Distributed Integral Column Generation for Set Partitioning Problems

Column generation (CG) is widely used to solve industrial optimization problems, namely vehicle and crew scheduling problems. This method becomes inefficient and takes huge time to reach an optimal solution for large instances due to degeneracy and the size of the branching tree. Often, finding an integer solution comes very late after several hours of calculation or even days for large crew pairing problems for instance, which is not appreciated in practice. In the present work, we propose a generic framework for distributed integral column generation (DICG) that can yield faster solutions for such problems. Computational tests show that DICG shows excellent results and outperforms DRMH, a distributed version of the well-known restricted master heuristic. DICG yields in minutes optimal or near optimal solutions for difficult instances DRMH cannot solve.