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New Models for Commercial Territory Design

NETWORKS & SPATIAL ECONOMICS 2011年第3期11卷 487-507页

作者： Angelica Salazar-Aguilar, Maria Rios-Mercado, Roger Z. Cabrera-Rios, Mauricio Univ Autonoma Nuevo Leon Grad Program Syst Engn San Nicolas De Los Garza 66450 NL Mexico Univ Puerto Rico Dept Ind Engn Mayaguez PR 00681 USA

In this work, a series of novel formulations for a commercial territory design problem motivated by a real-world case are proposed. The problem consists on determining a partition of a set of units located in a territory that meets multiple criteria such as compactness, connectivity, and balance in terms of customers and product demand. Thus far, different versions of this problem have been approached with heuristics due to its NP-completeness. The proposed formulations are integer quadratic programming models that involve a smaller number of variables than heretofore required. These models have also enabled the development of an exact solution framework, the first ever derived for this problem, that is based on branch and bound and a cut generation strategy. The proposed method is empirically evaluated using several instances of the new quadratic models as well as of the existing linear models. The results show that the quadratic models allow solving larger instances than the linear counterparts. The former were also observed to require fewer iterations of the exact method to converge. Based on these results the combination of the quadratic formulation and the exact method are recommended to approach problem instances associated with medium-sized cities.

关键词： Mixed-integer linear programming integer quadratic programming Territory design Location Valid inequalities

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Placement of Synchronized Measurements for Power System Observability

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IEEE TRANSACTIONS ON POWER DELIVERY 2009年第1期24卷 12-19页

作者： Chakrabarti, Saikat Kyriakides, Elias Eliades, Demetrios G. Univ Cyprus CY-1678 Nicosia Cyprus

This paper presents a method for the use of synchronized measurements for complete observability of a power system. The placement of phasor measurement units (PMUs), utilizing time-synchronized measurements of voltage and current phasors, is studied in this paper. An integer quadratic programming approach is used to minimize the total number of PMUs required, and to maximize the measurement redundancy at the power system buses. Existing conventional measurements can also be accommodated in the proposed PMU placement method. Complete observability of the system is ensured under normal operating conditions as well as under the outage of a single transmission line or a single PMU. Simulation results on the IEEE 14-bus, 30-bus, 57-bus, and 118-bus test systems as well as on a 298-bus test system are presented in this paper.

关键词： integer quadratic programming observability optimal placement phasor measurement units (PMUs) synchronized measurements

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Align Protein Surface Structures to Identify Evolutionally and Structurally Conserved Residues

Align Protein Surface Structures to Identify Evolutionally a...

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第三届最优化与系统生物学国际研讨会

作者： Lin Wang Ji-Guang Wang Luonan Chen Computer Science and Information Engineering College Tianjin University of Science and Technology Academy of Mathematics and Systems Science Chinese Academy of Sciences Department of Electronics Information and Communication EngineeringOsaka Sangyo UniversityOsaka 574-8530Japan

Protein-protein interface underlies the protein protein *** mutation of protein-protein interface residues has shown that the distribution of binding free energy is not average among the interface ***,there are hot spots in the protein interfaces that contribute most binding *** we provide a new method based on integer quadratic programming that systematically aligns protein surface structures shared by a set of *** method incorporates protein sequence and structure data,and can correctly identify residues having evolutional and structural conservation between different *** is sequence order independent, so can unravel the evolutional similarity between distant ***,it can be used to predict hot spots with ROC area AUC=*** with most hot spot prediction methods,our method does not need prior knowledge for the structure of protein complex or even the structure of the binding partner.

关键词： Hot spots Protein surface Residue conservation integer quadratic programming

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A new variable reduction technique for convex integer quadratic programs

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APPLIED MATHEMATICAL MODELLING 2008年第2期32卷 224-231页

作者： Hua, Zhongsheng Zhang, Bin Xu, Xiaoyan Univ Sci & Technol China Sch Management Anhua 230026 Peoples R China

Convex integer quadratic programming involves minimization of a convex quadratic objective function with affine constraints and is a well-known NP-hard problem with a wide range of applications. We proposed a new variable reduction technique for convex integer quadratic programs (IQP). Based on the optimal values to the continuous relaxation of IQP and a feasible solution to IQP, the proposed technique can be applied to fix some decision variables of an IQP simultaneously at zero without sacrificing optimality. Using this technique, computational effort needed to solve IQP can be greatly reduced. Since a general convex bounded IQP (BIQP) can be transformed to a convex IQP, the proposed technique is also applicable for the convex BIQP. We report a computational study to demonstrate the efficacy of the proposed technique in solving quadratic knapsack problems. (c) 2006 Elsevier Inc. All rights reserved.

关键词： integer quadratic programming variable reduction convex quadratic programming quadratic knapsack problem

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Portfolio Selection under Piecewise Affine Transaction Costs: An integer quadratic Formulation

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2nd International Conference on Modelling, Computation and Optimization in Information Systems and Management Sciences

作者： Lemrabott, Mohamed Gueye, Serigne Yassine, Adnan Rakotondratsimba, Yves Lab Math Appl Havre 25 Rue Philippe Lebon F-76600 Le Havre France ECE F-75007 Paris France

ISBN: (纸本)9783540874768

In this paper we consider the problem of selecting assets for which transaction costs are given by piecewise affine functions. Given practical constraints related to budget and buy-in thresholds, our purpose is to determine the number of each asset i that can produce the maximum return of a portfolio composed of (n + 1) assets (one of them is free of risk). The problem is formulated as an integer quadratic problem and afterwards linearized. some numerical experiments, using Ilog Cplex 10.1, has been performed. They show that the methodology is promising.

关键词： Piecewise transaction costs integer quadratic programming portfolio selection Linearization

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An approximation algorithm for haplotype inference by maximum parsimony 05

An approximation algorithm for haplotype inference by maximu...

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Proceedings of the 2005 ACM symposium on Applied computing

作者： Yao-Ting Huang Kun-Mao Chao Ting Chen National Taiwan University Taipei Taiwan University of Southern California Los Angeles CA

ISBN: (纸本)9781581139648

This paper studies haplotype inference by maximum parsimony using population data. We define the optimal haplotype inference (OHI) problem as given a set of genotypes and a set of related haplotypes, find a minimum subset of haplotypes that can resolve all the genotypes. We prove that OHI is NP-hard and can be formulated as an integer quadratic programming (IQP) problem. To solve the IQP problem, we propose an iterative semi-definite programming based approximation algorithm, (called SDPHapInfer). We show that this algorithm finds a solution within a factor of O(logn) of the optimal solution, where n is the number of genotypes. This algorithm has been implemented and tested on a variety of simulated and biological data. In comparison with three other methods: HAPAR, HAPLOTYPER, and PHASE, the experimental results indicate that SDPHapInfer and HAPLOTYPER have similar error rates. In addition, the results generated by PHASE have lower error rates on some data but higher error rates on others. The error rates of HAPAR are higher than the others on biological data. In terms of efficiency, SDPHapInfer, HAPLOTYPER, and PHASE output a solution in a stable and consistent way, and they run much faster than HAPAR when the number of genotypes becomes large.

关键词： algorithm haplotype inference integer quadratic programming maximum parsimony semi-definite programming

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A HEURISTIC-BASED BRANCH-AND-BOUND ALGORITHM FOR UNCONSTRAINED quadratic ZERO-ONE programming

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COMPUTING 1995年第4期54卷 283-301页

作者： PALUBECKIS, G Department of Practical Informatics Kaunas University of Technology Studentu St. 50 3028 Kaunas Lithuania

In this paper we describe a branch and bound algorithm for solving the unconstrained quadratic 0-1 programming problem. The salient features of it are the use of quadratic programming heuristics in the transformation of subproblems and exploiting some classes of facets of the polytope related to the quadratic problem in deriving upper bounds on the objective function. We develop facet selection procedures that form a basis of the bound computation algorithm. We present computational experience on four series of randomly generated problems and 14 real instances of a quadratic problem arising in design automation. We remark that the same ideas can also be applied to some other combinatorial optimization problems.

关键词： integer quadratic programming BRANCH AND BOUND GRAPHS

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GENERALIZATION OF BARAHONAS ALGORITHM FOR CASES OF integer NONLINEAR-programming WITH BOX CONSTRAINTS

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OPERATIONS RESEARCH LETTERS 1993年第2期13卷 99-105页

作者： BALDICK, R LAWRENCE BERKELEY LAB DEPT ELECT & COMP ENGNBERKELEYCA 94720

Barahona described a linear time algorithm for a class of 0-1 quadratic programming problems. The algorithm was based on a transformation to a max-cut problem. We describe a linear algorithm that treats a slightly more general problem directly in its original form. We then give a pseudopolynomial algorithm for even more general problems.

关键词： integer quadratic programming SERIES-PARALLEL GRAPHS POLYNOMIAL ALGORITHMS PSEUDOPOLYNOMIAL ALGORITHMS BOX CONSTRAINTS DYNAMIC programming

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CONSTRUCTION OF TEST PROBLEMS IN quadratic BIVALENT programming

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 1991年第1期17卷 74-87页

作者： PARDALOS, PM Pennsylvania State Univ. University Park

A method of constructing test problems for constrained bivalent quadratic programming is presented. For any feasible integer point of a given domain, the method generates quadratic functions whose minimum over the given domain occurs at the selected point. Certain properties of unconstrained quadratic zero-one programs that determine the difficulty of the test problems are also discussed. In addition, a standardized random test problem generator for unconstrained quadratic zero-one programming is given.

关键词： GLOBAL OPTIMIZATION integer quadratic programming TEST PROBLEMS

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ON LOWER BOUNDS FOR A CLASS OF quadratic-0, 1 PROGRAMS

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OPERATIONS RESEARCH LETTERS 1985年第4期4卷 175-180页

作者： ASSAD, AA XU, WX CHINESE ACAD SCI INST APPL MATHBEIJINGPEOPLES R CHINA

We present a new method of obtaining lower bounds for a class of quadratic 0, 1 programs that includes the quadratic assignment problem. The method generates a monotonic sequence of lower bounds and may be interpreted as a Lagrangean dual ascent procedure. We report on a computational comparison of our bounds with earlier work in [2] based on subgradient techniques.

关键词： integer quadratic programming quadratic assignment problem lower bounding techniques

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