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

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.

[1]  Willy Herroelen,et al.  On the use of flow dominance in complexity measures for facility layout problems , 1985 .

[2]  Peter L. Hammer,et al.  Discrete Applied Mathematics , 1993 .

[3]  Mauro Dell'Amico,et al.  Annotated Bibliographies in Combinatorial Optimization , 1997 .

[4]  Andrew Whinston,et al.  An Algorithm for the Quadratic Assignment Problem , 1970 .

[5]  Franz Rendl,et al.  QAPLIB – A Quadratic Assignment Problem Library , 1997, J. Glob. Optim..

[6]  C. Le Conte De Poly Barbut.  Automorphismes du permutoèdre et votes de Condorcet , 1990 .

[7]  Panos M. Pardalos,et al.  Implementation of a Variance Reduction-Based Lower Bound in a Branch-and-Bound Algorithm for the Quadratic Assignment Problem , 1997, SIAM J. Optim..

[8]  Catherine Roucairol,et al.  Difficulties of Exact Methods for Solving the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[9]  Eranda Çela,et al.  The quadratic assignment problem : theory and algorithms , 1999 .

[10]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[11]  Vassilis Zissimopoulos,et al.  On the Quality of Local Search for the Quadratic Assignment Problem , 1998, Discret. Appl. Math..

[12]  Thomas E. Vollmann,et al.  ON PREDICTING COMPUTATIONAL TIME OF A BRANCH AND BOUND ALGORITHM FOR THE ASSIGNMENT OF FACILITIES , 1976 .

[13]  Elwood S. Buffa,et al.  The Facilities Layout Problem in Perspective , 1966 .

[14]  Claude Le Conte de Poly-Barbut.  Automorphismes du permutoèdre et votes de Condorcet , 1990 .

[15]  J. W. Gavett,et al.  The Optimal Assignment of Facilities to Locations by Branch and Bound , 1966, Oper. Res..

[16]  Panos M. Pardalos,et al.  The Quadratic Assignment Problem: A Survey and Recent Developments , 1993, Quadratic Assignment and Related Problems.