We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form QAP(A,B), by showing that the identity permutation is optimal when A and B are respectively a Robinson similarity and dissimilarity matrix and one of A or B is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along rows and columns when moving away from the diagonal, and such matrices arise in the classical seriation problem.
Additional Metadata
Keywords quadratic assignment, polynomial time algorithm, Robinson matrix, seriation problem
THEME Logistics (theme 3)
Publisher North-Holland
Journal Operations Research Letters
Project Mixed-Integer Nonlinear Optimization
Note Published paper: DOI: 10.1016/j.orl.2014.12.009
Grant This work was funded by the European Commission 7th Framework Programme; grant id h2020/764759 - Mixed-Integer Non-Linear Optimisation Applications (MINOA)
Citation
Laurent, M, & Seminaroti, M. (2014). The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure. Operations Research Letters, available onlin(18 December 2014).