# Arc Routing with Time-Dependent Travel Times and Paths

arXiv: https://arxiv.org/abs/2004.14473 · HTML: https://mlsanity.com/paper/2004.14473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [KAYROS: An Anytime and Exact Open-Source Solver for Duration-Minimization Time-Dependent Vehicle Routing. A Technical Report and a Case Study in Human-AI Engineering](https://mlsanity.com/paper/2607.23116/) (2026)

## Abstract (arXiv)

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, as well as heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules and completion bounds to find optimal solutions for problem counting up to 75 services. Based on these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.