A reference point approach for the resource constrained shortest path problems

Transportation Science

Volumn 47, Issue 2, 2013, Pages 247-265

  Di Puglia Pugliese, Luigi ^a   Guerriero, Francesca ^a  

^a UNIVERSITY OF CALABRIA   (Italy)

Author keywords

Constrained shortest paths; Interactive method; Label correcting method; Lower and upper bounds

Indexed keywords

BENCHMARKING;

COMPUTATIONAL RESULTS; CONSTRAINED SHORTEST PATH; INTERACTIVE METHODS; LABEL CORRECTING; LOWER AND UPPER BOUNDS; SCIENTIFIC LITERATURE; SHORTEST PATH PROBLEM; STATE-OF-THE-ART APPROACH;

GRAPH THEORY;

EID: 84877956755     PISSN: 00411655     EISSN: 15265447     Source Type: Journal    
DOI: 10.1287/trsc.1120.0418     Document Type: Article

References (53)

1. Aneja YP, Aggarwal V, Nair KPK (1983) Shortest chain subject to side constraints. Networks 13(2): 295-302.
2. Avella P, Boccia M, Sforza A (2004) Resource constrained shortest path problems in path planning for fleet management. J. Math. Model. Algorithms 3(1): 1-17.
3. Azevedo JA, Martins EQV (1991) An algorithm for the multiobjective shortest path problem on acyclic networks. Investigacao Oper. 11: 52-69.
4. Azevedo JA, Madeira J, Costa M, Martins EQV, Pires F (1994) A computational improvement for a shortest paths ranking algorithm. Eur. J. Oper. Res. 73(1): 188-191.
5. Barnhart C, Boland N, Clarke L, Johnson EL, Nemhauser GL, Shenoi RG (1998) Flight string models for aircraft fleeting and routing. Transportation Sci. 32(3): 208-220.
6. Beasley JE, Christofides N (1989) An algorithm for the resource constrained shortest path problem. Networks 19(4): 379-394.
7. Buchanan J, Gardiner L (2003) A comparison of two reference point methods in multiple objective mathematical programming. Eur. J. Oper. Res. 149(1): 17-34.
8. Carlyle WM, Royset JO, Wood RK (2008) Lagrangian relaxation and enumeration for solving constrained shortest-path problems. Networks 52(4): 256-270.
9. Carraway RL, Morin TL, Moskowitz H (1990) Generalized dynamic programming for multicriteria optimization. Eur. J. Oper. Res. 44(1): 95-104.
10. Climaco JCN, Martins EQV (1982) A bicriterion shortest path algorithm. Eur. J. Oper. Res. 11(4): 399-404.
11. Coutinho-Rodrigues JM, Climaco JCN, Current JR (1999) An interactive bi-objective shortest path approach: Searching for unsupported nondominated solutions. Comput. Oper. Res. 26(8): 789-798.
12. Desrochers M, Soumis F (1988) A generalized permanent labeling algorithm for the shortest path problem with time windows. INFOR: Inform. Systems Oper. Res. 26: 191-212.
13. Desrosiers J, Pelletier P, Soumis F (1983) Plus court chemin avec constraints d'horaires. RAIRO. Recherche op Oerationnelle 17: 357-377.
14. Dumitrescu I, Boland N (2003) Improved preprocessing, labeling and scaling algorithms for the weight-constrained shortest path problem. Networks 42(3): 135-153.
15. Elimam A, Kohler D (1997) Two engineering applications of a constrained shortest path model. Eur. J. Oper. Res. 103(3): 426-438.
16. Espinoza D, Garcia R, Goycoolea M, Nemhauser GL, Savelsbergh MWP (2008) Per-seat, on-demand air transportation part I: Problem description and an integer multicommodity flow model. Transportation Sci. 42(3): 263-278.
17. Garey MR, Johnson DS (1979) Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco).
18. Granat J, Guerriero F (2003) The interactive analysis of the multicriteria shortest path problem by the reference point method. Eur. J. Oper. Res. 151(1): 103-118.
19. Hallam C, Harrison KJ, Ward JA (2001) A multiobjective optimal path algorithm. Digital Signal Processing 11(2): 133-143.
20. Halpern J, Priess J (1974) Shortest paths with time constraints on moving and parking. Networks 4(3): 241-253.
21. Handler GY, Zang I (1980) A dual algorithm for the constrained shortest path problem. Networks 10(4): 293-309.
22. Hassin R (1992) Approximation schemes for the restricted shortest path problem. Math. Oper. Res. 17(1): 36-42.
23. Henig MI (1986) The domination property in multicriteria optimization. J. Math. Anal. Appl. 114(1): 7-16.
24. Jaffe JM (1984) Algorithms for finding paths with multiple constraints. Networks 14(1): 95-116.
25. Jaumard B, Semet F, Vovor T (1996) A two-phase resource constrained shortest path algorithm for acyclic graphs. Technical report G-96-48, Les Cahier du GERAD, Montréal.
26. Jimenez V, Marzal A (1999) Computing the k shortest paths: A new algorithm and an experimental comparison. Proc 3rd Workshop on Algorithm Engrg. (WAE99), Lecture Notes in Computer Science, 1668 (Springer-Verlag, Berlin, Heidelberg) 15-29.
27. Joksch HC (1966) The shortest route problem with constraints. J. Math. Anal. Appl. 14: 191-197.
28. Jüttner A (2006) Parametric in Combinatorial Optimization and Their Applications in Telecommunication. Unpublished doctoral thesis, Eövotös Loránd University, Faculty of Science, Budapest, Hungary.
29. Kelley JE (1960) The cutting plane method for solving convex programs. J. SIAM 8(4): 703-712.
30. Lawler EL (1976) Combinatorial Optimization: Networks and Matroids (Holt, Rinehart and Winston, New York).
31. Luque M, Mittinen K, Eskelinen P, Ruiz F (2009) Incorporating preference information in interactive reference point methods for multiobjective optimization. Omega 37(2): 450-462.
32. Martins EQV, Santos JLE (1997) An algorithm for the quickest path problem. Oper. Res. Lett. 20(4): 195-198.
33. Mehlhorn K, Ziegelmann M (2000) Resource constrained shortest paths. 7th Ann Eur. Symp Algorithms (ESA2000), Lecture Notes in Computer Science, 1879 (Springer-Verlag, Berlin, Heidelberg), 326-337.
34. Mirchandani PB, Wiecek MM (1993) Routing with nonlinear multiattribute cost functions. Appl. Math. Comput. 54(2-3): 215-239.
35. Modesti P, Sciomachen A (1998) A utility measure for finding multiobjective shortest paths in urban multimodal transportation networks. Eur. J. Oper. Res. 111(3): 495-508.
36. Mote I, Murthy I, Olson DL (1991) A parametric approach to solving bicriterion shortest path problems. Eur. J. Oper. Res. 53(1): 81-92.
37. Muhandiramge R, Boland N (2009) Simultaneous solution of Lagrangean dual problems interleaved with preprocessing for the weight constrained shortest path problem. Networks 53(4): 358-381.
38. Murthy I, Olson DL (1994) An interactive procedure using domination cones for bicriterion shortest path problems. Eur. J. Oper. Res. 72(2): 417-431.
39. Nygaard R (2000) Shortest Path Methods in Representation and Compression of Signals and Image Contours. Unpublished doctoral thesis, Norwegian University of Science and Technology, Trondheim.
40. Ogryczak W (2001) On goal programming formulations of the reference point method. J. Oper. Res. Soc. 52(6): 691-698.
41. Ribeiro C, Minoux M (1985) A heuristic approach to hard constrained shortest path problems. Discrete Appl. Math. 10(2): 125-137.
42. Romero C, Tamiz M, Jones DF (1998) Goal programming, compromise programming and reference point method formulations: Linkages and utility interpretations. J. Oper. Res. Soc. 49(9): 986-991.
43. Santos L, Coutinho-Rodrigues J, Current JR (2007) An improved solution algorithm for the constrained shortest path problem. Transportation Res. Part B 41(7): 756-771.
44. Skriver AJV, Andersen KA (2000) A label correcting approach for solving bicriterion shortest-path problems. Comput. Oper. Res. 27(6): 507-524.
45. Tung CT, Chew KT (1992) A multicriteria Pareto-optimal path algorithm. Eur. J. Oper. Res. 62(2): 203-209.
46. Warburton A (1987) Approximation of pareto optima in multiple objective shortest path problems. Oper. Res. 35(1): 70-79.
47. Wierzbicki A (1977) Basic properties of scalarizing functionals for multiobjective optimization. Mathematische Operationsforschung und Statistik, s. Optim. 8(1): 55-60.
48. Wierzbicki A, Makowski M, Wessels J (2000) Modelbased Decision Support Methodology with Environmental Applications (Kluwer Academic Publishers, Dordrecht, The Netherlands).
49. Xue G (2000) Primal-dual algorithms for computing weightconstrained shortest paths and weight-constrained minimum spanning trees. Proc. 19th IEEE Internat. Performance, Comput., Comm. Conf. (IPCCC), 271-277.
50. Yen JY (1971) Finding the k-shortest loopless paths in a network. Management Sci 17(11): 711-715.
51. Zabarankin M, Uryasev S, Pardalos P (2001) Optimal risk path algorithms. Murphey R, Pardalos P, eds. Cooperative Control, and Optimization (Kluwer, Dordrecht, The Netherlands), 271-303.
52. Ziegelmann M (2001) Constrained shortest paths and related problems. Unpublished doctoral thesis, Computer Science, Saarbücken, Germany.
53. Ziegelmann M (2007) Constrained Shortest Paths and Related Problems (VDM-Verlag, Saarbrücken, Germany).