An efficient branch-and-bound algorithm for the one-to-many shortest path problem with additional disjunctive conflict constraints

In this work we study an extension of the ordinary one-to-many shortest path problem that also considers additional disjunctive conflict relations between the arcs: an optimal shortest path tree is not allowed to include any conflicting arc pair. As is the case with many polynomially solvable combinatorial optimization problems, the addition of conflict relations makes the problem $\mathrm{NP}$-hard. We propose a novel branch-and-bound algorithm, which benefits from the solution of the one-to-many shortest path relaxations, an efficient primal–dual reoptimization scheme and a fast infeasibility detection procedure for pruning the branch-and-bound tree. According to the extensive computational tests it is possible to say that the novel algorithm is very efficient.