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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 91 (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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OCTANE: A New Heuristic for Pure 01 Programs
, 1998
"... We propose a new heuristic for pure 01 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and explain how our heuristic can be embedded in a branchandcut ..."
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Cited by 14 (0 self)
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We propose a new heuristic for pure 01 programs, which finds feasible integer points by enumerating extended facets of the octahedron, the outer polar of the unit hypercube. We give efficient algorithms to carry out the enumeration, and explain how our heuristic can be embedded in a branchandcut framework. Finally, we present computational results on a set of pure 01 programs taken from MIPLIB and other sources.
SmoothandDive Accelerator: A PreMILP Primal Heuristic applied to Scheduling
, 2002
"... This article describes an effective and simple primal heuristic to greedily encourage a reduction in the number of binary or 01 logic variables before an implicit enumerativetype search heuristic is deployed to find integerfeasible solutions to “hard” production scheduling problems. The basis of ..."
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Cited by 3 (1 self)
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This article describes an effective and simple primal heuristic to greedily encourage a reduction in the number of binary or 01 logic variables before an implicit enumerativetype search heuristic is deployed to find integerfeasible solutions to “hard” production scheduling problems. The basis of the technique is to employ wellknown smoothing functions used to solve complementarity problems to the local optimization problem of minimizing the weighted sum over all binary variables the product of themselves multiplied by their complement. The basic algorithm of the “smoothanddive accelerator ” (SDA) is to solve successive linear programming (LP) relaxations with the smoothing functions added to the existing problem’s objective function and to use, if required, a sequence of binary variable fixings known as “diving”. If the smoothing function term is not driven to zero as part of the recursion then a branchandbound or branchandcut search heuristic is called to close the procedure finding at least integerfeasible primal infeasible solutions. The heuristic’s effectiveness is illustrated by its application to an oilrefinery’s crudeoil blendshop scheduling problem, which has commonality to many other production scheduling problems in the continuous and semicontinuous (CSC) process domains.
HEURISTICS FOR INTEGER PROGRAMS
"... Permission is hereby granted to the University of Alberta Library to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the ..."
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Permission is hereby granted to the University of Alberta Library to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis, and except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatever without the author’s prior written permission.
Pivot, Cut, and Dive: A Heuristic for 01 Mixed Integer Programming
, 2001
"... We present a heuristic method for general 01 mixed integer programming, intended for eventual incorporation into parallel branchandbound methods for solving such problems exactly. The core of the heuristic is a rounding method based on simplex pivots, employing only gradient information, for a st ..."
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We present a heuristic method for general 01 mixed integer programming, intended for eventual incorporation into parallel branchandbound methods for solving such problems exactly. The core of the heuristic is a rounding method based on simplex pivots, employing only gradient information, for a strictly concave, differentiable merit function measuring integer feasibility. When local minima of this merit function are not integerfeasible, several additional layers of the heuristic come into play. These successive layers include explicit probing of adjacent vertices, modification of the merit function, adjoining of "convexity" cuts to the formulation, and a diving procedure that attempts to fix multiple variables simultaneously. We present "standalone" computational results, running the heuristic by itself without an accompanying branchandbound optimization, on a variety of problems from the MIPLIB collection.
EXPLOITING STRUCTURE IN INTEGER PROGRAMS
, 2011
"... This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a wellknown optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear eq ..."
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This dissertation argues the case for exploiting certain structures in integer linear programs. Integer linear programming is a wellknown optimisation problem, which seeks the optimum of a linear function of variables, whose values are required to be integral as well as to satisfy certain linear equalities and inequalities. The state of the art in solvers for this problem is the “branch and bound ” approach. The performance of such solvers depends crucially on four types of inbuilt heuristics: primal, improvement, branching, and cutseparation or, more generally, bounding heuristics. Such heuristics in generalpurpose solvers have not, until recently, exploited structure in integer linear programs beyond the recognition of certain types of singlerow constraints. Many alternative approaches to integer linear programming can be cast in the following, novel framework. “Structure” in any integer linear program