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Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior

COMPUTERS & OPERATIONS RESEARCH 2018年 100卷 54-65页

作者： Kang, Yongha Albey, Erinc Uzsoy, Reha Samsung SDS Smart Factory Team Seoul South Korea Ozyegin Univ Dept Ind Engn TR-34794 Istanbul Turkey North Carolina State Univ Edward P Fitts Dept Ind & Syst Engn Raleigh NC 27695 USA

We present heuristics for solving a difficult nonlinear integer programming (NIP) model arising from a multi-item single machine dynamic lot-sizing problem. The heuristic obtains a local optimum for the continuous relaxation of the NIP model and rounds the resulting fractional solution to a feasible integer solution by solving a series of shortest path problems. We also implement two benchmarks: a version of the well-known Feasibility Pump heuristic and the Surrogate Method developed for stochastic discrete optimization problems. Computational experiments reveal that our shortest path based rounding procedure finds better production plans than the previously developed myopic heuristic and the benchmarks. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： nonlinear integer programming Dynamic lot-sizing Production planning Queueing Rounding heuristic Feasibility pump heuristic Surrogate problem method

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Asymptotic strong duality for bounded integer programming: A logarithmic-exponential dual formulation

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MATHEMATICS OF OPERATIONS RESEARCH 2000年第4期25卷 625-644页

作者： Sun, XL Li, D Shanghai Univ Dept Math Shanghai 200436 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Sha Tin Hong Kong Peoples R China

A logarithmic-exponential dual formulation is proposed in this paper for bounded integer programming problems. This new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem. These prominent features are achieved by exploring a novel nonlinear Lagrangian function, deriving an asymptotic zero duality gap, investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation. One other feature of the logarithmic-exponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold-values.

关键词： integer programming nonlinear integer programming duality theory logarithmic-exponential dual formulation strong duality primal feasibility

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Queue-Aware Transmission Scheduling for Cooperative Wireless Communications

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IEEE TRANSACTIONS ON COMMUNICATIONS 2015年第4期63卷 1149-1161页

作者： Wang, Ning Gulliver, T. Aaron Univ Victoria Dept Elect & Comp Engn Victoria BC V8W 2Y2 Canada

Queue-aware transmission scheduling for cooperative wireless communications with sub-fading-block scheduling to better balance load and capacity in low mobility environments is investigated. The scheduling problem for joint cooperation scheduling and resource allocation is formulated as a constrained nonlinear integer optimization problem over an integer convex set based on a source buffer queueing analysis. It is shown that with queue-aware scheduling, the state transition matrix of the source buffer queue has a highly dynamic form. As a result, the objective function of the optimization problem does not have an analytic form in general. The constrained discrete Rosenbrock search algorithm, which is a gradient-free directed discrete search algorithm, is employed to solve the nonlinear integer problem. The output of the directed integer search algorithm is used for queue-aware transmission scheduling for the cooperative system. Numerical results are presented which show that, for cooperative transmission scheduling, the Rosenbrock search based queue-aware algorithm significantly outperforms the equal partitioning, random partitioning, and gradient-based algorithms under quasi-static channel assumptions. Under practical system conditions with unsaturated traffic, the proposed queue-aware scheduling scheme achieves the true optima, and maintains a large stability region for the buffer queue, over a wide range of channel and traffic conditions. It is also shown that when fading channel dynamics are taken into consideration, the performance of the proposed queue-aware scheduling algorithm significantly outperforms fixed relaying and fixed direct transmission channel-aware scheduling strategies.

关键词： Cooperative communications discrete search modulation and coding scheme nonlinear integer programming QoS provisioning queue-aware scheduling sub-fading-block scheduling

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Classic group testing with cost for grouping and testing

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第10期58卷 1930-1935页

作者： Turner, Danny W. Stamey, James D. Young, Dean M. Baylor Univ Dept Stat Sci Waco TX 76798 USA Winthrop Univ Dept Math Rock Hill SC 29733 USA

We generalize the classical group testing problem to incorporate costs associated with pooling and inspection, both of which are significant factors in actual applications. We formulate the expected cost model as a nonlinear integer programming problem, prove several propositions and a theorem concerning when pooling is more efficient than individual testing, and determine the optimal group size such that the expected cost is minimized. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Blood testing Cost functions Expected costs nonlinear integer programming

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Reconstruction algorithm for unknown cavities via Feynman-Kac type formula

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2015年第1期61卷 101-133页

作者： Kawakami, Hajime Akita Univ Dept Comp Sci & Engn Akita 0108502 Japan

In this paper, we consider an inverse problem of identifying one or more unknown cavities in a heat conductor. We propose an algorithm for reconstructing the position and shape of the unknown cavities using the measured surface temperature of the heat conductor. The heat conductor is discretized into small components, and we attempt to determine the components of the unknown cavities. Each of the components of the cavities is encoded as and each of the other components is encoded as Thus, the inverse problem is translated into a binary optimization problem. Our algorithm is based on a discrete probabilistic representation of a solution of an initial boundary value problem for the heat equation, which we call a discrete Feynman-Kac type formula. It uses a set of sample paths generated by the Monte-Carlo method. We can use this formula to naturally transform the binary optimization problem to an optimization problem with continuous variables. This continuous approach is used by the algorithm. Although the algorithm comprises some iterations, each iteration step can use a common set of sample paths. Thus, we only need one round of the Monte-Carlo-based simulation to obtain the set of sample paths. Our experiments suggest that the algorithm has an acceptable performance when there are one or two cavities.

关键词： Inverse problem Heat equation nonlinear integer programming Binary variables Continuous approach Monte-Carlo method

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Diversified Software Deployment for Long-Term Risk Mitigation in Cyber-Physical Power Systems

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第1期37卷 377-387页

作者： Zhang, Zhimei Huang, Shaowei Chen, Ying Li, Boda Mei, Shengwei Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Since modern cyber-physical power systems are vulnerable to coordinated wide-area cyber attacks, it is necessary to mitigate the potential risk as much as possible. At the planning stage, the defender can utilize software diversity, which is a common phenomenon that the cyber software of different substations comes from different competing vendors. Therefore, different kinds of software may not be exposed to the same zero-day security loophole, preventing the attacker from taking charge of multiple substations at the same time. In this paper, the optimal scheme of software deployment considering long-term risk mitigation is studied. Firstly, the framework of diversity-based cyber defense against malicious attacks is formulated. Secondly, the risk index based on representative attack patterns is constructed, which is the objective to be minimized. Thirdly, considering that the deployment scheme is long-term stable while the operating mode varies with time, we construct a multiobjective nonlinear stochastic programming to mitigate the average risk of operating modes. Then the optimization problem is solved by the multiobjective genetic algorithm. Lastly, results of the IEEE 39-node CPPS and and the Virtual European Grid demonstrate that the proposed method can considerably reduce the attack risk.

关键词： Substations Cyberattack Software Power systems Indexes Security Risk management Cyber-physical power system multiobjective genetic algorithm (MOGA) nonlinear integer programming risk mitigation stochastic programming software diversity

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Study neighborhood field optimization algorithm on nonlinear sorptive barrier design problems

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NEURAL COMPUTING & APPLICATIONS 2017年第4期28卷 783-795页

作者： Zhang, Xin Wu, Zhou Tianjin Normal Univ Coll Elect & Commun Engn Tianjin Peoples R China Chongqing Univ Sch Automat Chongqing Peoples R China

Using a simulation-based approach, sorptive barrier design can be expressed as a nonlinear and mixed-integer optimization problem, and metaheuristic searching algorithms are suitable optimization methods to find optimal configurations of design. A recently proposed neighborhood field optimization (NFO) algorithm is applied to deal with the sorptive barrier design problem. NFO is originally proposed for continuous optimization problems, then, it is extended to binary NFO for discontinuous optimization problems. In this paper, integer NFO (INFO) is proposed by using forward and backward transformations. For the sorptive barrier design, NFO variants are compared with genetic algorithms and the best performer reported previously. Based on statistical analysis, NFO variants show better performance than GA variants in terms of accuracy and convergence speed, and INFO improves the best known results on all test instances. It can be concluded that the proposed INFO is suitable for the sorptive barrier design with significant performance improvement.

关键词： Sorptive barrier design Environmental simulation Neighborhood field optimization Discrete optimization nonlinear integer programming Genetic algorithm

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A fast algorithm for near cost optimal line plans

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2004年第2期59卷 205-220页

作者： Bussieck, MR Lindner, T Lübbecke, ME GAMS Dev Corp Washington DC 20007 USA Siemens Transportat Syst D-38126 Braunschweig Germany Tech Univ Berlin Math Inst D-10623 Berlin Germany

We consider the design of line plans in public transport at a minimal total cost. Both, linear and nonlinear integer programming are adequate and intuitive modeling approaches for this problem. We present a heuristic variable fixing procedure which builds on problem knowledge from both techniques. We derive and compare lower bounds from different linearizations in order to assess the quality of our solutions. The involved integer linear programs are strengthened by means of problem specific valid inequalities. Computational results with practical data from the Dutch Railways indicate that our algorithm gives excellent solutions within minutes of computation time.

关键词： integer programming nonlinear integer programming cutting planes public transport line planning

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An optimal plan of zero-defect single-sampling by attributes for incoming inspections in assembly lines

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第3期246卷 907-915页

作者： Qin, Ruwen Cudney, Elizabeth A. Hamzic, Zlatan Missouri Univ Sci & Technol Dept Engn Management & Syst Engn Rolla MO 65409 USA

This paper proposes a nonlinear integer program for determining an optimal plan of zero-defect, single-sampling by attributes for incoming inspections in assembly lines. Individual parts coming to an assembly line differ in the non-conforming (NC) risk, NC severity, lot size, and inspection cost-effectiveness. The proposed optimization model is able to determine the inspection sample size for each of the parts in a resource constrained condition where a product's NC risk is not a linear combination of NC risks of the individual parts. This paper develops a three-step solution procedure that effectively reduces the solution time for larger size problems commonly seen in assembly lines. The proposed optimization model provides insightful implications for quality management. For example, it reveals the principle of sample size decisions for heterogeneous, dependent parts waiting for incoming inspections;as well as provides a tool for quantifying the expected return from investing additional inspection resources. The optimization model builds a foundation for extensions to advanced inspection sampling plans. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： Quality management Incoming inspection Quality attributes Acceptance sampling nonlinear integer programming

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An algorithm for nonlinear optimization problems with binary variables

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2010年第2期47卷 257-288页

作者： Murray, Walter Ng, Kien-Ming Stanford Univ Syst Optimizat Lab Dept Management Sci & Engn Stanford CA 94305 USA Natl Univ Singapore Dept Ind & Syst Engn Singapore 117548 Singapore

One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables. A vexing difficulty is the rate the work to solve such problems increases as the number of discrete variables increases. Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables. However, the transformed problems usually have astronomically large numbers of local minimizers, making them harder to solve than typical global optimization problems. Despite this apparent disadvantage, we show that the approach is not futile if we use smoothing techniques. The method we advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution. To illustrate how well the algorithm performs we show the computational results of applying it to problems taken from the literature and new test problems with known optimal solutions.

关键词： nonlinear integer programming Discrete variables Smoothing methods

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