# Multicriteria Route Planning for In-Operation Mass Transit under Urban Data
## 2 Related Work
By replacing the precomputed shortest paths with single edges, the subset with shortcuts can be used to accelerate parts of the query [31; 32]. Next, for the path separator, the concept is to view a path as intermediary so as to compute distance between vertices. Explicitly, similar to the procedure of vertex separator, a subset of vertices whose removal could decompose the original graph into cells is first labelled. A rooted spanning tree is then defined by viewing the original graph as an undirected one, and three paths from the root triangle could be identified through planarity testing. Consequently, these three paths not only correspond to at most six directed paths in the original graph, but also separate the original graph into cells where each cell has a size no greater than half the original size [33; 34]. Despite variations in the setting of separators, some research focuses on the multimodal routing computation and adopts a multimodal separators-based algorithm by applying the time-dependent state automaton to achieve less runtime with tolerable inaccuracy [35]. Meanwhile, when dealing with multimodal route planning in urban space [36; 37], some emphasize the transportation network hierarchy with the intention of easing the time consumption. Its concept is to bypass the meticulous road network according to its hierarchy to accelerate. Precisely, the hierarchy is based on input-defined road categories, and only vertices of subnetwork are scanned given queried target far from source. However, there is also no guarantee that it will find the exact shortest paths [38; 39]. On the other hand, some focus on the contraction hierarchy; that is, the original network structure, is converged into a small arterial network by exploiting its inherent hierarchy. The proposed method suggests to heuristically order the vertices by importance from the least to the highest, and vertices are then repeatedly contracted and replaced by shortcuts in the original graph. Hence, a bidirectional search could be adopted to only visit arcs leading to vertices holding higher importance, where two frontiers of bidirectional search are supposed to meet at the highest-ranked vertex instead of the first vertex scanned by both sides [40]. Some adopt the concept of hop labelling, in which distances between pairs of vertices are precomputed as virtual shortcuts. Then, the shortest path of each pair of vertices is represented as two hops consisting of a path and a vertex that correspond to the origin or destination for the pair. By encoding the vertices that a certain vertex could go to and come from, one can identify a shortest path connecting a certain pair of vertices through the vertex kept in both subsets. As a consequence, by maximizing the coverage of hops on shortest path, the time consumption could be reduced [41; 42]. **Inference-then-Planning Framework for Constrained Route Planning**. A number of studies focus on an inference-then-planning framework, in which multicriteria route planning is conducted with heuristics or cost function, based on the estimated results of an inference model [43]. For instance, some deal with the constrained taxi-cruising problem based on predicting pick-up and drop-off locations with the profit and trust optimized [44], distributed competitive searching for parking slots that optimizes the drivers' searching experience with various preference towards time consumption and the resource utilization for social welfare based on limited accessibility to data for the parking slots' availability inference [45]. They use traffic penalty charges and the results of predicting parking infringements to plan a multidepot route that maximizes profit and minimizes time [46], or multicriteria route planning focusing on either waste collection [47] or emergency vehicles [48; 49] with relevant information estimation. To be more precise, with the rise of mobility systems in the urban space, several studies focus on the constrained taxi cruising problem.