A Primal-Dual Approach for Large Scale Integer Problems

This paper presents a refined approach to using column generation to solve specific type of large integer problems. A primal-dual approach is presented to solve the Restricted Master problem belonging to the original optimization task. Firstly, this approach allows a faster convergence to the optimum of the LP relaxation of the problem. Secondly, the existence of both an upper and lower bound of the LP optimum at each iteration allows a faster searching of the Branch-and-Bound tree. To achieve this an early termination approach is presented. The technique is demonstrated on the Generalized Assignment problem and Parallel Machine Scheduling problem as two reference applications