomized (alpha - epsilon)-approximation algorithm for the discrete problem. We use this relation to obtain an (e(-1) - epsilon)-approximation for the problem, and a nearly optimal (1 - e(-1) - epsilon)-approximation ratio for the monotone case, for any epsilon > 0. We further show that the probabilistic domain defined by a continuous solution can be reduced to yield a polynomial-size domain, given an oracle for the extension by expectation. This leads to a deterministic version of our technique.

关键词： submodular maximization knapsack constraints maximum coverage generalized assignment problem randomization approximation algorithms

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Fleet management: A vehicle and driver assignment model

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期278卷 64-75页

作者： Monnerat, Filipe Dias, Joana Alves, Maria Joao Univ Coimbra CeBER Av Dias da Silva 165 P-3000 Coimbra Portugal Univ Coimbra Fac Econ Av Dias da Silva 165 P-3000 Coimbra Portugal Univ Fed Vicosa Vicosa MG Brazil Univ Coimbra DEEC INESC Coimbra Polo 2 P-3030290 Coimbra Portugal

Many institutions have their own vehicle fleet and hired drivers that can be assigned to working trips to ensure that they all take place within the desired time periods. In these situations, it is important that vehicles and drivers are assigned to planned trips in an optimal and automated way. Trips are planned to occur over a given planning horizon and have a number of characteristics that have to be taken into account: a trip is characterized by a starting time, start and end locations, travelling distance and time, number of drivers needed for each assigned vehicle, number of passengers, and so on. This paper considers the problem of assigning both vehicles and drivers to a set of planned trips, having as objective the minimization of total cost. To properly address this problem it is necessary to consider a number of features, like the possibility of vehicles being shared between different trips if the timeframes and destinations are compatible. The mathematical model developed and presented in this paper takes all these features into account. The problem was motivated by a case study in the context of a public Brazilian university. This case study is also described and computational experiments using a general solver are reported. The general solver is capable of calculating optimal solutions in reasonable computational times, but problems where the fleet is mainly composed of small vehicles are more challenging. A matheuristic has been developed and tested, that seems to be competitive for these type of problems. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization generalized assignment problem Fleet management

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A matheuristic approach to the integration of worker assignment and vehicle routing problems: Application to home healthcare scheduling

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EXPERT SYSTEMS WITH APPLICATIONS 2019年 125卷 317-332页

作者： Moussavi, S. E. Mandjoub, M. Grunder, O. Univ Bourgogne Franche Comte UTBM Nanomed Lab F-90010 Belfort France Univ Bourgogne Franche Comte UTBM ELLIADD Lab F-25200 Montbeliard France

To model a home health care planning problem by classical VRP and AP formulation, the dimensions of the problem are: 1. The staff, 2. The patients, 3. The routes (sequence of the patients for each staff member). In this study, we present an extension of the home health care planning problem by adding the extra dimension of time so that the staff are not only assigned to the patients, but they are also assigned to daily periods. The scope of the planning problem extends to multiple days in which the patient required services vary from one day to another. Hence, the problem concerns a sequence of schedules (one schedule for each day) for the staff members. This variant of the home health care planning problem is modeled mathematically by employing the sequencing generalized assignment formulation and solved by applying the Gurobi mixed-integer solver. Considering that the studied combinatorial optimization is NP-complete, a matheuristic approach based on the decomposition of the formulation is proposed in this research to simplify the mathematical model and reduce the computational time needed to solve the problem. The numerical experiences and statistical analysis show that our matheuristic approach solves 90% of the instances to optimality with a significant reduction in the computational times. (C)2019 Elsevier Ltd. All rights reserved.

关键词： Matheuristic optimization algorithm Home healthcare routing and scheduling Human resource planning generalized assignment problem

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Customized bus service design for jointly optimizing passenger-to-vehicle assignment and vehicle routing

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2017年 85卷 451-475页

作者： Tong, Lu (Carol) Zhou, Leishan Liu, Jiangtao Zhou, Xuesong Beihang Univ Sch Elect & Informat Engn Beijing 100091 Peoples R China Natl Engn Lab Comprehens Transportat Big Data App Beijing 100091 Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Arizona State Univ Sch Sustainable Engn & Built Environm Tempe AZ 85287 USA

Emerging transportation network services, such as customized buses, hold the promise of expanding overall traveler accessibility in congested metropolitan areas. A number of internet-based customized bus services have been planned and deployed for major origin-destination (OD) pairs to/from inner cities with limited physical road infrastructure. In this research, we aim to develop a joint optimization model for addressing a number of practical challenges for providing flexible public transportation services. First, how to maintain minimum loading rate requirements and increase the number of customers per bus for the bus operators to reach long-term profitability. Second, how to optimize detailed bus routing and timetabling plans to satisfy a wide range of specific user constraints, such as passengers' pickup and delivery locations with preferred time windows, through flexible decision for matching passengers to bus routes. From a space-time network modeling perspective, this paper develops a multi-commodity network flow based optimization model to formulate a customized bus service network design problem so as to optimize the utilization of the vehicle capacity while satisfying individual demand requests defined through space-time windows. We further develop a solution algorithm based on the Lagrangian decomposition for the primal problem and a space-time prism based method to reduce the solution search space. Case studies using both the illustrative and real-world large-scale transportation networks are conducted to demonstrate the effectiveness of the proposed algorithm and its sensitivity under different practical operating conditions.

关键词： Customized buses Space-time network Vehicle routing problem generalized assignment problem Ridesharing

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Maximal covering code multiplexing access telecommunication networks

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第1期159卷 219-238页

作者： Barbas, J Marín, A Univ Politecn Madrid Dept Matemat Aplicada & Estadist ETSI Aeronaut E-28040 Madrid Spain

We present a maximal covering model for the network design of code division multiplexing access (CDMA) telecommunication system. Properties of the solution and the algorithm have been studied. The model has been developed to solve actual problems;they are extremely large so exact decomposition methods cannot be used to solve it. A Lagrangian decomposition heuristic has been defined. Different algorithm options have been computationally compared using random generated and actual data. Model and algorithm parameters have been adjusted and sensibility of the solution to the data has been considered in these tests. (C) 2003 Elsevier B.V. All rights reserved.

关键词： telecommunications code division multiplexing access systems large scale optimization integer programming generalized assignment problem set covering problem Lagrangian decomposition Branch and bound

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A polynomial time approximation scheme for the multiple knapsack problem

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SIAM JOURNAL ON COMPUTING 2006年第3期35卷 713-728页

作者： Chekuri, C Khanna, S Bell Labs Murray Hill NJ 07974 USA Univ Penn Dept Comp & Informat Sci Philadelphia PA 19104 USA

The multiple knapsack problem (MKP) is a natural and well-known generalization of the single knapsack problem and is defined as follows. We are given a set of n items and m bins ( knapsacks) such that each item i has a profit p( i) and a size s( i), and each bin j has a capacity c( j). The goal is to find a subset of items of maximum profit such that they have a feasible packing in the bins. MKP is a special case of the generalized assignment problem ( GAP) where the profit and the size of an item can vary based on the specific bin that it is assigned to. GAP is APX-hard and a 2-approximation, for it is implicit in the work of Shmoys and Tardos [ Math. Program. A, 62 ( 1993), pp. 461 - 474], and thus far, this was also the best known approximation for MKP. The main result of this paper is a polynomial time approximation scheme (PTAS) for MKP. Apart from its inherent theoretical interest as a common generalization of the well-studied knapsack and bin packing problems, it appears to be the strongest special case of GAP that is not APX-hard. We substantiate this by showing that slight generalizations of MKP are APX-hard. Thus our results help demarcate the boundary at which instances of GAP become APX-hard. An interesting aspect of our approach is a PTAS-preserving reduction from an arbitrary instance of MKP to an instance with O(log n) distinct sizes and profits.

关键词： multiple knapsack problem generalized assignment problem polynomial time approximation scheme approximation algorithm

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A probabilistic analysis of the multi-period single-sourcing problem

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DISCRETE APPLIED MATHEMATICS 2001年第1-3期112卷 301-328页

作者： Romeijn, HE Morales, DR Maastricht Univ Fac Econ & Business Adm NL-6200 MD Maastricht Netherlands Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA

The multi-period single-sourcing problem (MPSSP) is the problem of finding an assignment, over time, of customers to warehouses such that each customer is assigned to exactly one warehouse in each period, subject to capacity constraints, such that the total transportation and inventory costs are minimized. We propose a general stochastic model for the MPSSP, and derive a tight condition on this stochastic model under which the MPSSP is feasible with probability I when the number of customers goes to infinity. This result can be used to generate suitable experimental data. Moreover, we show that the normalized optimal value of the problem converges almost surely to a constant, for which we provide an explicit expression;this property can be useful in constructing asymptotically optimal heuristics for the problem. The rate of convergence to the limiting value is illustrated empirically. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： probabilistic analysis generalized assignment problem dynamic assignments

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Demand allocation in multiple-product, multiple-facility, make-to-stock systems

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MANAGEMENT SCIENCE 2004年第10期50卷 1431-1448页

作者： Benjaafar, S Elhafsi, M de Véricourt, F Univ Minnesota Dept Mech Engn Grad Program Ind Engn Minneapolis MN 55455 USA Univ Calif Riverside A Gary Anderson Grad Sch Management Riverside CA 92521 USA Duke Univ Fuqua Sch Business Durham NC 27708 USA

We consider the problem of allocating demand arising from multiple products to multiple production facilities with finite capacity and load-dependent lead times. Production facilities can choose to manufacture items either to stock or to order. Products vary in their demand rates, holding and backordering costs, and service-level requirements. We develop models and solution procedures to determine the optimal allocation of demand to facilities and the optimal inventory level for products at each facility. We consider two types of demand allocation, one in which we allow the demand for a product to be split among multiple facilities and the other in which demand from each product must be entirely satisfied by a single facility. We also consider two forms of inventory warehousing, one in which inventory locations are factory based and one in which they are centralized. For each case, we offer a solution procedure to obtain optimal demand allocations and optimal inventory base-stock levels. For systems with multiple customer classes, we also determine optimal inventory rationing levels for each class for each product. We use the models to characterize analytically several properties of the optimal solution. In particular, we highlight eight principles that relate the effects of cost, congestion, inventory pooling, multiple sourcing, customer segmentation, inventory rationing, and process and demand variability.

关键词： production/inventory systems queueing systems generalized assignment problem multi-item/multifacility systems

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Registration of PE segment contour deformations in digital high-speed videos

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MEDICAL IMAGE ANALYSIS 2008年第3期12卷 318-334页

作者： Stiglmayr, Michael Schwarz, Raphael Klamroth, Kathrin Leugering, Guenter Lohscheller, Joerg Univ Erlangen Nurnberg Inst Appl Math D-91058 Erlangen Germany Univ Erlangen Nurnberg Dept Phoniatr & Pediat Audiol D-91058 Erlangen Germany

Oncologic therapy of laryngeal cancer may necessitate a total excision of the larynx which results in loss of voice. Voice rehabilitation can be achieved using mucosal tissue vibrations at the upper part of the esophagus which serves as substitute voice generating element (PE segment). The quality of the substitute voice is closely related to vibratory characteristics of the PE segment. By means of a highspeed camera the dynamics of the PE segment can be recorded in real-time. Using image processing the deformations of the PE segment are extracted from the image series as deforming contours. Commonly, the characterization of PE dynamics bases on the spectral analysis of the time varying contour area. However, this constitutes an integral approach which masks most of the specific dynamics of PE deformations. We present an algorithm that automatically registers one segmented contour in a frame of the video sequence to the contour in the next frame to derive discrete 2-D trajectories of PE vibrations. By concatenation of the obtained transformations this approach provides a total registration of PE segment contours. We suggest a mixed-integer programming formulation for the problem that combines an advanced outlier and deformation handling with the introduction of dummy points in regions that newly open up, and that includes normal information in the objective function to avoid unwanted deformations. Numerical experiments show that the implemented alternate convex search algorithm produces robust results which is demonstrated at the example of five high-speed recordings of laryngectomee subjects. (C) 2007 Elsevier B.V. All rights reserved.

关键词： substitute voice PE segment digital high-speed videos point matching shape registration generalized assignment problem 2-D trajectories

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