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A mathematical programming based procedure for breast cancer classification

Journal of Mathematical Modelling and Algorithms 2010年第3期9卷 247-255页

作者： Masmoudi, Youssef Chabchoub, Habib Hanafi, Saïd Rebaï, Ahmed LOGIQ Research Unit Institut Supérieur de Gestion Industrielle de Sfax 3018 Sfax BP 1164 Tunisia GIAD research Unit Faculté des sciences économiques et de gestion de Sfax 3018 Sfax BP 1088 Tunisia LAMIH UMR CNRS 8530 Université de Valenciennes Le Mont-Houy 59313 Valenciennes Cedex 9 France Centre de Biotechnologie de Sfax 3018 Sfax BP 1177 Tunisia

In this paper we propose a new procedure for classification based on a hybrid approach. The classification problem is solved by minimizing the distance between the components of each clusters and the centers of the clusters. The determination of the cluster centers is therefore a critical step in our approach and was addressed used the k-means algorithm. Once the centers of each class are determined, the rule of center neighbourhood is applied to assign an element to a class using mathematical programming. The implementation of our hybrid approach was validated on benchmark datasets and applied to an original biological dataset on 84 breast cancer tumours. Each tumour was measured for five parameters corresponding to the expression of five biomarkers (proteins). The obtained classification was discussed using biological knowledge and classical clinical experts' classification of breast tumors. © 2010 Springer Science+Business Media B.V.

关键词： Breast cancer Classification Clustering CPLEX k-means Mathematical programming mixed-integer programming

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WORKFORCE-CONSTRAINED MAINTENANCE SCHEDULING FOR AIRCRAFT FLEET: A CASE STUDY

WORKFORCE-CONSTRAINED MAINTENANCE SCHEDULING FOR AIRCRAFT FL...

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16th ISSAT International Conference on Reliability and Quality in Design

作者： Safaei, Nima Banjevic, Dragan Jardine, Andrew K. S. Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

ISBN: (纸本)9780976348665

The problem is related to the operation of a fleet of aircraft with a certain flying program in which making the availability of the aircraft sufficient to meet the flying program is a challenging issue. During the pre- or after-flight inspections, some component failures of the aircraft(s) may be found. In such cases, the aircraft(s) are sent to the repair shop to be scheduled as maintenance jobs, consisting of failure repairs or preventive maintenance tasks. The objective is to schedule the jobs in such a way that sufficient number of aircraft is available for the next flight programs. The main resource, as well as the main constraint, in the shop is skilled-workforce. The problem is formulated as a mixed-integer mathematical programming model in which the network flow structure is used to compute the skilled-workforce requirements.

关键词： Maintenance Scheduling Skilled-workforce mixed-integer programming Network Flow

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An In-Out Approach to Disjunctive Optimization

An In-Out Approach to Disjunctive Optimization

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7th International Conference Integration of AI and OR Techniques in Constraint programming for Combinatorial Optimization Problems

作者： Fischetti, Matteo Salvagnin, Domenico Univ Padua DEI I-35100 Padua Italy Univ Padua dmpa Padua Italy

ISBN: (纸本)9783642135194

Cutting plane methods are widely used for solving convex optimization problems and are of fundamental importance, e.g., to provide tight bounds for mixed-integer Programs (MIPs). This is obtained by embedding a cut-separation module within a search scheme. The importance of a sound search scheme is well known in the Constraint programming (CP) community. Unfortunately, the "standard" search scheme typically used for MIP problems, known as the Kelley method, is often quite unsatisfactory because of saturation issues. In this paper we address the so-called Lift-and-Project closure for 0-1 MIPs associated with all disjunctive cuts generated from a given set of elementary disjunction. We focus on the search scheme embedding the generated cuts. In particular, we analyze a general meta-scheme for cutting plane algorithms, called in-out search, that was recently proposed by Ben-Ameur and Neto [1]. Computational results on test instances from the literature are presented, showing that using a more clever meta-scheme on top of a black-box cut generator may lead to a significant improvement.

关键词： mixed-integer programming cutting planes disjunctive optimization

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A Novel Approach to Construct Discrete Support Vector Machine Classifiers

A Novel Approach to Construct Discrete Support Vector Machin...

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32nd Annual Conference of the German-Classification-Society

作者： Caserta, Marco Lessmann, Stefan Voss, Stefan Univ Hamburg Inst Informat Syst D-20146 Hamburg Germany

ISBN: (纸本)9783642010439

Discrete support vector machines (DSVM) are recently introduced classifiers that might be preferable to the standard support vector machine due to a more appropriate modeling of classification errors. However, this advantage comes at the cost of an increased computational effort. In particular, DSVM rely upon a mixed-integer program, whose optimal solution is prohibitively expensive to obtain. Therefore, heuristics are needed to construct respective classifiers. This paper proposes a novel heuristic incorporating recent advances from the field of integer programming and demonstrates its effectiveness by means of empirical experimentation. Furthermore, the appropriateness of the DSVM formulation is examined to shed light on the degree of agreement between the classification aim and its implementation in form of a mathematical program.

关键词： Classification Meta-heuristics mixed-integer programming Support vector machines

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A Relax-and-Cut Framework for Gomory's mixed-integer Cuts

A Relax-and-Cut Framework for Gomory's Mixed-Integer Cuts

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7th International Conference Integration of AI and OR Techniques in Constraint programming for Combinatorial Optimization Problems

作者： Fischetti, Matteo Salvagnin, Domenico Univ Padua DEI I-35100 Padua Italy Univ Padua DMPA Padua Italy

ISBN: (纸本)9783642135194

Gomory's mixed-integer Cuts (GMICs) are widely used in modern branch-and-cut codes for the solution of mixed-integer Programs. Typically, GMICs are iteratively generated from the optimal basis of the current Linear programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach prone to instability. In this paper we analyze a different scheme for the generation of rank-1 GMIC read from a basis of the original LP-the one before the addition of any cut. We adopt a relax-and-cut approach where the generated GMIC are not added to the current LP, but immediately relaxed in a Lagrangian fashion. Various elaborations of the basic idea are presented, that lead to very fast-yet accurate-variants of the basic scheme. Very encouraging computational results are presented, with a comparison with alternative techniques from the literature also aimed at improving the GMIC quality, including those proposed very recently by Balas and Bonami and by Dash and Goycoolea.

关键词： mixed-integer programming Gomory's cuts Lagrangian relaxation Relax and Cut

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A parallel between two classes of pricing problems in transportation and marketing

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JOURNAL OF REVENUE AND PRICING MANAGEMENT 2010年第1-2期9卷 110-125页

作者： Heilporn, Geraldine Labbe, Martine Marcotte, Patrice Savard, Gilles CIRRELT Montreal PQ Canada HEC Montreal Distribut Management Montreal PQ Canada Univ Libre Bruxelles Sci Fac Brussels Belgium Univ Montreal Comp Sci & Operat Res Dept Montreal PQ Canada Ecole Polytech Res & Innovat Montreal PQ Canada GERAD Montreal PQ Canada HEC Montreal CP 6128Succursale Ctr Ville Montreal PQ H3C 3J7 Canada

In this study, we establish a parallel between two classes of pricing problems that have attracted the attention of researchers in marketing, theoretical computer science and operations research, each community addressing issues from its own vantage point. More precisely, we contrast the problems of pricing a network or a product line, in order to achieve maximum revenue, given that customers maximize their individual utility. Throughout the article, we focus on problems that can be formulated as mixed-integer programs.

关键词： pricing networks mixed-integer programming

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A mixed-integer mathematical modeling approach to exam timetabling

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COMPUTATIONAL MANAGEMENT SCIENCE 2010年第1期7卷 19-46页

作者： Al-Yakoob, Salem M. Sherali, Hanif D. Al-Jazzaf, Mona Kuwait Univ Coll Sci Dept Math & Comp Sci POB 5969 Safat 13060 State Of Kuwait Kuwait Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA

This paper explores mathematical programming models for an exam timetabling problem related to Kuwait University (KU). In particular, we consider two subproblems: (a) the ExamTimetabling Problem (ETP), which is concerned with assigning exams to designated exam-periods and classrooms, and (b) the Proctor Assignment Problem (PAP), which deals with the assignment of proctors to exams. While this exam timetabling problem is ubiquitous in many academic institutions worldwide, idiosyncrasies of the problem related to gender-based policies and having multiple exam centers at KU require novel models. A mixed-integer exam timetabling programming model (ETM) is developed for ETP, which takes into account restrictions related to exam-period conflicts, facility and human resources, and commuting and traffic considerations. Assuming that exam-periods are specified for all exams as determined by ETM, another mixed-integer programming model is formulated for PAP, denoted by PAM, which incorporates the proctors' preferences for specific days and exam-periods. Computational results are reported and analyzed for solving ETM and PAM directly using the CPLEX Optimization Software (version 9.0), and for implementing a specialized sequential LP-based heuristic for solving PAM. The results obtained significantly improve upon those derived via the existing manual approach implemented at KU, in terms of eliminating conflicts as well as from the overall efficiency and equity points of view.

关键词： Exam timetabling mixed-integer programming Mathematical programming Optimization

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Outage Probability Based Resource Allocation in Wireless Mesh Networks

Outage Probability Based Resource Allocation in Wireless Mes...

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Shao, Xuning Hua, Cunqing Huang, Aiping Zhejiang Univ Inst Informat & Commun Engn Hangzhou 310027 Peoples R China

ISBN: (纸本)9781424456383

In this paper, we propose a link outage probability based resource allocation scheme for multi-radio multi-channel wireless mesh networks. The objective is to optimize the link outage probability under the effect of channel variation and external interference while preserving the end-to-end traffic demand requirements. The problem is formulated as a mixed-integer nonlinear programming problem, which is solved by decomposing it into a feasibility-checking problem and an outage probability search problem so that the original problem can be solved iteratively with reduced complexity. Numerical results are provided to show that the proposed algorithm is superior to the existing scheme in reducing the outage probability.

关键词： end-to-end traffic demand feasibility-checking problem integer programming mixed-integer programming multi-channel networks multi-radio networks nonlinear programming nonlinear programming outage probability probability resource allocation resource alloca

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A mixed-integer linear programming model for the continuous casting planning

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2006年第2期104卷 260-270页

作者： Bellabdaoui, A. Teghem, J. Fac Polytech Mons B-7000 Mons Belgium

The development of optimization models for planning and scheduling is one of the most useful tools for improving productivity of a large number of manufacturing companies. This paper presents a mixed-integer programming model for scheduling steelmaking-continuous casting production. We first review the recent works in continuous casting planning. We focus on a model inspired from an application of steelmaking-continuous casting by Arcelor Group in Liege, Belgium. The process scheduling is characterized by several constraints: job grouping, technological interdependence, no dead time inside the same group of jobs and dynamic processing time of jobs. We present a formulation with mixed-integer linear programming which can be solved using standard software packages. Finally, we treat a few examples to illustrate this application and we conclude this paper with some comments and directions for future extensions. (c) 2004 Elsevier B.V. All rights reserved.

关键词： steelmaking continuous casting mixed-integer programming production planning

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Robust optimization for designing reliable telecommunication networks with node failure scenarios

Robust optimization for designing reliable telecommunication...

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2010 IEEE International Conference on Emergency Management and Management Sciences(2010 IEEE应急管理与管理科学国际会议 ICEMMS)

作者： Tie Liu Wenguo Yang Jingxing Liao Jun Huang Graduate University of Chinese Academy of Sciences Beijing China

The design of telecommunication network concerns the selection of arcs in a graph with involved cost as low as possible, but satisfies constraints such as point-to-point demands routed across the network, arc capacity, hop constraints and so on. Such a design must allocate enough flows and diverse routing paths through the network to ensure that feasible information flows continue to exist, even when components of the network fail. In this paper, we propose a reliable mathematical model to optimally design a minimum-cost survivable telecommunication network that continues to support a good communication under any node failure scenario.

关键词： mixed-integer programming robust optimization routing node failure scenario

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