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The Quadratic Assignment Problem: A Survey and Recent Developments
 In Proceedings of the DIMACS Workshop on Quadratic Assignment Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1994
"... . Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment probl ..."
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Cited by 114 (16 self)
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. Quadratic Assignment Problems model many applications in diverse areas such as operations research, parallel and distributed computing, and combinatorial data analysis. In this paper we survey some of the most important techniques, applications, and methods regarding the quadratic assignment problem. We focus our attention on recent developments. 1. Introduction Given a set N = f1; 2; : : : ; ng and n \Theta n matrices F = (f ij ) and D = (d kl ), the quadratic assignment problem (QAP) can be stated as follows: min p2\Pi N n X i=1 n X j=1 f ij d p(i)p(j) + n X i=1 c ip(i) ; where \Pi N is the set of all permutations of N . One of the major applications of the QAP is in location theory where the matrix F = (f ij ) is the flow matrix, i.e. f ij is the flow of materials from facility i to facility j, and D = (d kl ) is the distance matrix, i.e. d kl represents the distance from location k to location l [62, 67, 137]. The cost of simultaneously assigning facility i to locat...
An Interior Point Algorithm to Solve Computationally Difficult Set Covering Problems
, 1990
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A survey on the continuous nonlinear resource allocation problem
 Eur. J. Oper. Res
, 2008
"... Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering a ..."
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Cited by 23 (1 self)
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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 1 Introduction and
Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions
 ANNALS OF OPERATIONS RESEARCH
, 2000
"... ... Knapsack Problems to fix some variables to zero and to separate the rest into two groups those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem w ..."
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Cited by 12 (5 self)
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... Knapsack Problems to fix some variables to zero and to separate the rest into two groups those that tend to be zero and those that tend to be one, in an optimal integer solution. Using an initial feasible integer solution, we generate logic cuts based on our analysis before solving the problem with branch and bound. Computational testing, including the set of problems in the ORlibrary and our own set of difficult problems, shows our approach helps to solve difficult problems in a reasonable amount of time and, in most cases, with a fewer number of nodes in the search tree than leading commercial software. ______________________________________________________________________________________
A survey on a classic core problem in operations research
, 2005
"... Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering ..."
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Cited by 4 (0 self)
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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common technique is based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. 1 Introduction and
Higherorder cover cuts from zero–one knapsack constraints augmented by twosided bounding inequalities
, 2008
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A twolevel approach to large mixedinteger programs with application to cogeneration in energyefficient buildings
, 2015
"... We study a twostage mixedinteger linear program (MILP) with more than 1 million binary variables in the second stage. We develop a twolevel approach by constructing a semicoarse model (coarsened with respect to variables) and a coarse model (coarsened with respect to both variables and constrain ..."
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Cited by 1 (1 self)
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We study a twostage mixedinteger linear program (MILP) with more than 1 million binary variables in the second stage. We develop a twolevel approach by constructing a semicoarse model (coarsened with respect to variables) and a coarse model (coarsened with respect to both variables and constraints). We coarsen binary variables by selecting a small number of prespecified daily on/off profiles. We aggregate constraints by partitioning them into groups and summing over each group. With an appropriate choice of coarsened profiles, the semicoarse model is guaranteed to find a feasible solution of the original problem and hence provides an upper bound on the optimal solution. We show that solving a sequence of coarse models converges to the same upper bound with proven finite steps. This is achieved by adding violated constraints to coarse models until all constraints in the semicoarse model are satisfied. We demonstrate the effectiveness of our approach in cogeneration for buildings. The coarsened models allow us to obtain good approximate solutions at a fraction of the time required by solving the original problem. Extensive numerical experiments show that the twolevel approach scales to large problems that are beyond the capacity of stateoftheart commercial MILP solvers.
Hierarchical Topological Network Design
"... Abstract—We present a hierarchical solution method to approximately solve the topological network design problem: given positive integers ( 1), minimize the number of arcs required to interconnect nodes, so that the network diameter does not exceed, the maximum node degree does not exceed 1, and the ..."
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Abstract—We present a hierarchical solution method to approximately solve the topological network design problem: given positive integers ( 1), minimize the number of arcs required to interconnect nodes, so that the network diameter does not exceed, the maximum node degree does not exceed 1, and the network is single node survivable. The method uses dynamic programming to piece together small networks to create larger networks. The method was used to plan two highspeed packet networks at AT&T. Index Terms—Dynamic programming, hierarchical design, network design, survivability. I. INTRODUCTION AND PROBLEM DEFINITION PLANNING the evolution of a large communications network requires a variety of approximations and estimates. A demand forecast for the various services is required, as well as lowlevel service planning assumptions (e.g., card redundancy).
A Binary Integer Linear ProgrammingBased Approach for Solving the Allocation Problem in Multiprocessor Partitioned Scheduling
"... Abstract—Scheduling is a main issue of realtime systems because it involves meeting the deadlines. In this paper, we address the problem of scheduling a set of periodic tasks on m processors under EDF (Earliest Deadline First) using a partitioned scheme. The allocation problem is transformed into a ..."
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Abstract—Scheduling is a main issue of realtime systems because it involves meeting the deadlines. In this paper, we address the problem of scheduling a set of periodic tasks on m processors under EDF (Earliest Deadline First) using a partitioned scheme. The allocation problem is transformed into a binary integer linear program. Then, it is solved by applying Geoffrion’s version of Balas ’ additive method, optimized for the realtime scheduling problem. In order to assess the feasibility of the approach for a small size practical problem, some experimental results are shown. KeywordsBalas ’ additive algorithm, binary integer programming, multiprocessor realtime scheduling, partitioned scheme I.