Models and heuristics for a minimum arborescence problem

Networks

Volumn 51, Issue 1, 2008, Pages 34-47

  Duhamel, Christophe ^a   Gouveia, Luis ^b   Moura, Pedro ^b   Souza, Mauricio ^c  

^a CNRS   (France)

^b UNIVERSITY OF LISBON   (Portugal)

^c FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Arborescence; Connectivity constraints; Lagrangean relaxation; Local search; Reformulation; Steiner tree

Indexed keywords

GRAPH THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING; SEARCH ENGINES;

ARBORESCENCE; CONNECTIVITY CONSTRAINTS; LAGRANGEAN RELAXATION; LOCAL SEARCH; STEINER TREE;

HEURISTIC METHODS;

EID: 38149127181     PISSN: 00283045     EISSN: 10970037     Source Type: Journal    
DOI: 10.1002/net.20194     Document Type: Article

References (24)

1. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin, Network flows: theory, algorithms, and applications, Prentice Hall, New Jersey, 1993.
2. J. Beasley, An algorithm for the Steiner problem in graphs, Networks 14(1984), 147-159.
3. J. Beasley and N. Christofides, An algorithm for the resource constrained shortest path problem, Networks 19 (1989), 379-394.
4. C. Blum and M. Blesa, New metaheuristic approaches for the edge-weighted K-cardinality tree problem, Comput Oper Res 32 (2005), 1355-1377.
5. B.V. Cherkassky and A.V. Goldberg, Negative-cycle detection algorithms, Mathematical Programming 85 (1999), 277-311.
6. T. Crainic, A. Frangioni, and B. Gendron, Bundle-based relaxation methods for multicommodity capacitated fixed charge network design problems, Disc Appl Math 112 (2001 ), 73-99.
7. K.A. Dowsland, Hill-climbing, simulated annealing and the Steiner problem in graphs. Eng Optim 17 (1991), 91-107.
8. J. Edmonds, Optimum branchings, J Res Nat Bur Stand B71 (1967), 233-240.
9. S. Engevall, M. Gothe-Lundgren, and P. Varbrand, A strong lower bound for the node weighted Steiner tree problem, Networks 31 (1998), 11-17.
10. M. Fischetti, H. Hamacher, K. Jornsten, and F. Maffioli, Weighted k-cardinality trees: complexity and polyhedral study, Networks 24 (1994), 11-21.
11. G. Gallo and S. Pallottino, Shortest path algorithms, Ann Oper Res 13 (1988), 3-79.
12. B. Gendron, T. Crainic, and A. Frangioni, "Multicommodity capacitated network design," Telecommunications network planning, B. Sansò and P. Soriano (Editors), Kluwer Academic Publishers, Dordrecht, 1999, pp. 1-20.
13. A. Geoffrion, Lagrangean relaxation for integer programming, Math Prog Study 2 (1974), 82-114.
14. M. Goemans, Arborescence polytopes for series-parallel graphs, Disc Appl Math 51 (1994), 277-289.
15. L. Gouveia and E. Janssen, Designing reliable tree networks with two cable technologies, Eur J Oper Res 105 (1998), 552-568.
16. L. Gouveia and C. Requejo, A new lagrangean relaxation approach for the hop-constrained minimum spanning tree problem, Eur J Oper Res 132 (2001), 539-552.
17. M. Held, P. Wolfe, and H. Crowder, Validation of subgradient optimization, Math Prog 6 (1974), 62-88.
18. K. Holmberg and D. Yuan, A lagrangean heuristic based branch-and-bound approach for the capacitated network design problem, Oper Res 48 (2000), 461-481.
19. N. Maculan, A new linear programming formulation for the shortest s-directed spanning tree problem, J Combinator Infor Syst Sci 11 (1986), 53-56.
20. T. Magnanti and L. Wolsey, "Optimal trees," Network models, Handbooks in Operations Research and Management Science, M.O. Ball, T.L. Magnanti, C.L. Monma, and G.L. Nemhauser (Editors), vol. 7, Elsevier, Amsterdam, 1996, pp. 503-615.
21. A.B. Philpott and N. Wormald, On the optimal extraction of ore from an open-cast mine, School of Engineering Report 596, Auckland University, 1995, New Zealand.
22. V.V. Rao and R. Sridharan, Minimum-weight rooted notnecessarily-spanning arborescence problem, Networks 39 (2002), 77-87.
23. A. Segev, The node-weighted Steiner tree problem, Networks 17(1987), 1-17.
24. R.E. Tarjan, Finding optimum branchings, Networks 7 (1977), 25-35.