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 territ...
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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.
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...
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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.
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 sp...
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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.
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 vari...
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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 integerquadratic 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.
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 det...
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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 integerquadratic problem and afterwards linearized. some numerical experiments, using Ilog Cplex 10.1, has been performed. They show that the methodology is promising.
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 su...
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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.
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 quadraticprogramming heuristics in the transformation ...
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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 quadraticprogramming 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.
Barahona described a linear time algorithm for a class of 0-1 quadraticprogramming problems. The algorithm was based on a transformation to a max-cut problem. We describe a linear algorithm that treats a slightly mor...
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Barahona described a linear time algorithm for a class of 0-1 quadraticprogramming 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.
A method of constructing test problems for constrained bivalent quadraticprogramming is presented. For any feasible integer point of a given domain, the method generates quadratic functions whose minimum over the giv...
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A method of constructing test problems for constrained bivalent quadraticprogramming 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.
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...
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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.
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