Solution to the quadratic assignment problem using semi-Lagrangian relaxation

The semi-Lagrangian relaxation (SLR), a new exact method for combinatorial optimization problems with equality constraints, is applied to the quadratic assignment problem (QAP). A dual ascent algorithm with finite convergence is developed for solving the semi-Lagrangian dual problem associated to the QAR. We perform computational experiments on 30 moderately difficult QAP instances by using the mixed integer programming solvers, Cplex, and SLR+Cplex, respectively. The numerical results not only further illustrate that the SLR and the developed dual ascent algorithm can be used to solve the QAP reasonably, but also disclose an interesting fact: comparing with solving the unreduced problem, the reduced oracle problem cannot be always effectively solved by using Cplex in terms of the CPU time.