A biobjective Dijkstra algorithm

Abstract We generalize the Dijkstra algorithm to the Biobjective Shortest Path (BSP) problem. The proposed method keeps only one candidate label per node in a priority queue of size n. In this way, we introduce a novel algorithm to solve the one-to-all BSP problem determining all non-dominated points in the outcome space and one efficient path associated with each of them. For the case of the one-to-one BSP problem, we incorporate the classical bidirectional search scheme in the proposed algorithm to reduce the number of iterations in practice. The proposed algorithm also includes pruning strategies to avoid the computation of unnecessary labels. The result is a fast algorithm to solve the one-to-one BSP problem in large networks. A computational experiment comparing the performance of the proposed method and the state-of-the-art methods is included.

[1]  I. Murthy,et al.  A parametric approach to solving bicriterion shortest path problems , 1991 .

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

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

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

[5]  Piet Demeester,et al.  Speeding up Martins’ algorithm for multiple objective shortest path problems , 2013, 4OR.

[6]  Wilco van den Heuvel,et al.  Analysis of FPTASes for the multi-objective shortest path problem , 2016, Comput. Oper. Res..

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

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

[9]  Lawrence Mandow,et al.  Multiobjective heuristic search in road maps , 2012, Expert Syst. Appl..

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

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

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

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

[14]  José Rui Figueira,et al.  Solving bicriteria 0-1 knapsack problems using a labeling algorithm , 2003, Comput. Oper. Res..

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

[16]  Andrea Raith,et al.  A Dijkstra-like method computing all extreme supported non-dominated solutions of the biobjective shortest path problem , 2015, Comput. Oper. Res..

[17]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1987, JACM.

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

[19]  Andrés L. Medaglia,et al.  An exact method for the biobjective shortest path problem for large-scale road networks , 2015, Eur. J. Oper. Res..