Results 1  10
of
30
QAPLIB–A Quadratic Assignment Problem Library
 European Journal of Operational Research
, 1991
"... ..."
Solving Large Quadratic Assignment Problems on Computational Grids
, 2000
"... The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computat ..."
Abstract

Cited by 82 (7 self)
 Add to MetaCart
The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Some instances of size n = 30 have remained unsolved for decades. The solution of these problems requires both improvements in mathematical programming algorithms and the utilization of powerful computational platforms. In this article we describe a novel approach to solve QAPs using a stateoftheart branchandbound algorithm running on a federation of geographically distributed resources known as a computational grid. Solution of QAPs of unprecedented complexity, including the nug30, kra30b, and tho30 instances, is reported.
Lower Bounds for the Quadratic Assignment Problem Based Upon a Dual Formulation
"... A new bounding procedure for the Quadratic Assignment Problem (QAP) is described which extends the Hungarian method for the Linear Assignment Problem (LAP) to QAPs, operating on the four dimensional cost array of the QAP objective function. The QAP is iteratively transformed in a series of equivalen ..."
Abstract

Cited by 39 (8 self)
 Add to MetaCart
A new bounding procedure for the Quadratic Assignment Problem (QAP) is described which extends the Hungarian method for the Linear Assignment Problem (LAP) to QAPs, operating on the four dimensional cost array of the QAP objective function. The QAP is iteratively transformed in a series of equivalent QAPs leading to an increasing sequence of lower bounds for the original problem. To this end, two classes of operations which transform the four dimensional cost array are defined. These have the property that the values of the transformed objective function Z' are the corresponding values of the old objective function Z, shifted by some amount C. In the case that all entries of the transformed cost array are nonnegative, then C is a lower bound for the initial QAP. If, moreover, there exists a feasible solution U to the QAP, such that its value in the transformed problem is zero, then C is the optimal value of Z and U is an optimal solution for the original QAP. The transformations are iteratively applied until no significant increase in constant C as above is found, resulting in the so called Dual Procedure (DP). Several strategies are listed for appropriately determining C, or equivalently, transforming the cost array. The goal is the modification of the elements in the cost array so as to obtain new equivalent problems which bring the QAP closer to solution. In some cases the QAP is actually solved, though solution is not guaranteed. The close relationship between the DP and the Linear Programming formulation of Adams and Johnson is presented. The DP attempts to solve Adams and Johnsons CLP, a continuous relaxation of a linearization of the QAP. This explains why the DP produces bounds close to the optimum values for CLP calculated by Johnson in her dissertation and by...
A New Bound for the Quadratic Assignment Problem Based on Convex Quadratic Programming
 MATHEMATICAL PROGRAMMING
, 1999
"... We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be comp ..."
Abstract

Cited by 37 (4 self)
 Add to MetaCart
(Show Context)
We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the wellknown projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoff between bound quality and computational effort.
Solving Quadratic Assignment Problems Using Convex Quadratic Programming Relaxations
, 2000
"... ..."
(Show Context)
On the Best Search Strategy in Parallel BranchandBound  BestFirstSearch vs. Lazy DepthFirstSearch.
 Annals of Operations Research
, 1996
"... or because pruning and evaluation tests are more effective in DFS due to the presence of better incumbents. 1 Introduction. One of the key issues of searchbased algorithms in general and B&Balgorithms in particular is the search strategy employed: In which order should the unexplored parts ..."
Abstract

Cited by 24 (4 self)
 Add to MetaCart
(Show Context)
or because pruning and evaluation tests are more effective in DFS due to the presence of better incumbents. 1 Introduction. One of the key issues of searchbased algorithms in general and B&Balgorithms in particular is the search strategy employed: In which order should the unexplored parts of the solution space be searched? Different search strategies have different properties regarding time efficiency and memory consumption, both when considered in a sequential and a parallel setting. Supported by the EU HCM project SCOOP and the Danish NSF project EPOS M. Perregaard and J. Clausen / Search Strategies in Parallel Branch and Bound 2 In parallel B&B one often regards the BestFirstSearch strategy (BeFS) and the DepthFirstSearch strategy (DFS) to be two of the prime candidates  BeFS due to expectations of efficiency and theoretical properties regarding anomalies, and DFS for reasons of space efficiency. However BeFS requires that the bou
Branch and Bound Algorithms  Principles And Examples
, 1999
"... A large number of realworld planning problems called combinatorial optimization problems share the following properties: They are optimization problems, are easy to state, and have a finite but usually very large number of feasible solutions. While some of these as e.g. the Shortest Path proble ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
A large number of realworld planning problems called combinatorial optimization problems share the following properties: They are optimization problems, are easy to state, and have a finite but usually very large number of feasible solutions. While some of these as e.g. the Shortest Path problem and the Minimum Spanning Tree problem have polynomial algoritms, the majority of the problems in addition share the property that no polynomial method for their solution is known. Examples here are vehicle
The Quadratic Assignment Problem with a Monotone AntiMonge and a Symmetric Toeplitz Matrix: Easy and hard cases
"... This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an AntiMonge matrLx with nondecreasing rows and columns and the other coefficient matrLx is a symmetric Toeplitz matrLx. This restricted version is called the AntiMo ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
This paper investigates a restricted version of the Quadratic Assignment Problem (QAP), where one of the coefficient matrices is an AntiMonge matrLx with nondecreasing rows and columns and the other coefficient matrLx is a symmetric Toeplitz matrLx. This restricted version is called the AntiMongeToeplitz QAP. There are three wellknown combinatorial problems that can be modeled via the AntiMongeToeplitz QAP: (P1) The "Turbine Problem", i.e. the assignment of given masses to the vertices of a regular polygon such that the distance of the center of gravity of the resulting system to the center of the polygon is minimized. (P2) The Traveling Salesman Problem on symmetric Monge distance matrices. (P3) The arrangement of data records with given access probabilities in a linear storage medium in order to minimize the average access time. We identify
MultiStart Tabu Search and Diversification Strategies for the Quadratic Assignment Problem
, 2006
"... The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several mul ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
(Show Context)
The quadratic assignment problem (QAP) is a well known combinatorial optimization problem most commonly used to model the facilitylocation problem. The widely acknowledged difficulty of the QAP has made it the focus of many metaheuristic solution approaches. In this study, we introduce several multistart tabu search variants and show the benefit of utilizing strategic diversification within the tabu search framework for the QAP. Computational results for a set of problems obtained from QAPLIB demonstrate the ability of our TS multistart variants to improve on the classic tabu search approach that is one of the principal and most widely used methods for the QAP. We also show that our new procedures are highly competitive with the best recently introduced methods from the literature, including more complex hybrid approaches that incorporate a classic tabu search method as a subroutine.
A Hybrid Fuzzy Variable Neighborhood Particle Swarm Optimization Algorithm . . .
 JOURNAL OF UNIVERSAL COMPUTER SCIENCE
, 2007
"... Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper ..."
Abstract

Cited by 14 (7 self)
 Add to MetaCart
Recently, Particle Swarm Optimization (PSO) algorithm has exhibited good performance across a wide range of application problems. A quick review of the literature reveals that research for solving the Quadratic Assignment Problem (QAP) using PSO approach has not much been investigated. In this paper, we design a hybrid metaheuristic fuzzy scheme, called as variable neighborhood fuzzy particle swarm algorithm (VNPSO), based on fuzzy particle swarm optimization and variable neighborhood search to solve the QAP. In the hybrid fuzzy scheme, the representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. A new mapping is introduced between the particles in the swarm and the problem space in an efficient way. We also attempt to theoretically prove that the variable neighborhood particle swarm algorithm converges with a probability of 1 towards the global optimal. The performance of the proposed approach is evaluated and compared with other four different algorithms. Empirical results illustrate that the approach can be applied for solving quadratic assignment problems effectively.