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Reputation-Aware Federated Learning Client Selection Based on stochastic integer programming

IEEE TRANSACTIONS ON BIG DATA 2024年第6期10卷 953-964页

作者： Tan, Xavier Ng, Wei Lim, Wei Xiong, Zehui Niyato, Dusit Yu, Han Nanyang Technol Univ Alibaba NTU Singapore Joint Res Inst Singapore 639798 Singapore Alibaba Grp Hangzhou Peoples R China Singapore Univ Technol & Design Singapore 487372 Singapore Nanyang Technol Univ Sch Comp Sci & Engn Singapore 639798 Singapore

Federated Learning(FL) has attracted wide research interest due to its potential in building machine learning models while preserving users' data privacy. However, due to the distributive nature of FL, it is vulnerable to misbehavior from participating worker nodes. Thus, it is important to select clients to participate in FL. Recent studies on FL client selection focus on the perspective of improving model training efficiency and performance, without holistically considering potential misbehavior and the cost of hiring. To bridge this gap, we propose a first-of-its-kind reputation-aware stochastic integer programming-based FL Client Selection method (SCS). It can optimally select and compensate clients with different reputation profiles. Extensive experiments show that SCS achieves the most advantageous performance-cost trade-off compared to other existing state-of-the-art approaches.

关键词： Biological system modeling Training Computational modeling Uncertainty Costs stochastic processes Data models Federated learning reputation client selection stochastic integer programming

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A multi-stage stochastic integer programming approach for capacity expansion under uncertainty

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JOURNAL OF GLOBAL OPTIMIZATION 2003年第1期26卷 3-24页

作者： Ahmed, S King, A Parija, G Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA IBM Corp Thomas J Watson Res Ctr Math Sci Div Yorktown Hts NY 10598 USA

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost functions to model the economies of scale in expansion costs, we develop a multi-stage stochastic integer programming formulation for the problem. A reformulation of the problem is proposed using variable disaggregation to exploit the lot-sizing substructure of the problem. The reformulation significantly reduces the LP relaxation gap of this large scale integer program. A heuristic scheme is presented to perturb the LP relaxation solutions to produce good quality integer solutions. Finally, we outline a branch and bound algorithm that makes use of the reformulation strategy as a lower bounding scheme, and the heuristic as an upper bounding scheme, to solve the problem to global optimality. Our preliminary computational results indicate that the proposed strategy has significant advantages over straightforward use of commercial solvers.

关键词： capacity expansion stochastic integer programming reformulation heuristic branch & bound

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A stochastic integer programming Approach to Air Traffic Scheduling and Operations

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OPERATIONS RESEARCH 2020年第5期68卷 1375-1402页

作者： Wang, Kai Jacquillat, Alexandre MIT Sloan Sch Management Cambridge MA 02142 USA

Air traffic management measures comprise tactical operating procedures to minimize delay costs and strategic scheduling interventions to control overcapacity scheduling. Although interdependent, these problems have been treated in isolation. This paper proposes an integrated model of scheduling and operations in airport networks that jointly optimizes scheduling interventions and ground-holding operations across airports networks under operating uncertainty. It is formulated as a two-stage stochastic program with integer recourse. To solve it, we develop an original decomposition algorithm with provable solution quality guarantees. The algorithm relies on new optimality cuts-dual integer cuts-that leverage the reduced costs of the dual linear programming relaxation of the second-stage problem. The algorithm also incorporates neighborhood constraints, which shift from exploration to exploitation at later stages. We also use a scenario generation approach to construct representative scenarios from historical records of operations-using integer programming. Computational experiments show that our algorithm yields near-optimal solutions for the entire U.S. National Airspace System network. Ultimately, the proposed approach enhances airport demand management models through scale integration (by capturing network-wide interdependencies) and scope integration (by capturing interdependencies between scheduling and operations).

关键词： airport demand management stochastic integer programming Benders decomposition benefits of integration

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Platelet ordering policies at hospitals using stochastic integer programming model and heuristic approaches to reduce wastage

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COMPUTERS & INDUSTRIAL ENGINEERING 2017年 110卷 151-164页

作者： Rajendran, Suchithra Ravindran, A. Ravi Univ Missouri Dept Ind & Mfg Syst Engn Columbia MO 65211 USA Univ Missouri Dept Mkt Columbia MO 65211 USA Penn State Univ Harold & Inge Marcus Dept Ind & Mfg Engn University Pk PA 16802 USA

Demand uncertainty coupled with a short shelf life of blood platelets has led to a significant wastage at hospitals. An important objective is to minimize wastage of platelets while maintaining a specified service level. To achieve this objective, a mixed integer stochastic programming model under demand uncertainty is developed. Due to the computational complexity of the problem, three heuristic rules are proposed for determining the platelet ordering policy at the hospital. The performance of these three ordering policies is compared against that of the periodic review order-up-to policy proposed in the literature using real-life data obtained from a medical center. The shelf life of arriving platelets, coefficient of variation of demand and cost parameters are varied, and their impact is analyzed on the performance measures and the best rule with respect to each setting is determined. Based on the shelf life setting and cost prioritization, the decision maker can choose the most suitable rule for the hospital. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Platelet Wastage stochastic integer programming Heuristic ordering policies

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Equity and Strength in stochastic integer programming Models for the Dynamic Single Airport Ground-Holding Problem

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TRANSPORTATION SCIENCE 2020年第4期54卷 944-955页

作者： Estes, Alexander S. Ball, Michael O. Univ Minnesota Inst Math & Its Applicat Minneapolis MN 55455 USA Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA Univ Maryland Inst Syst Res College Pk MD 20742 USA

We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.

关键词： air traffic flow management single airport ground holding problem stochastic integer programming facet-defining inequalities equity properties

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CONTINUITY PROPERTIES OF EXPECTATION FUNCTIONS IN stochastic integer programming

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MATHEMATICS OF OPERATIONS RESEARCH 1993年第3期18卷 578-589页

作者： SCHULTZ, R

Sufficient conditions for the (Lipschitz) continuity of the expectation of second-stage costs are given for two-stage stochastic programs, where the optimization problem in the second stage is a mixed-integer linear program. We also present counterexamples to show that, in general, the results can no longer be maintained when relaxing assumptions as well as multivariate probability distributions for which the theory works.

关键词： stochastic programs with recourse stochastic integer programming parametric integer optimization Lipschitz continuous functions

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A new risk-based optimisation method for the iron ore production scheduling using stochastic integer programming

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RESOURCES POLICY 2019年 62卷 571-579页

作者： Ngoc Luan Mai Topal, Erkan Erten, Oktay Sommerville, Bruce Curtin Univ Western Australian Sch Mines Bentley WA 6102 Australia Rio Tinto Perth WA 6000 Australia Nazarbayev Univ Astana Kazakhstan

stochastic integer programming (SIP) has recently been studied to manage the risk caused by geological uncertainty when solving mine planning and production scheduling problems of open pit mines. However, similar to other mathematical programming techniques that deploy integer variables, the main obstacle of applying SIP on real-life datasets stems from the enormous number of integer variables required by its mathematical formulation, which is a function of number of mining blocks being processed and lifespan of the mining project. In this paper, a new framework is proposed for stochastic mine planning process which makes the application of SIP on large-scale datasets tractable. Firstly, mining blocks of simulated orebody models are clustered using TopCone algorithm to significantly reduce the scale of the data. A new SIP model is then developed to work on aggregated blocks so not only the net present value (NPV) is maximised and the risk of not meeting production targets is minimised, but also solution can be obtained in a practical timeframe. The scheduling result of the new SIP model is also compared to an integer programming (IP) model to highlight the ability to manage risk and generating higher NPV on a case study of a large-scale multi-element iron ore deposit in Pilbara region, Western Australia.

关键词： stochastic integer programming Large-scale optimisation Iron ore production scheduling Open pit mining TopCone algorithm

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A stochastic integer programming model for incorporating day-ahead trading of electricity into hydro-thermal unit commitment

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OPTIMIZATION AND ENGINEERING 2005年第2期6卷 163-176页

作者： Nowak, MP Schultz, R Westphalen, M Univ Duisburg Essen Dept Math D-47048 Duisburg Germany SINTEF Ind Management NO-7465 Trondheim Norway

We develop a two-stage stochastic integer programming model for the simultaneous optimization of power production and day-ahead power trading in a hydro-thermal system. The model rests on mixed-integer linear formulations for the unit commitment problem and for the price clearing mechanism at the power exchange. Foreign bids enter as random components into the model. We solve the stochastic integer program by a decomposition method combining Lagrangian relaxation of nonanticipativity with branch-and-bound in the spirit of global optimization. Finally, we report some first computational experiences.

关键词： stochastic integer programming power optimization

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A two-stage stochastic integer programming model for air traffic flow management

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2017年第1期28卷 19-40页

作者： Corolli, Luca Lulli, Guglielmo Ntaimo, Lewis Venkatachalam, Saravanan Univ Trieste Dipartimento Ingn & Architettura Trieste Italy Univ Milano Bicocca Dipartimento Informat Sistemist & Comunicaz Milan Italy Texas A&M Univ Dept Ind & Syst Engn College Stn TX USA

The high cost of flight delays for airlines has motivated scientific research in air traffic flow management (ATFM). The majority of ATFM models in the literature are deterministic and do not take into account stochastic factors such as weather. In this paper, new stochastic programming models for ATFM are proposed. The models include as tactical control options: ground holding, airborne holding and rerouting. To solve the models, a new heuristic method that takes advantage of the problem structure is derived and illustrated. Computational results show that the heuristic method provides practical computation times. Furthermore, the value of the stochastic solution is up to 14% for cases where adverse weather affects a significant part of the network. This implies that using the proposed approach to make air traffic flow decisions can lead to tangible monetary benefits for airlines.

关键词： air traffic flow management stochastic integer programming uncertainty progressive binary heuristic

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Modeling and solving real-time scheduling problems by stochastic integer programming

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 1087-1103页

作者： Sand, G Engell, S Univ Dortmund Proc Control Lab D-44221 Dortmund Germany

This contribution deals with scheduling problems of flexible chemical batch processes with a special emphasis on their real-time character. This implies not only the need for sufficiently short response times, but in particular the burden of in-complete knowledge about the future. To solve such problems, the application of two-stage stochastic integer programming techniques on moving horizons is proposed. They reflect the need for immediately applicable decisions and the potential of later recourse actions to cope with realized uncertainties. In addition to the classical expected value objective, simple measures of risk can be included. Motivated by an example process, some essential modeling prerequisites are discussed. As an important first step, the master scheduling problem is studied and a number of master scheduling models are presented. Large mixed-integer linear problems arise, which are well-suited for a dual decomposition approach. Numerical experiments with a problem-specific solution algorithm demonstrate the applicability of the method to real-world problems. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： batch scheduling uncertainty stochastic integer programming

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