Route Planning with Flexible Objective Functions

We present the first fast route planning algorithm that answers shortest paths queries for a customizable linear combination of two different metrics, e. g. travel time and energy cost, on large scale road networks. The precomputation receives as input a directed graph, two edge weight functions t(e) and c(e), and a discrete interval [L, U]. The resulting flexible query algorithm finds for a parameter p ∈ [L, U] an exact shortest path for the edge weight t(e)+p·c(e). This allows for different tradeoffs between the two edge weight functions at query time. We apply precomputation based on node contraction, which adds all necessary shortcuts for any parameter choice efficiently. To improve the node ordering, we developed the new concept of gradual parameter interval splitting. Additionally, we improve performance by combining node contraction and a goal-directed technique in our flexible scenario.

[1]  E. Martins.  On a multicriteria shortest path problem , 1984 .

[2]  Peter Sanders,et al.  Fast Routing in Road Networks with Transit Nodes , 2007, Science.

[3]  Karsten Weihe,et al.  Pareto Shortest Paths is Often Feasible in Practice , 2001, WAE.

[4]  Peter Sanders,et al.  Engineering Route Planning Algorithms , 2009, Algorithmics of Large and Complex Networks.

[5]  Peter Sanders,et al.  Dynamic Highway-Node Routing , 2007, WEA.

[6]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[7]  Guy E. Blelloch,et al.  Compact representations of separable graphs , 2003, SODA '03.

[8]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[9]  Peter Sanders,et al.  Contraction Hierarchies: Faster and Simpler Hierarchical Routing in Road Networks , 2008, WEA.

[10]  Dorothea Wagner,et al.  Pareto Paths with SHARC , 2009, SEA.

[11]  Daniel Delling,et al.  SHARC: Fast and robust unidirectional routing , 2008, JEAL.

[12]  Dorothea Wagner,et al.  Partitioning graphs to speedup Dijkstra's algorithm , 2007, ACM J. Exp. Algorithmics.

[13]  Mark Ziegelmann.  Constrained shortest paths and related problems , 2001 .

[14]  Rolf H. Möhring,et al.  Verteilte Verbindungssuche im öffentlichen Personenverkehr Graphentheoretische Modelle und Algorithmen , 1999, Angewandte Mathematik, insbesondere Informatik.

[15]  Peter Sanders,et al.  Time Dependent Contraction Hierarchies -- Basic Algorithmic Ideas , 2008, ArXiv.

[16]  Andrew V. Goldberg,et al.  Computing the shortest path: A search meets graph theory , 2005, SODA '05.

[17]  Peter Sanders,et al.  Highway Hierarchies Hasten Exact Shortest Path Queries , 2005, ESA.

[18]  Hiroshi Imai,et al.  A fast algorithm for finding better routes by AI search techniques , 1994, Proceedings of VNIS'94 - 1994 Vehicle Navigation and Information Systems Conference.

[19]  Robert E. Tarjan,et al.  Faster parametric shortest path and minimum-balance algorithms , 1991, Networks.

[20]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[21]  Dorothea Wagner,et al.  Time-Dependent Route Planning , 2009, Encyclopedia of GIS.

[22]  Christian Vetter,et al.  Parallel Time-Dependent Contraction Hierarchies , 2009 .

[23]  Kurt Mehlhorn,et al.  Algorithms and data structures , 1984 .

[24]  Daniel Delling,et al.  Engineering and Augmenting Route Planning Algorithms , 2009 .

[25]  Andrew V. Goldberg,et al.  Computing Point-to-Point Shortest Paths from External Memory , 2005, ALENEX/ANALCO.

[26]  Dominik Schultes,et al.  Route Planning in Road Networks , 2008 .

[27]  Peter Sanders,et al.  Combining hierarchical and goal-directed speed-up techniques for dijkstra's algorithm , 2008, JEAL.

[28]  Peter Sanders,et al.  Engineering Fast Route Planning Algorithms , 2007, WEA.

[29]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[30]  Matthias Ehrgott,et al.  A comparison of solution strategies for biobjective shortest path problems , 2009, Comput. Oper. Res..

[31]  Haim Kaplan,et al.  Better Landmarks Within Reach , 2007, WEA.

[32]  Anna Sciomachen,et al.  A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks , 1998, Eur. J. Oper. Res..

[33]  Richard M. Karp,et al.  Parametric shortest path algorithms with an application to cyclic staffing , 1981, Discret. Appl. Math..

[34]  Robert L. Smith,et al.  Fastest Paths in Time-dependent Networks for Intelligent Vehicle-Highway Systems Application , 1993, J. Intell. Transp. Syst..

[35]  Rolf H. Möhring,et al.  Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems , 2009, Robust and Online Large-Scale Optimization.

[36]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..