Scenic Routes Now: Efficiently Solving the Time-Dependent Arc Orienteering Problem

Due to the availability of large transportation (e.g., road network sensor data) and transportation-related (e.g., pollution, crime) data as well as the ubiquity of car navigation systems, recent route planning techniques need to optimize for multiple criteria (e.g., travel time or distance, utility/value such as safety or attractiveness). In this paper, we introduce a novel problem called Twofold Time-Dependent Arc Orienteering Problem (2TD-AOP), which seeks to find a path from a source to a destination maximizing an accumulated value (e.g., attractiveness of the path) while not exceeding a cost budget (e.g., total travel time). 2TD-AOP has many applications in spatial crowdsourcing, real-time delivery, and online navigation systems (e.g., safest path, most scenic path). Although 2TD-AOP can be framed as a variant of AOP, existing AOP approaches cannot solve 2TD-AOP accurately as they assume that travel-times and values of network edges are constant. However, in real-world the travel-times and values are time-dependent, where the actual travel time and utility of an edge depend on the arrival time to the edge. We first discuss the practicality of this novel problem by demonstrating the benefits of considering time-dependency, empirically. Subsequently, we show that optimal solutions are infeasible (NP-hard) and solutions to the static problem are often invalid (i.e., exceed the cost budget). Therefore, we propose an efficient approximate solution with spatial pruning techniques, optimized for fast response systems. Experiments on a large-scale, fine-grained, real-world road network demonstrate that our approach always produces valid paths, is orders of magnitude faster than any optimal solution with acceptable accumulated value.