Best reduction of the quadratic semi-assignment problem Original Research Article

We consider the quadratic semi-assignment problem in which we minimize a quadratic pseudo-Boolean function F subject to the semi-assignment constraints. We propose in this paper a linear programming method to obtain the best reduction of this problem, i.e. to compute the greatest constant c such that F is equal to c plus F′ for all feasible solutions, F′ being a quadratic pseudo-Boolean function with nonnegative coefficients. Thus constant c can be viewed as a generalization of the height of an unconstrained quadratic 0–1 function introduced in (Hammer et al., Math. Program. 28 (1984) 121–155), to constrained quadratic 0–1 optimization. Finally, computational experiments proving the practical usefulness of this reduction are reported.