Cost-Optimal Time-dEpendent Routing with Time and Speed Constraints in Directed Acyclic Road Networks

Travel costs on road networks always change over time which implies road networks are time dependent. Most studies on time-dependent road networks simply find the shortest path with the least travel time without considering waiting at some nodes, or fuel consumption and toll fee. In real-world applications or computer games, waiting may be allowed at some nodes but disallowed at other nodes; a user can traverse an edge at different speeds; monetary travel cost contains fuel cost and toll fees; and users usually prefer the minimum-cost route under time and speed constraints. Therefore, we study Cost-Optimal Time-dEpendent Routing (COTER) problem with time and speed constraints. We utilize two fuel consumption models and compute the minimum fuel consumption with given travel time for highway edges via nonlinear optimization. We allow the toll fee function to be an arbitrary single-valued time-dependent function. We define an Optimal Cost (OC) function for each candidate node ni, and derive the recurrence relation formula between ni’s incoming neighbors’ OC-functions and ni’s OC-functions. To solve COTER, we propose a five-step algorithm, namely, ALG-COTER, which uses Fibonacci-heap optimized Dijkstra, topological sorting, dynamic programming, binary min-heap optimization, nonlinear optimization, and backtracking algorithms. Experimental results on three real-world road networks of different sizes demonstrate that our algorithm finds the optimal route efficiently and is scalable to different parameters.