The {MinSum}-{MinHop} and the {MaxMin}-{MinHop} Bicriteria Path Problems

The number of hops (or arcs) of a path is a frequent objective functionwith applications to problems where network resources utilization is to be minimized. In this chapter we solve bicriteria path problems involving this objective function and two other common metrics, the path cost and the path capacity. Labeling algorithms are introduced, which use a breadth-first search tree in order to compute the maximal and the minimal sets of non-dominated paths. Dominance rules are derived for the two bicriteria problems and the properties of this data structure are explored to better suit the number of hops objective function and thus simplify the labeling process. Computational experiments comparing the new methods with standard approaches on randomly generated test instances and on instances that simulate video traffic are presented and discussed. Results show a significant speed-up over generic standard methods.