An Unified Approach to Find an Optimal Parameterized Path in a Digraph with Multiple Features
Résumé
This paper is devoted to a class of problems which are modeled by a digraph, and such that each arc is characterized by several weights which depend on a parameter. This parameter takes its values in a set which characterizes the arc. The goal is to find a so-called parameterized path (i.e; a path and the values of the parameters corresponding to its arcs) that optimizes a criterion which is a combination of the weights of the arcs. The problem is introduced using transportation, communication and manufacturing problems. An unified formulation is provided, as well as an algorithm. A numerical example is proposed to illustrate this algorithm.