Comparing branch-and-price algorithms for the Multi-Commodity k-splittable Maximum Flow Problem

The Multi-Commodity k-splittable Maximum Flow Problem consists in routing as much flow as possible through a capacitated network such that each commodity uses at most k paths and the capacities are satisfied. The problem appears in telecommunications, specifically when considering Multi-Protocol Label Switching. The problem has previously been solved to optimality through branch-and-price. In this paper we propose two exact solution methods both based on an alternative decomposition. The two methods differ in their branching strategy. The first method, which branches on forbidden edge sequences, shows some performance difficulty due to large search trees. The second method, which branches on forbidden and forced edge sequences, demonstrates much better performance. The latter also outperforms a leading exact solution method from the literature. Furthermore, a heuristic algorithm is presented. The heuristic is fast and yields good solution values.

► The Multi-Commodity k-splittable Max Flow Problem is solved using branch and price (bp). ► The problem is Dantzig–Wolfe decomposed in two different ways. ► A new branching strategy and corresponding bp-algorithm are proposed. ► The new algorithm outperforms the leading exact method from the literature. ► Terminating the algorithm in the root node yields very good results.