Towards Pareto-optimality with Multi-level Bi-objective Routing: A Summary of Results

Given an origin, a destination, and a directed graph in which each edge is associated with a pair of non-negative costs, the bi-objective routing problem aims to find the set of all Pareto-optimal paths. This problem is societally important due to several applications, such as route finding that considers both vehicle travel time and energy consumption. The problem is challenging due to the potentially large number of candidate Pareto-optimal paths to be enumerated during the search, making existing compute-on-demand methods inefficient due to their high time complexity. One way forward is the introduction of precomputation algorithms. However, the large size of the Pareto-optimal set makes it infeasible to precompute and store all-pair solutions. In addition, generalizing traditional single-objective hierarchical algorithms to bi-objective cases is nontrivial because of the non-comparability of candidate paths and the need to accommodate multiple Pareto-optimal paths for each node pair. To overcome these limitations, we propose Multi-Level Bi-Objective Routing (MBOR) algorithms using three novel ideas: boundary multigraph representation, Pareto frontier encoding, and two-dimensional cost-interval based pruning. Computational experiments using real road network data demonstrate that the proposed methods significantly outperform baseline methods in terms of online runtime and precomputation time.