An effective algorithm for obtaining the minimal cost pair of disjoint paths with dual arc costs

Routing optimisation in some types of networks requires the calculation of the minimal cost pair of disjoint paths such that the cost functions associated with the arcs in the two paths are different. An exact algorithm for solving this NP-complete problem is proposed, based on a condition which guarantees that the optimal path pair cost has been obtained. This optimality condition is based on the calculation of upper and lower bounds on the optimal cost. A formal proof of the correctness of the algorithm is described. Extensive experimentation is presented to show the effectiveness of the algorithm, including a comparison with an integer linear programming formulation.