The multiobjective optimal path problem

The multiobjective optimal path problem is viewed as the optimization of a function defined over a subset of paths between a pair of nodes and with values in ℝ^k (k > 1); an order relation is considered in ℝ^k which allows to determine a set of solutions – the nondominated paths. The generalization for ℝ^k of the optimal path problems is considered as well as some of its properties. The multiobjective shortest path problem is then presented and particularized for the biobjective case (k = 2), being emphasised the properties of the non dominance relation for this case. Some new algorithms for the resolution of the multiobjective shortest path problem are also presented, as well as computational results for k = 2.