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A METHOD OF DETERMINING TARGET CONFIGURATIONS FOR POWER-SYSTEM RESTORATION USING A mixed-integer programming APPROACH

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ELECTRICAL ENGINEERING IN JAPAN 1995年第2期115卷 67-77页

作者： NAGATA, T SASAKI, H KITAGAWA, M HIROSHIMA UNIV HIROSHIMAJAPAN CHUGOKU ELECT POWER CO INC HIROSHIMAJAPAN

When electricity supply is interrupted due to a fault, it is essential that the power system be restored promptly according to an adequately planned restoration procedure. A problem of obtaining an appropriate target system for restoration is referred to as a power system restoration problem. The authors have already proposed a very efficient method based on the network simplex method which is in the category of mathematical programming approaches. Although the method is effective for most system conditions, it is likely to give an undesirable result in the case of abnormal network conditions. This paper proposes an effective and computationally fast solution algorithm based on the mixed integer programming approach, which can resolve the shortcoming of the former method. The solution speed is improved greatly by incorporating the restoration strategies of system operators. The following assumptions are postulated in this approach: (1) 0 - 1 variables are allocated to branches and loads to present their status;(2) continuous variables are taken to represent branch flows;and (3) costs are assigned to branches to represent their priorities during restorative operations and power flow limits. The proposed approach can be used to complement the former approach. The new approach has been applied to restoration problems of practical size, and simulation results demonstrate its advantage over the former method for intricate operating conditions.

关键词： POWER SYSTEM FAULT RESTORATION mixed integer programming

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A novel mixed integer programming for multi-biomarker panel identification by distinguishing malignant from benign colorectal tumors

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METHODS 2015年 83卷 3-17页

作者： Zou, Meng Zhang, Peng-Jun Wen, Xin-Yu Chen, Luonan Tian, Ya-Ping Wang, Yong Chinese Acad Sci Acad Math & Syst Sci Natl Ctr Math & Interdisciplinary Sci Beijing 100080 Peoples R China Chinese Peoples Liberat Army Gen Hosp Dept Clin Biochem State Key Lab Kidney Dis Beijing 100853 Peoples R China Chinese Acad Sci Shanghai Inst Biol Sci Inst Biochem & Cell Biol Key Lab Syst BiolInnovat Ctr Cell Signaling Netw Shanghai 200233 Peoples R China Shanghai Tech Univ Sch Life Sci & Technol Shanghai 201210 Peoples R China

Multi-biomarker panels can capture the nonlinear synergy among biomarkers and they are important to aid in the early diagnosis and ultimately battle complex diseases. However, identification of these multi-biomarker panels from case and control data is challenging. For example, the exhaustive search method is computationally infeasible when the data dimension is high. Here, we propose a novel method, MILP_k, to identify serum-based multi-biomarker panel to distinguish colorectal cancers (CRC) from benign colorectal tumors. Specifically, the multi-biomarker panel detection problem is modeled by a mixed integer programming to maximize the classification accuracy. Then we measured the serum profiling data for 101 CRC patients and 95 benign patients. The 61 biomarkers were analyzed individually and further their combinations by our method. We discovered 4 biomarkers as the optimal small multi-biomarker panel, including known CRC biomarkers CEA and IL-10 as well as novel biomarkers IMA and NSE. This multi-biomarker panel obtains leave-one-out cross-validation (LOOCV) accuracy to 0.7857 by nearest centroid classifier. An independent test of this panel by support vector machine (SVM) with threefold cross validation gets an AUC 0.8438. This greatly improves the predictive accuracy by 20% over the single best biomarker. Further extension of this 4-biomarker panel to a larger 13-biomarker panel improves the LOOCV to 0.8673 with independent AUC 0.8437. Comparison with the exhaustive search method shows that our method dramatically reduces the searching time by 1000-fold. Experiments on the early cancer stage samples reveal two panel of biomarkers and show promising accuracy. The proposed method allows us to select the subset of biomarkers with best accuracy to distinguish case and control samples given the number of selected biomarkers. Both receiver operating characteristic curve and precision-recall curve show our method's consistent performance gain in accuracy. Our method

关键词： Translational bioinformatics Multi-biomarker Colorectal cancer mixed integer programming

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A note on "A mixed integer programming model for advanced planning and scheduling (APS)"

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期203卷 784-785页

作者： Ornek, Arslan Ozpeynirci, Selin Ozturk, Cemalettin Izmir Univ Econ Dept Ind Syst Engn TR-35330 Izmir Turkey

In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European journal of Operational Research 181, 515-522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Scheduling MRP Advanced planning and scheduling mixed integer programming

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A BRANCH-AND-BOUND ALGORITHM FOR 0-1 PARAMETRIC mixed integer programming

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OPERATIONS RESEARCH LETTERS 1985年第1期4卷 41-45页

作者： OHTAKE, Y NISHIDA, N SCI UNIV TOKYO DEPT MANAGEMENT SCISHINJUKU KUTOKYO 162JAPAN

A branch-and-bound algorithm to solve 0–1 parametric mixed integer linear programming problems has been developed. The present algorithm is an extension of the branch-and-bound algorithm for parametric analysis on pure integer programming. The characteristic of the present method is that optimal solutions for all values of the parameter can be obtained.

关键词： parametric integer programming mixed integer programming branch-and-bound algorithm

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A mixed integer programming algorithm for minimizing the training sample misclassification cost in two-group classification

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ANNALS OF OPERATIONS RESEARCH 1997年第s期74卷 129-157页

作者： Silva, APD Stam, A UNIV CATOLICA PORTUGUESA FAC CIENCIES ECON & EMPRESARIAISCTR REG PORTO P-4150 PORTO PORTUGAL UNIV GEORGIA TERRY COLL BUSINESSDEPT MANAGEMENT ATHENS GA 30602 USA

In this paper, we introduce the Divide and Conquer (D&C) algorithm, a computationally attractive algorithm for determining classification rules which minimize the training sample misclassification cost in two-group classification. This classification rule can be derived using mixed integer programming (MIP) techniques. However, it is well-documented that the complexity of MIP-based classification problems grows exponentially as a function of the size of the training sample and the number of attributes describing the observations, requiring special-purpose algorithms to solve even small size problems within a reasonable computational time. The D&C algorithm derives its name from the fact that it relies, a.o., on partitioning the problem in smaller, more easily handled sub-problems, rendering it substantially faster than previously proposed algorithms. The D&C algorithm solves the problem to the exact optimal solution (i.e., it is not a heuristic that approximates the solution), and allows for the analysis of much larger training samples than previous methods. For instance, our computational experiments indicate that, on average, the D&C algorithm solves problems with 2 attributes and 500 observations more than 3 times faster, and problems with 5 attributes and 100 observations over 50 times faster than Soltysik and Yarnold's software, which may be the fastest existing algorithm. We believe that the D&C algorithm contributes significantly to the field of classification analysis, because it substantially widens the array of data sets that can be analyzed meaningfully using methods which require MIP techniques, in particular methods which seek to minimize the misclassification cost in the training sample. The programs implementing the D&C algorithm are available from the authors upon request.

关键词： classification analysis mixed integer programming nonparametric statistics

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Computational experience with parallel mixed integer programming in a distributed environment

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ANNALS OF OPERATIONS RESEARCH 1999年第s期90卷 19-43页

作者： Bixby, RE Cook, W Cox, A Lee, EK Rice Univ Dept Computat & Appl Math Houston TX 77001 USA Rice Univ Dept Comp Sci Houston TX 77001 USA Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

Numerical experiments for a parallel implementation of a branch-and-bound mixed 0/1 integer programming code are presented. Among its features, the code includes cutting-plane generation at the root node, and employs a new branching-variable selection rule within the search tree. The code runs on a loosely-coupled cluster of workstations using TreadMarks as the parallel software platform. Numerical tests were performed on all mixed 0/1 MIPLIB instances as well as two previously unsolved MIP instances, one arising from telecommunication networks and the other a multicommodity flow problem.

关键词： parallelism mixed integer programming

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Conflict resolution problems for air traffic management systems solved with mixed integer programming

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IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS 2002年第1期3卷 3-11页

作者： Pallottino, L Feron, EM Bicchi, A Univ Pisa Dept Elect Syst & Automat I-56100 Pisa Italy Univ Pisa Enrico Piaggio Interdept Res Ctr I-56100 Pisa Italy MIT Informat & Decis Syst Lab Dept Aeronaut & Astronaut Cambridge MA 02139 USA

This paper considers the problem of solving conflicts arising among several aircraft that are assumed to move in a shared airspace. Aircraft can not get closer to each other than a given safety distance in order to avoid possible conflicts between different airplanes. For such system of multiple aircraft, we consider the path planning problem among given waypoints avoiding all possible conflicts. In particular we are interested in optimal paths, i.e., we want to minimize the total flight time. We propose two different formulations of the multiaircraft conflict avoidance problem as a mixed-integer linear program: in the first case only velocity changes are admissible maneuvers, in the second one only heading angle changes are allowed. Due to the linear formulation of the two problems, solutions may be obtained quickly with standard optimization software, allowing our approach to be implemented in real time.

关键词： air traffic management systems conflict resolution mixed integer programming

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A survey for solving mixed integer programming via machine learning

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NEUROCOMPUTING 2023年 519卷 205-217页

作者： Zhang, Jiayi Liu, Chang Li, Xijun Zhen, Hui-Ling Yuan, Mingxuan Li, Yawen Yan, Junchi Shanghai Jiao Tong Univ Dept Comp Sci & Engn Shanghai Peoples R China Shanghai Jiao Tong Univ MoE Key Lab Artificial Intelligence Shanghai Peoples R China Huawei Ltd Noahs Ark Lab Shenzhen Peoples R China Beijing Univ Posts & Telecommun Sch Econ & Management Beijing Peoples R China

Machine learning (ML) has been recently introduced to solving optimization problems, especially for combinatorial optimization (CO) tasks. In this paper, we survey the trend of leveraging ML to solve the mixed-integer programming problem (MIP). Theoretically, MIP is an NP-hard problem, and most CO problems can be formulated as MIP. Like other CO problems, the human-designed heuristic algorithms for MIP rely on good initial solutions and cost a lot of computational resources. Therefore, researchers consider applying machine learning methods to solve MIP since ML-enhanced approaches can provide the solution based on the typical patterns from the training data. Specifically, we first introduce the for-mulation and preliminaries of MIP and representative traditional solvers. Then, we show the integration of machine learning and MIP with detailed discussions on related learning-based methods, which can be further classified into exact and heuristic algorithms. Finally, we propose the outlook for learning-based MIP solvers, the direction toward more combinatorial optimization problems beyond MIP, and the mutual embrace of traditional solvers and ML components. We maintain a list of papers that utilize machine learning technologies to solve combinatorial optimization problems, which is available at https://***/Thinklab-SJTU/awesome-ml4co. (c) 2022 Elsevier B.V. All rights reserved.

关键词： mixed integer programming Machine learning Combinatorial optimization

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A simulation scenario based mixed integer programming approach to airline reserve crew scheduling under uncertainty

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ANNALS OF OPERATIONS RESEARCH 2017年第2期252卷 335-363页

作者： Bayliss, Christopher De Maere, Geert Atkin, Jason A. D. Paelinck, Marc Univ Southampton ASAP Southampton Hants England KLM Headquarters KLM Royal Dutch Airlines KLM Decis Support Informat Serv Dept Amstelveen Netherlands

The environment in which airlines operate is uncertain for many reasons, for example due to the effects of weather, traffic or crew unavailability (due to delay or sickness). This work focuses on airline reserve crew scheduling under crew absence uncertainty and delay for an airline operating a single hub and spoke network. Reserve crew can be used to cover absent crew or delayed connecting crew. A fixed number of reserve crew are available for scheduling and each requires a daily standby duty start time. This work proposes a mixed integer programming approach to scheduling the airline's reserve crew. A simulation of the airline's operations with stochastic journey time and crew absence inputs (without reserve crew) is used to generate input disruption scenarios for the mixed integer programming simulation scenario model (MIPSSM) formulation. Each disruption scenario corresponds to a record of all of the disruptions that may occur on the day of operation which are solvable by using reserve crew. A set of disruption scenarios form the input of the MIPSSM formulation, which has the objective of finding the reserve crew schedule that minimises the overall level of disruption over the set of input scenarios. Additionally, modifications of the MIPSSM are explored, a heuristic solution approach and a reserve use policy derived from the MIPSSM are introduced. A heuristic based on the proposed MIPSSM outperforms a range of alternative approaches. The heuristic solution approach suggests that including the right disruption scenarios is as important as the quantity of disruption scenarios that are added to the MIPSSM. An investigation into what makes a good set of scenarios is also presented.

关键词： Airline reserve crew scheduling Simulation mixed integer programming

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Decomposition techniques with mixed integer programming and heuristics for home healthcare planning

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ANNALS OF OPERATIONS RESEARCH 2017年第1期256卷 93-127页

作者： Laesanklang, Wasakorn Landa-Silva, Dario Univ Nottingham Sch Comp Sci ASAP Res Grp Jubilee CampusWollaton Rd Nottingham NG8 1BB England

We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporatemixed integer programming solvers and heuristics. Homehealthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which sub-problems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time.

关键词： Home healthcare planning Workforce scheduling and routing mixed integer programming Problem decomposition Heuristic decomposition

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