Speeding up Martins’ algorithm for multiple objective shortest path problems

The latest transportation systems require the best routes in a large network with respect to multiple objectives simultaneously to be calculated in a very short time. The label setting algorithm of Martins efficiently finds this set of Pareto optimal paths, but sometimes tends to be slow, especially for large networks such as transportation networks. In this article we investigate a number of speedup measures, resulting in new algorithms. It is shown that the calculation time to find the Pareto optimal set can be reduced considerably. Moreover, it is mathematically proven that these algorithms still produce the Pareto optimal set of paths.

[1]  Paolo Serafini,et al.  Some Considerations about Computational Complexity for Multi Objective Combinatorial Problems , 1987 .

[2]  E. Martins,et al.  An algorithm for the ranking of shortest paths , 1993 .

[3]  Marta M. B. Pascoal,et al.  On algorithms for the tricriteria shortest path problem with two bottleneck objective functions , 2010, Comput. Oper. Res..

[4]  D. Shier,et al.  An empirical investigation of some bicriterion shortest path algorithms , 1989 .

[5]  R. Musmanno,et al.  Label Correcting Methods to Solve Multicriteria Shortest Path Problems , 2001 .

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

[7]  T. Lindvall.  ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

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

[9]  Xavier Gandibleux,et al.  Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys , 2013 .

[10]  E. Martins.  An algorithm for ranking paths that may contain cycles , 1984 .

[11]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[12]  Eric Ruppert.  Finding the k Shortest Paths in Parallel , 1997, STACS.

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

[14]  Jose Luis Esteves dos Santos,et al.  A new ranking path algorithm for the multi-objective shortest path problem , 2008 .

[15]  Stefano Giordano,et al.  A survey on multi-constrained optimal path computation: Exact and approximate algorithms , 2010, Comput. Networks.

[16]  Claudio T. Bornstein,et al.  Multiobjective combinatorial optimization problems with a cost and several bottleneck objective functions: An algorithm with reoptimization , 2012, Comput. Oper. Res..

[17]  Andrea Raith.  Speed-up of Labelling Algorithms for Biobjective Shortest Path Problems , 2010 .

[18]  T. A. J. Nicholson,et al.  Finding the Shortest Route between Two Points in a Network , 1966, Comput. J..

[19]  Claudio T. Bornstein,et al.  The tricriterion shortest path problem with at least two bottleneck objective functions , 2009, Eur. J. Oper. Res..

[20]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[21]  Andrés Marzal,et al.  Computing the K Shortest Paths: A New Algorithm and an Experimental Comparison , 1999, WAE.

[22]  J. M. Paixão,et al.  Labeling Methods for the General Case of the Multi-objective Shortest Path Problem – A Computational Study , 2013 .

[23]  J. Paixão,et al.  LABELLING METHODS FOR THE GENERAL CASE OF THE MULTI-OBJECTIVE SHORTEST PATH PROBLEMA COMPUTATIONAL STUDY , 2007 .

[24]  Laurence R. Rilett,et al.  Heuristic shortest path algorithms for transportation applications: State of the art , 2006, Comput. Oper. Res..

[25]  Chelsea C. White,et al.  Multiobjective A* , 1991, JACM.

[26]  João C. N. Clímaco,et al.  Multicriteria path and tree problems: discussion on exact algorithms and applications , 2012, Int. Trans. Oper. Res..

[27]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[28]  Gerrit K. Janssens,et al.  Evolutionary Algorithms for the Multiobjective Shortest Path Problem , 2007 .

[29]  Kim Allan Andersen,et al.  A label correcting approach for solving bicriterion shortest-path problems , 2000, Comput. Oper. Res..

[30]  Ernesto de Queirós Vieira Martins,et al.  Ranking multiobjective shortest paths , 2007 .

[31]  Xavier Gandibleux,et al.  Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function , 2006, 4OR.

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

[33]  Haim Kaplan,et al.  Reach for A*: Efficient Point-to-Point Shortest Path Algorithms , 2006, ALENEX.

[34]  Marta M. B. Pascoal,et al.  Deviation Algorithms for Ranking Shortest Paths , 1999, Int. J. Found. Comput. Sci..

[35]  Piet Demeester,et al.  Multimodal transport planning in a dynamic environment , 2008 .

[36]  E. Martins,et al.  A bicriterion shortest path algorithm , 1982 .

[37]  T. N. Janakiraman,et al.  New Algorithms For Multi Objective Shortest Path Problem , 2003 .

[38]  Ernesto de Queirós Vieira Martins,et al.  A new improvement for a K shortest paths algorithm , 2001 .

[39]  Marta M. B. Pascoal,et al.  Labeling Algorithms For Ranking Shortest Paths , 1999 .

[40]  Andrés Marzal,et al.  A Lazy Version of Eppstein's K Shortest Paths Algorithm , 2003, WEA.

[41]  Johannes Jahn,et al.  Recent Advances and Historical Development of Vector Optimization , 1987 .

[42]  Yann Disser,et al.  Multi-criteria Shortest Paths in Time-Dependent Train Networks , 2008, WEA.