Protected shortest path visiting specified nodes

In this paper heuristics are proposed for finding the shortest loopless path, from a source node to a target node, that visits a given set of nodes in a directed graph, such that it can be protected using a node-disjoint path. This type of problem may arise due to network management constraints. The problem of calculating the shortest path that visits a given set of nodes is at least as difficult as the traveling salesman problem, and it has not received much attention. Nevertheless an efficient integer linear programming (ILP) formulation has been recently proposed for this problem. Here, the ILP formulation is adapted to include the constraint that the obtained path will be able to be protected by a node-disjoint path. Computational experiments show that this approach, namely in large networks, may fail to obtain a solution in a reasonable amount of time. Therefore three versions of a heuristic are proposed, for which extensive computational results show that they are able to find a solution in most cases, and that the calculated solutions present an acceptable relative error regarding the cost of the optimal active path. Further the CPU time required by the heuristics is significantly smaller than the required by the used ILP solver.