Heuristic Branch-and-Price-and-Cut to Solve a Network Design Problem

We present a Heuristic Branch&Price&Cut (BPC) approach for a network design problem. This algorithm integrates several original features including: • a multi-commodity multi-capacity network design problem path based model, • a pricing scheme using pools of generators and promising columns, • cutting-planes applied to the path-based formulation to obtain better lower bounds, to make better heuristic decisions, and to prune a larger part of the tree, • several heuristics and search strategies for quicker primal solutions. The effectiveness of the algorithm is assessed on a large set of benchmarks based on real data. The computational results and comparisons with other well known techniques show that the algorithm is able to produce not only tight lower bounds, but also high quality heuristic solutions (upper bounds). The algorithm has been implemented using the Maestro BPC framework.