Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Best reduction of the quadratic semi-assignment problem
Discrete Applied Mathematics
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
QAPLIB – A Quadratic Assignment ProblemLibrary
Journal of Global Optimization
A dynamical systems approach to weighted graph matching
Automatica (Journal of IFAC)
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We present a cutting planes algorithm for the Quadratic Assignment Problem based upon a semidefinite relaxation, and we report experiments for classical instances. Our lower bound is compared with the ones obtained by linear and semidefinite approaches. Our tests show that the cuts we use (originally proposed for a linear approach) allow to improve significantly on the bounds obtained by the other approaches. Moreover, this is achieved within a moderate additional computing effort, and even in a shorter total time sometimes. Indeed, thanks to the strong tailing off effect of the SDP solver we have used (SB), we obtain in a reasonable time an approximate solution which is suitable to generate efficient cutting planes which speed up the convergence of SB.