Classes of quadratic assignment problem instances: isomorphism and difficulty measure using a statistical approach

Authors:
Nair Maria Maia de Abreu;Paulo Oswaldo Boaventura Netto;Tania Maia Querido;Elizabeth Ferreira Gouvea
Affiliations:
Program of Production Engineering, COPPE/UFRJ, Brazil;Program of Production Engineering, COPPE/UFRJ, Brazil;CEFET/RJ, Brazil;Program of Production Engineering, COPPE/UFRJ, Brazil and Federal University of Rio Grande do Norte, Brazil
Venue:
Discrete Applied Mathematics - Workshop on discrete optimization DO'99, contributions to discrete optimization
Year:
2002

Citing 2
Cited 1

On the quality of local search for the quadratic assignment problem

Discrete Applied Mathematics
Implementation of a Variance Reduction-Based Lower Bound in a Branch-and-Bound Algorithm for the Quadratic Assignment Problem

SIAM Journal on Optimization

Review: Measuring instance difficulty for combinatorial optimization problems

Computers and Operations Research

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Abstract

In this work, we introduce the variance expression for quadratic assignment problem (QAP) costs. We also define classes of QAP instances, described by a common linear relaxation form. The use of the variance in these classes leads to the study of isomorphism and allows for a definition of a new difficulty index for QAP instances. This index is then compared to a classical measure found in the literature.