Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm

The bin packing problem with conflicts consists in packing items in a minimum number of bins of limited capacity while avoiding joint assignments of items that are in conflict. Our study demonstrates the comparatively good performance of a generic Branch-and-Price algorithm for this problem. We made use of our black-box solver BaPCod, relying on its generic branching scheme and primal heuristics, while developing a specific pricing oracle. For the case where the conflict graph is an interval graph, we developed a dynamic programming algorithm for pricing, while for the general case, we implemented a depth-first-search branch-and-bound approach. The algorithm is tested on instances from the literature where the conflict graph is an interval graph, as well as on newly generated instances with an arbitrarily conflict graph. The computational results show that our generic algorithm outperforms special purpose algorithms of the literature, closing all open instances in one hour of CPU time.