A comparison of solution strategies for biobjective shortest path problems

We consider the biobjective shortest path (BSP) problem as the natural extension of the single-objective shortest path problem. BSP problems arise in various applications where networks usually consist of large numbers of nodes and arcs. Since obtaining the set of efficient solutions to a BSP problem is more difficult (i.e. NP-hard and intractable) than solving the corresponding single-objective problem there is a need for fast solution techniques. Our aim is to compare different strategies for solving the BSP problem. We consider a standard label correcting and label setting method, a purely enumerative near shortest path approach, and the two phase method, investigating different approaches to solving problems arising in phases 1 and 2. In particular, we investigate the two phase method with ranking in phase 2. In order to compare the different approaches, we investigate their performance on three different types of networks. We employ grid networks and random networks, as is generally done in the literature. Furthermore, road networks are utilized to compare performance on networks with a structure that is more likely to actually arise in applications.

[1]  Anthony Przybylski,et al.  Two phase algorithms for the bi-objective assignment problem , 2008, Eur. J. Oper. Res..

[2]  H. W. Corley,et al.  Shortest paths in networks with vector weights , 1985 .

[3]  Dimitri P. Bertsekas,et al.  Network optimization : continuous and discrete models , 1998 .

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

[5]  Daniel Vanderpooten,et al.  Enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite , 2002, Eur. J. Oper. Res..

[6]  F. Benjamin Zhan,et al.  Shortest Path Algorithms: An Evaluation Using Real Road Networks , 1998, Transp. Sci..

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

[8]  W. Matthew Carlyle,et al.  Near-shortest and K-shortest simple paths , 2005 .

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

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

[11]  Xavier Gandibleux,et al.  Multiobjective Combinatorial Optimization — Theory, Methodology, and Applications , 2003 .

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

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

[14]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[15]  J. Y. Yen.  An algorithm for finding shortest routes from all source nodes to a given destination in general networks , 1970 .

[16]  William H. Cunningham,et al.  A network simplex method , 1976, Math. Program..

[17]  T. N. Janakiraman,et al.  New polynomial time algorithms to compute a set of Pareto optimal paths for multi-objective shortest path problems , 2005, Int. J. Comput. Math..

[18]  Andrew V. Goldberg,et al.  Shortest paths algorithms: Theory and experimental evaluation , 1994, SODA '94.

[19]  Roger Hartley.  Vector Optimal Routing by Dynamic Programming , 1985 .

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

[21]  Karsten Weihe,et al.  On the cardinality of the Pareto set in bicriteria shortest path problems , 2006, Ann. Oper. Res..

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

[23]  M. I. Henig.  The shortest path problem with two objective functions , 1986 .

[24]  Paola Festa,et al.  Shortest Path Algorithms , 2006, Handbook of Optimization in Telecommunications.

[25]  R. Helgason,et al.  Chapter 2 Primal simplex algorithms for minimum cost network flows , 1995 .

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

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

[28]  C. T. Tung,et al.  A multicriteria Pareto-optimal path algorithm , 1992 .

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

[30]  S. Pallottino,et al.  Shortest Path Algorithms in Transportation models: classical and innovative aspects , 1997 .