On a relaxed maximally disjoint path pair problem: a bicriteria approach

In some application areas in telecommunication and transportation networks, there are problems requiring the determination of pairs of paths, aiming at minimizing the number of links, or link groups that they share, and their total cost. In this paper, a new bicriteria algorithm is proposed to deal with this problem. The algorithm is based on ranking pairs of paths by order of the total cost, using an adaptation of a path-ranking algorithm, after a suitable modification of the network topology. Nondominated solutions are then filtered by means of a dominance test. First, computational experiments are reported in order to assess the efficiency of the algorithm to calculate the whole set of nondominated pairs of paths. Second, we present computational results focused on the nondominated solutions close to the maximal disjoint pair (i.e., quasi-disjoint pairs only, for a predefined admissible relaxation value) because in some application problems, such as shared risk link group pairs of paths, only those solutions have practical relevance.