Formulations and algorithms for the multi-path selection problem in network routing

Traffic bifurcation over multiple paths may be used to balance load on telecommunication networks. This balancing of load not only improves resilience against link failures but also provides an indication of the margin available for growth in demand values. In this paper, we present a novel mixed integer programming formulation for minimization of maximum link utilization in the case of link failure. The new formulation is much more compact than a previously proposed formulation. Additionally, we propose a local search heuristic with exact neighborhood search to tackle larger problems within reasonable computational time. The empirical examination on several test problems demonstrates that, with the new compact problem formulation, CPLEX is able to find solutions much quicker. The heuristic works well and in several cases yields better solutions than ILP in a given time limit, or provides solutions for problems where ILP could not even find one valid solution in the given time limit. In cases where ILP is able to find the optimal solution, the heuristic algorithm obtains the same solution usually in less time.