Multi-Cost Optimal Route Planning Under Time-Varying Uncertainty Bin Yang 1 , Chenjuan Guo 1 , Christian S. Jensen 1 , Manohar Kaul 1 , Shuo Shang 2 1 Department of Computer Science, Aarhus University, Denmark 2 Department of Computer Science, Aalborg University, Denmark {byang, cguo, csj, mkaul}@cs.au.dk, sshang@cs.aau.dk Abstract— Different uses of a road network call for the consideration of different travel costs: in route planning, travel time and distance are typically considered, and green house gas (GHG) emissions are increasingly being considered. Further, costs such as travel time and GHG emissions are time-dependent and uncertain. To support such uses, we propose techniques that enable the construction of a multi-cost, time-dependent, uncertain graph (MTUG) model of a road network based on GPS data from vehicles that traversed the road network. Based on the MTUG, we define optimal routes that consider multiple costs and time- dependent uncertainty, and we propose efficient algorithms to retrieve optimal routes for a given source-destination pair and a start time. Empirical studies with three road networks in Denmark and a substantial GPS data set offer insight into the design properties of the MTUG and the efficiency of the optimal route algorithms. I. I NTRODUCTION Reduction in green house gas (GHG) emissions from trans- portation is crucial in combating global warming. For example, in the EU, emissions from transportation account for nearly a quarter of all GHG emissions, and the EU has committed to reduce emissions to 20% below the 1990 levels by 2020. To achieve politically agreed-upon reductions, and due to an increasing public awareness of environmental protection, fleet owners and individual drivers increasingly perform eco- routing [1], taking into account GHG emissions, in addition to travel time and distance, when planing routes. Eco-routing calls for solutions that contend with three challenging charac- teristics. Multiple Costs: Multiple travel costs, e.g., travel times, distances, and GHG emissions, need to be considered. A recent study [2] suggests that neither the shortest nor the fastest routes generally have the lowest GHG emissions. GHG emissions are highly related to instantaneous velocities and accelerations [1] and are only loosely correlated with travel times and distances. Thus, eco-routing algorithms must be able to return optimal routes that consider multiple, loosely- correlated costs. Time Dependence: Travel costs such as travel times and GHG emissions are time-dependent. For example, traversing a road during peak hours may take much longer than that during off-peak hours. Further, different roads have different traffic behaviors, with some roads having clear peak and off- peak hours and some roads exhibiting nearly constant travel times. Thus, to support eco-routing, time dependence must be modeled appropriately and must be considered by routing algorithms. Uncertainty: Some travel costs are inherently uncertain. For example, given the same road, aggressive driving may generate more GHG emissions (but shorter travel time) than does moderate driving. The resulting uncertainty may vary across time. For instance, during peak hours, the uncertainty of travel costs may be low because congestion forces drivers to drive similarly, while during off-peak hours, drivers have more freedom to drive fast or slow, thus increasing the travel cost uncertainty. Effective routing algorithms must take into account time-varying uncertainty. We present techniques that enable the construction of a multi-cost, time-dependent and uncertain graph (MTUG) model of a road network that is capable of capturing mul- tiple time-varying and uncertain travel costs. Specifically, each cost on a road segment is modeled as a vector of (interval , random variable ) pairs. The proposed techniques build an MTUG from a massive collection of GPS data collected from vehicles traveling in the road network. Based on the MTUG, we define the cost of a route, a dominance relationship between routes based on their costs, and a natural notion of an optimal route for a given source- destination pair and a trip starting time. An optimal route is a “good” route with the property that no other route is better when considering all travel costs of interest. Finally, we propose efficient methods to retrieve optimal routes. While existing routing services and navigation devices offer alternative routes, they generally return routes based on a single criterion (e.g., based on distance) or routes satisfying some road type constraints (e.g., avoiding toll roads). None of these provide a set of routes that takes into account multiple travel costs, and they consider neither GHG emissions nor the combination of time-dependence and uncertainty. We extend existing routing functionality to support optimal routes that consider multiple, time-varying and uncertain travel costs. Optimal routes are of interest to both individual drivers and entities that control fleets of vehicles. For example, FlexDanmark 1 , a large public fleet coordinator in Denmark, is interested in using the most eco-friendly routes while considering travel times and distances. To the best of our knowledge, this paper is the first to 1 https://www.flexdanmark.dk/