Calculating the Best Dual Bound for Problems with Multiple Lagrangian Relaxations

Abstract

There are often many ways in which a given problem can be relaxed in a Lagrangian fashion. It is not obvious a priori, which relaxation produces the best bound. Moreover, a bound may appear to be the best for a certain data set, while being among the worst for another problem instance. We consider here an optimization problem over the set of Lagrangian relaxations with the objective to indicate the relaxation producing the best dual bound. An iterative technique to solve this problem is proposed based on constraints generation scheme. The approach is illustrated by a computational study for a class of the two-stage capacitated facility location problem.