The determination of the path with minimum-cost norm value

The multiobjective shortest path problem (MSPP) consists of finding the best nondominated path linking two specified nodes in a network where k > 1 different criteria are considered for the arc costs. Solving the MSPP implies determining all the nondominated paths; there may be many such paths, making the selection process a very hard task to accomplish. A traditional way of dealing with such a difficulty is using a utility function where the parameters are aggregated with different weights. In this work, an alternatve utility function based on the norm value associated with each path is considered. Two algorithms for solving the minimum-cost norm path problem are then proposed and some computational results are presented.