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Solving the edge-disjoint paths problem using a two-stage method

There exists a wide variety of network problems where several connection requests occur simultaneously. In general, each request is attended by finding a route in the network, where the origin and destination of such a route are those hosts that wish to establish a connection for information exchange. As it is well documented in the related literature, the exchange of information through disjoint routes increases the effective bandwidth, velocity, and the probability of receiving the corresponding information. The definition of disjoint paths may refer to nodes, edges, or both. As far as we know, the most studied variant is the one where disjointness implies not to share edges. This optimization problem is usually known as the maximum edge-disjoint paths (EDP) problem. This NP-hard optimization problem has applications in real-time communications, VLSI-design, scheduling, bin packing, or load balancing. The proposed approach hybridizes an Integer Linear Programming formulation of the problem with an Evolutionary Algorithm. Empirical results using 174 previously reported instances show that the proposed procedure compares favorably to previous metaheuristics for this problem. We finally confirm the significance of the results by conducting non-parametric statistical tests.