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46th Annual ACM Symposium on Theory of Computing (STOC)

作者： Kesselheim, Thomas Radke, Klaus Toennis, Andreas Voecking, Berthold Cornell Univ Ithaca NY 14850 USA Rhein Westfal TH Aachen Aachen Germany

ISBN: (纸本)9781450327107

We study packing LPs in an online model where the columns are presented to the algorithm in random order. This natural problem was investigated in various recent studies motivated, e.g., by online ad allocations and yield management where rows correspond to resources and columns to requests specifying demands for resources. Our main contribution is a 1 0(.\/(log d) I)_ competitive online algorithm. Here d denotes the column, sparsity, i.e., the maximum number of resources that occur in a single column, and B denotes the capacity ratio B, i.e., the ratio between the capacity of a resource and the maximum demand for this resource. In other words, we achieve a (1 0-approximation if the capacity ratio satisfies B =), which is known to be best-possible for any (randomized) online algorithms. Our result improves exponentially on previous work with respect to the capacity ratio. In contrast to existing results on packing LP problems, our algorithm does not use dual prices to guide the allocation of resources over time. Instead, the algorithm simply solves, for each request, a scaled version of the partially known primal program and randomly rounds the obtained fractional solution to obtain an integral allocation for this request. We show that this simple algorithmic technique is not restricted to packing LPs with large capacity ratio of order ()(log d), but it also yields close-to optimal competitive ratios if the capacity ratio is bounded by a constant. In particular, we prove an upper bound on the competitive ratio of Q(c/-"B-1)), for any B > 2. In addition, we show that our approach can be combined with VCG payments and obtain an incentive compatible (1 competitive mechanism for packing LPs with B = where m is the number of constraints. Finally, we apply our technique to the generalized assignment problem for which we obtain the first online algorithm with competitive ratio 0(1).

关键词： Online Packing LP Random Order generalized assignment problem Secretary problem

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iFogStor: an IoT Data Placement Strategy for Fog Infrastructure 1

iFogStor: an IoT Data Placement Strategy for Fog Infrastruct...

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1st IEEE International Conference on Fog and Edge Computing (ICFEC)

作者： Naas, Mohammed Islam Parvedy, Philippe Raipin Boukhobza, Jalil Lemarchand, Laurent Orange Rennes France Univ Bretagne Occidentale Lab STICC UMR 6285 F-29200 Brest France

ISBN: (纸本)9781509030477

Internet of Things (IoT) will be one of the driving application for digital data generation in the next years as more than 50 billions of objects will be connected by 2020. IoT data can be processed and used by different devices spread all over the network. The traditional way of centralizing data processing in the Cloud can hardly scale because it cannot satisfy many of the latency critical IoT applications. In addition, it generates a too high network traffic when the number of objects and services increase. Fog infrastructure provides a beginning of an answer to such an issue. In this paper, we present a data placement strategy for Fog infrastructures called iFogStor. The objective of iFogStor is to take profit of the heterogeneity and location of Fog nodes to reduce the overall latency of storing and retrieving data in a Fog. We formulated the data placement problem as a generalized assignment problem (GAP) and proposed two ways to solve it: 1) an exact solution using integer programming and 2) a heuristic one based on geographical zoning to reduce the solving time. Both solutions proved very good performance as they reduced the latency by more than 86% as compared to a Cloud based solution and by 60% as compared to a naive Fog solution. Using geographical zoning heuristic can allow solving problems with large number of Fog nodes efficiently and in a couple of seconds making iFogStor feasible in runtime and scalable.

关键词： Internet of Things Fog Data Placement Storage Optimization generalized assignment problem

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Building "problem solving engines" for combinatorial optimization problems

Building "problem solving engines" for combinatorial optimiz...

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International Conference on Informatics Research for Development of Knowledge Society Infrastructure

作者： Ibaraki, T Kyoto Univ Grad Sch Informat Kyoto 6068501 Japan

ISBN: (纸本)0769521509

We describe in this paper our attempts to build problem solving engines that together cover a large portion of combinatorial optimization problems encountered in real world applications. Our approach is to select a list of standard problems, and develop their solvers as engines. All the engines we developed are based on the idea of local search and metaheuristics. As standard problems, we have chosen so far CSP (constraint satisfaction problem), RCPSP (recource constrained project scheduling problem), GAP (generalized assignment problem), VRP (vehicle routing problem), SCP (set covering problem), MAX-SAT (maximum satisfiability problem), 2PP (2-dimensional packing problem) and others. In this paper we outline definitions of these problems, algorithmic contents of engines, and some computational results, putting emphasis on RCPSP and VRR.

关键词： problem solving optimisation computability computational complexity real-time systems combinatorial mathematics problem solving engines combinatorial optimization problem real world application local search metaheuristics constraint satisfaction problem recourse constrained project scheduling problem generalized assignment problem vehicle routing problem set covering problem maximum satisfiability problem 2-dimensional packing problem

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A model for aeromedical routing and scheduling

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International Transactions in Operational Research 1999年第1期6卷 57-73页

作者： Ruland, K.S. Systems and Electronics Inc. United States

The Aeromedical Airlift Wing of the United States Air Force is responsible for the transportation of military personnel in need of specialized medical treatment to and from various military hospitals. Over eight million active and retired personnel, spouses and dependents benefit from the system. The system operates under a variety of regulations to ensure timely service and safe operation of the aircraft. This paper presents a model of the system to assist the route planners in generating solutions minimizing patient inconvenience. This is achieved by assigning patients to sequences of aircraft while minimizing layovers. © 1999 Blackwell Publishing Ltd.

关键词： generalized assignment problem Medical transporation Vehicle routing

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Combining data reduction, MIP solver and iterated local search for generalized assignment

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INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE AND ENGINEERING MANAGEMENT 2022年第2期17卷 93-102页

作者： Haddadi, S. Gattal, E. LabSTIC Guelma Algeria

This work is motivated by a memory allocation problem (MAP) in an embedded system which is modeled as a generalized assignment problem (GAP) with side constraints. Thus, this paper aims to design a fast and sufficiently accurate method for GAP that will be used in future research to obtain a solution for MAP. Since this solution barely satisfies the conflict constraints, it will be repaired and then improved using local search . In the current research, the proposed method for GAP combines data reduction, a MIP solver, and iterated local search (ILS). The generic data reduction procedure is based on useful information provided by applying subgradient optimization to the Lagrangian relaxation of the knapsack constraints. In practice, it can eliminate up to 96% of GAP variables. The reduced GAP left by this procedure is small and sparse. Furthermore, its optimal solution can be easily extended to an optimal or near-optimal solution of GAP. An ILS metaheuristic is designed for solving the reduced GAP and the entire method is tested on a widely used benchmark of large and difficult instances. Its comparison with recently published methods shows that it is competitive in terms of solution quality;it is also by far the fastest.

关键词： generalized assignment problem data reduction iterated local search MIP solver

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Graph Balancing with Orientation Costs 27

Graph Balancing with Orientation Costs

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27th Annual European Symposium on Algorithms (ESA)

作者： Schwartz, Roy Yeheskel, Ran Technion Israel Inst Technol Haifa Israel

ISBN: (纸本)9783959771245

Motivated by the classic generalized assignment problem, we consider the Graph Balancing problem in the presence of orientation costs: given an undirected multi-graph G = (V, E) equipped with edge weights and orientation costs on the edges, the goal is to find an orientation of the edges that minimizes both the maximum weight of edges oriented toward any vertex (makespan) and total orientation cost. We present a general framework for minimizing makespan in the presence of costs that allows us to: (1) achieve bicriteria approximations for the Graph Balancing problem that capture known previous results (Shmoys-Tardos [Math. Progrm. '93], Ebenlendr-KrcalSgall [Algorithmica '14], and Wang-Sitters [Inf. Process. Lett. '16]);and (2) achieve bicriteria approximations for extensions of the Graph Balancing problem that admit hyperedges and unrelated weights. Our framework is based on a remarkably simple rounding of a strengthened linear relaxation. We complement the above by presenting bicriteria lower bounds with respect to the linear programming relaxations we use that show that a loss in the total orientation cost is required if one aims for an approximation better than 2 in the makespan.

关键词： Graph Balancing generalized assignment problem

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Improving banch-and-price algorithms and applying them to Stochastic programs

Improving banch-and-price algorithms and applying them to St...

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作者： Silva, Eduardo Ferreira Naval Postgraduate School

学位级别：博士

The first phase of this research demonstrates improvements in the performance of branch-and-price algorithms (B&P) for solving integer programs by (i) stabilizing dual variables during column generation, (ii) performing strong branching, (iii) inserting multiple near-optimal columns from each subproblem, (iv) heuristically improving feasible integer solutions, and by applying several other techniques. Computational testing on generalized-assignment problems shows that solution times decrease over "naive" B&P by as much as 96%; and, some problems that could not be solved by standard branch and bound on the standard model formulation have become easy. In the second phase, this research shows how to solve a class of difficult, stochastic mixed-integer programs using B&P. A new, column-oriented formulation of a stochastic facility-location problem (SFLP), using a scenario representation of uncertainty, provides a vehicle for demonstrating this method's viability. Computational results show that B&P can be orders of magnitude faster than solving the original problem by branch and bound, and this can be true even for single-scenario problems; i. e., for deterministic problems. B&P also solves SFLP exactly when random parameters are modeled through certain continuous probability distributions. In practice, these problems solve more quickly than comparable scenario-based problems, with say, 50 scenarios.

关键词： branch-and-price integer programming stochastic programming generalized assignment problem facility-location problem

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Deadline-aware Energy Management in Data Centers 8

Deadline-aware Energy Management in Data Centers

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8th IEEE International Conference on Cloud Computing Technology and Science (CloudCom)

作者： Hasan, Cengis Haas, Zygmunt J. Univ Edinburgh Sch Informat Edinburgh Midlothian Scotland Cornell Univ Sch Elect & Comp Engn Ithaca NY USA

ISBN: (纸本)9781509014453

We study the dynamic energy optimization problem in data centers. We formulate and solve the following offline problem: given a set of jobs to process, where the jobs are characterized by arrival instances, required processing time, and completion deadlines, and given the energy requirements of switching servers ON or OFF, in which time-slot which server has to be assigned to which job;and in which time-slot which server has to be switched ON or OFF, so that the total energy is optimal for some time horizon. We formulate the offline problem as a binary integer program that can be considered as a new version of generalized assignment problem which includes new constraints stemming from deadline characteristics of jobs and the activation energy of servers. We propose an online algorithm that solves the problem heuristically, and we compare it to random assignment solution.

关键词： job scheduling data centers deadline-aware energy management generalized assignment problem online algorithm

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The use of the multiple knapsack problem in strategic management of a private Polish university Case study

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INTERNATIONAL JOURNAL OF EDUCATIONAL MANAGEMENT 2019年第2期33卷 335-358页

作者： Kuchta, Dorota Rynca, Radoslaw Skorupka, Dariusz Duchaczek, Artur Politechika Wroclawska Wroclaw Poland Wyzszaj Szkola Oficerska Wojsk Ladowych Gen Tadeu Wroclaw Poland

Purpose In the literature, there are many methods that can be helpful in strategic management of universities. Some of them are related to the aspect of sustainability, in terms of balancing the level of fulfillment of different, often conflicting objectives, which must be considered when building strategies. These methods include product/service portfolio ones. However, their use is often intuitive and detached from the quantitative aspects of management. The purpose of this paper is to present a proposal of the modification of the portfolio methods through the use of one of discrete optimization problems, namely, the multiple knapsack problem. The proposal is applied to a selected university. The results are presented and discussed. Design/methodology/approach The research methodology consists in a conceptual work: combining non-quantitative portfolio methods used in strategic management and the quantitative multiple knapsack problem. The analogy is established between a market sector (capacity) and a knapsack (capacity), a university department value and an object value, the university improvement budget and a knapsack, an object cost and an improvement measure cost. Then, the case study is used to conduct an initial validation of the proposed approach. Findings A quantitative model for strategic management of university as a whole or university departments is proposed. It allows to plan and control the application of improvement measures, allowing the university units to take on a better position in the educational market. It has been initially applied to a small university.

关键词： University management generalized assignment problem Multiple knapsack problem Portfolio planning methods

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A constructive search algorithm for combinatorial dynamic optimization problems

A constructive search algorithm for combinatorial dynamic op...

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IEEE International Conference on Evolving and Adaptive Intelligent Systems (EAIS)

作者： Baykasoglu, Adil Ozsoydan, Fehmi Burcin Dokuz Eylul Univ Dept Ind Engn Izmir Turkey

ISBN: (纸本)9781467366984

In most of the optimization studies, the problem related data is assumed to be exactly known beforehand and remain stationary throughout whole optimization process. However, majority of real life problems and their practical applications are dynamic in their nature due to the reasons arising from unpredictable events, such as rush orders, fluctuating capacities of manufacturing constraints, changes in costs or profits. A problem, carrying one of these features is known as dynamic optimization problem (DOP) in the related literature. In DOPs the aim is not only to find the optimum of the current problem configuration, but to keep track of the moving optima. Dynamic optimization is a hot research area and a notable variety of solution methodologies are developed for DOPs in the past decade. As a contribution to the existing literature of DOPs, in the current work, the idea of using a multi-start and constructive search algorithm and thus breaking the dependency to the previously found solutions is presented. The performance tests are conducted on the generalized assignment problem, which has numerous real life applications. In regard to the obtained results, the proposed method is found promising.

关键词： dynamic optimization greedy randomized adaptive search procedure generalized assignment problem

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