Strategies For Iteratively Refining Layered Graph Models

We consider a framework for obtaining a sequence of converging primal and dual bounds based on mixed integer linear programming formulations on layered graphs. The proposed iterative algorithm avoids the typically rather large size of the full layered graph by approximating it incrementally. We focus in particular on this refinement step that extends the graph in each iteration. Novel path-based approaches are compared to existing variants from the literature. Experiments on two benchmark problems the traveling salesman problem with time windows and the rooted distance-constrained minimum spanning tree problem show the effectiveness of our new strategies. More-over, we investigate the impact of a strong heuristic component within the algorithm, both for improving convergence speed and for improving the potential of an employed reduced cost fixing step.