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Erratum to “A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling” [Appl. Math. Modell. 34 (2010) 655–670]

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Applied Mathematical Modelling 2011年第12期35卷 5921-5932页

作者： N. Ramkumar P. Subramanian T.T. Narendran K. Ganesh Department of Management Studies Indian Institute of Technology Madras Chennai 600036 Tamilnadu India Global Business Services – Global Delivery IBM India Private Limited Bandra East Mumbai 400051 Maharashtra India

This study analyzes Mixed integer linear program (MILP) proposed by G. Kannan, P. Sasikumar M. Devika, (2010) in their paper titled ‘A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling’, Applied Mathematical Modelling , (34, 655–670). The model in Kannan et al. (2010) is found to be inadequate for the problem described. It is erroneous/infeasible in terms of constraints, objective and variables. In this work, we list down the flaws in the published work and propose modifications to rectify the flaws. The revised model is presented and illustrated using hypothetical problems.

关键词： Closed loop supply chain integer linear program Recycling

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Enhanced Double Via Insertion Using Wire Bending

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IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS 2010年第2期29卷 171-184页

作者： Lee, Kuang-Yao Lin, Shing-Tung Wang, Ting-Chi Taiwan Semicond Mfg Co Design & Technol Platform Org Hsinchu 30013 Taiwan Natl Tsing Hua Univ Dept Comp Sci Hsinchu 30013 Taiwan

Redundant via insertion is highly recommended for improving chip yield and reliability. In this paper, we studied the problem of simultaneous double via insertion and wire bending (DVI/WB) in a postrouting stage, where a single via can have at most one redundant via inserted next to it. Aside from this, we are allowed to bend existing signal wires for enhancing the insertion rate of double vias. The primary goal of the DVI/WB problem is to insert as many double vias as possible;the secondary objective is to minimize the amount of layout perturbation. We formulate the DVI/WB problem as that of finding a minimum-weight maximum independent set (mWMIS) on an enhanced conflict graph. We proposed algorithms to perform wire bending and to construct the enhanced conflict graph from a given design. We also proposed a zero-one integer linear program (0-1 ILP)-based approach to solve the mWMIS problem. Moreover, we studied the problem of DVI/WB with the consideration of via density and extended our 0-1 ILP-based approach to solve it. Experimental results show that our approaches can improve the insertion rate by up to 6.34% at the expense of up to 1.29% wirelength increase when compared with the state-of-the-art double via insertion methods that do not consider wire bending. Moreover, when compared with an existing method that considers wire bending, our DVI/WB approach can insert 2% more double vias and produce 32% less wirelength increase rate on average.

关键词： integer linear program redundant via wire bending

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Stability of p-Cycles under Dynamic Traffic

Stability of p-Cycles under Dynamic Traffic

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Jaumard, Brigitte Metnani, Ammar Concordia Univ CIISE Montreal PQ H3G 1M8 Canada Univ Montreal DIRO Montreal PQ H3C 3J7 Canada

ISBN: (纸本)9781424456383

p-Cycles offer a protection that corresponds to an efficient pre-configured and pre-cross-connected protection scheme. Thereafter, we study the stability and the efficient reconfiguration of p-cycles in the context of dynamic asymmetric traffic. The literature acknowledges it as a difficult problem, but which is of paramount importance in the selection of p-cycles as a protection scheme in Intelligent Optical Networks (IONs). We investigate two p-cycle updating models which differ mainly by their objective criteria. The first objective is the classical one, aiming at minimizing the spare capacity. The second one is new and corresponds to the number of pre-cross-connections that needs to be set/reset after each traffic variation, while attempting to maximize the re-use of previously established pre-cross-connection settings in spite of the modifications of the p-cycles. Note that the second model needs to explicitly include wavelength continuity constraints and is therefore slightly more complex. Results show that (i) the proposed ILP tools are scalable, and (ii) while p-cycles appear not to be very stable with the first criterion, they emerge as highly stable with the second criterion.

关键词： ILP tool ION dynamic asymmetric traffic integer linear program integer programming intelligent networks intelligent optical networks linear programming optical fibre networks p-cycle stability preconfigured protection scheme precross-connected protection

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On the non-existence of a projective (75, 4,12, 5) set in PG(3, 7)

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JOURNAL OF GEOMETRY 2010年第1-2期97卷 29-44页

作者： Chan, Aaron Davis, James Jedwab, Jonathan Univ Waterloo Dept Combinator & Optimizat 200 Univ Ave West Waterloo ON N2L 3G1 Canada Univ Richmond Dept Math & Comp Sci Richmond VA 23173 USA Simon Fraser Univ Dept Math Burnaby BC V5A 1S6 Canada

We show by a combination of theoretical argument and computer search that if a projective (75, 4, 12, 5) set in PG(3, 7) exists then its automorphism group must be trivial. This corresponds to the smallest open case of a coding problem posed by H. Ward in 1998, concerning the possible existence of an infinite family of projective two-weight codes meeting the Griesmer bound.

关键词： Centraliser conjugacy class Griesmer bound integer linear program linear code prescribed automorphism group projective code projective set rational canonical form two-weight code

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Optimizing Marine Corps pilot conversion to the Joint Strike Fighter

Optimizing Marine Corps pilot conversion to the Joint Strike...

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作者： Holloway, Shannon V. Naval Postgraduate School

学位级别：硕士

The United States Marine Corps is replacing its fixed wing fighter and attack aircraft with the new F-35 Joint Strike Fighter. Retirement of F/A-18 Hornets and AV-8B Harriers will make their associated military occupational specialties obsolete. The conversion of personnel to the new aircraft must be carefully managed to ensure appropriate manning levels for the Joint Strike Fighter, while maintaining adequate quantities of experienced personnel in the legacy communities. The Deputy Commandant for Aviation manages the manpower requirements to support the new aircraft through boards which select the best qualified applicants for transition and conversion training. Transition or conversion training serves to balance current aviator inventories with future Marine Corps requirements. This thesis presents the Marine Corps Pilot Conversion Analysis Tool which uses an integer linear program to prescribe pilots for accession and conversion to the new aircraft based on military occupational specialty, years of commissioned service, and level of experience. Our analysis shows that the current plan meets the total pilot accession and conversion requirement, but does not select enough junior-ranking officers to maintain the hierarchical structure desired. Further analysis shows that significantly increasing new accessions and conversions of junior officers provides the best pilot-to-billet matches while generating the smallest training flight-hour backlog.

关键词： integer linear program Optimization Manpower Model F-35 Joint Strike Fighter United States Marine Corps

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Constructing majority-rule supertrees

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ALGORITHMS FOR MOLECULAR BIOLOGY 2010年第1期5卷 2-2页

作者： Dong, Jianrong Fernandez-Baca, David McMorris, F. R. Iowa State Univ Dept Comp Sci Ames IA 50011 USA IIT Dept Appl Math Chicago IL 60616 USA

Background: Supertree methods combine the phylogenetic information from multiple partially-overlapping trees into a larger phylogenetic tree called a supertree. Several supertree construction methods have been proposed to date, but most of these are not designed with any specific properties in mind. Recently, Cotton and Wilkinson proposed extensions of the majority-rule consensus tree method to the supertree setting that inherit many of the appealing properties of the former. Results: We study a variant of one of Cotton and Wilkinson's methods, called majority-rule (+) supertrees. After proving that a key underlying problem for constructing majority-rule (+) supertrees is NP-hard, we develop a polynomial-size exact integer linear programming formulation of the problem. We then present a data reduction heuristic that identifies smaller subproblems that can be solved independently. While this technique is not guaranteed to produce optimal solutions, it can achieve substantial problem-size reduction. Finally, we report on a computational study of our approach on various real data sets, including the 121-taxon, 7-tree Seabirds data set of Kennedy and Page. Conclusions: The results indicate that our exact method is computationally feasible for moderately large inputs. For larger inputs, our data reduction heuristic makes it feasible to tackle problems that are well beyond the range of the basic integer programming approach. Comparisons between the results obtained by our heuristic and exact solutions indicate that the heuristic produces good answers. Our results also suggest that the majority-rule (+) approach, in both its basic form and with data reduction, yields biologically meaningful phylogenies.

关键词： integer linear program Representative Selection Input Tree integer linear program Formulation Supertree Method

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Optimal aircraft load balancing

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2009年第6期16卷 767-787页

作者： Kaluzny, Bohdan L. Shaw, R. H. A. David Def Res & Dev Canada Ctr Operat Res & Anal Ottawa ON Canada

The Canadian Forces employ cargo aircraft for countless missions to deliver equipment, supplies and passengers. Maximizing the payload while maintaining a safe load balance is of high importance. This paper details a mathematical formulation, a Mixed integer linear program model, to solve the problem of determining the arrangement of a set of items in a cargo hold that optimizes the load balance. Items are modelled as rectangles with specified dimensions, mass and centre of gravity offsets. The main decision variables determine the orientation and placement of a given set of items. The objective function can be chosen to minimize deviation of the centre of gravity from the target position or to maximize a function of the items loaded (cardinality, priority, etc.). The formulation models item rotation, spacing requirements, load ordering, macro items, obstacles and constrained placement. Furthermore, specialized cut and transitivity constraints are developed that limit the solution search space.

关键词： bin packing load balancing aircraft loading integer linear program centre of gravity

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Mining Discrete Patterns via Binary Matrix Factorization 09

Mining Discrete Patterns via Binary Matrix Factorization

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15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

作者： Shen, Bao-Hong Ji, Shuiwang Ye, Jieping Arizona State Univ Tempe AZ 85287 USA

ISBN: (纸本)9781605584959

Mining discrete patterns in binary data is important for sub-sampling, compression, and clustering. We consider rank-one binary matrix approximations that identify the dominant patterns of the data, while preserving its discrete property. A best approximation on such data has a minimum set of inconsistent entries, i.e., mismatches between the given binary data and the approximate matrix. Due to the hardness of the problem, previous accounts of such problems employ heuristics and the resulting approximation may be far away from the optimal one. In this paper, we show that the rank-one binary matrix approximation can be reformulated as a 0-1 integer linear program (ILP). However, the ILP formulation is computationally expensive even for small-size matrices. We propose a linear program (LP) relaxation, which is shown to achieve a guaranteed approximation error bound. We further extend the proposed formulations using the regularization technique, which is commonly employed to address overfitting. The LP formulation is restricted to medium-size matrices, due to the large number of variables involved for large matrices. Interestingly, we show that the proposed approximate formulation can be transformed into an instance of the minimum s-t cut problem, which can be solved efficiently by finding maximum flows. Our empirical study shows the efficiency of the proposed algorithm based on the maximum flow. Results also confirm the established theoretical bounds.

关键词： Binary matrix factorization rank-one integer linear program regularization minimum cut maximum flow

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A New Cost Function to Solve RWA Problem in Wavelength Routed Optical Network Using Genetic Algorithms

A New Cost Function to Solve RWA Problem in Wavelength Route...

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World Congress on Nature and Biologically Inspired Computing

作者： Barpanda, Ravi Sankar Turuk, Ashok Kumar Sahoo, Bibhudatta Natl Inst Technol Dept Comp Sci & Engn Rourkela India

ISBN: (纸本)9781424450534

Routing and Wavelength Assignment Problem in wavelength division multiplexed optical network is represented as an integer linear program which is found to be NP-Complete. Our attention is devoted to such networks operating under wavelength continuity constraint, in which a lightpath must occupy the same wavelength on all the links it traverses. In setting up a lightpath, a route must be selected and a wavelength must be assigned to the lightpath. We have proposed ILP formulations for MaxRWA and MinRWA problems with a new cost function. The cost function is based on congestion with delay and hop-count is of secondary importance. Genetic Algorithms provide an attractive approach to compute sub-optimal solutions for the RWA problem. This paper discusses a genetic algorithm way of solving the RWA problem on standard networks such as ARPANET.

关键词： Routing and Wavelength Assignment integer linear program WDM Networks Wavelength continuity constraint lightpath Genetic Algorithm

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Scheduling Physician Working Periods of A Chemotherapy Outpatient Unit

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IFAC Proceedings Volumes 2009年第4期42卷 768-773页

作者： Alexandre Mazier Xiaolan Xie Ecole des Mines de Saint Etienne Engineering and Health Division 158 cours Fauriel 42023 Saint Etienne Cedex France

Treatment of cancer diseases is hard to support for patient. An overloaded day can easily cause stress and others mental trouble which deteriorate patient's health. A well balanced workload is an advantage both for the patient and the staff of hospital. In this paper we propose a scheduling method for physician working period. It is based on e new integer linear program model that takes into account all relevant constraints such as patient treatment protocols, bed capacity and physician planning. Numerical results on data sets derived from real life instances clearly prove the interest of a better physician planning for a well balanced workload. It opens the way for many future research opportunities.

关键词： Health care staff scheduling patient scheduling oncology integer linear program

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