Continuous and Discrete Time Label Setting Algorithms for the Time Dependent Bi-Criteria Shortest Path Problem

In this paper we address the bi-criteria shortest path problem in a network with timedependent cost functions, a travel time constraint and zero waiting time at nodes. We propose a discrete time forward label setting algorithm which outperforms other approaches in the literature. We also propose a second, more general, forward label setting algorithm that can handle both discrete and continuous travel time functions. A speeding up technique for the proposed algorithms is also provided. The algorithms are compared with a backward algorithm, the best so far algorithm in the literature that solves the problem at hand and the experimental results confirm the higher efficiency of the proposed algorithms.