A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem

European Journal of Operational Research

Volumn 132, Issue 3, 2001, Pages 539-552

  Gouveia, Luís ^a   Requejo, Cristina ^b  

^a UNIVERSITY OF LISBON   (Portugal)

^b UNIVERSITY OF COIMBRA   (Portugal)

Author keywords

Design of centralized networks; Hop constraints; Lagrangean relaxation; Multicommodity flows; Quality of service constraints

Indexed keywords

BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; LAGRANGE MULTIPLIERS; LINEAR PROGRAMMING; PROBLEM SOLVING; QUALITY OF SERVICE; RELAXATION PROCESSES;

HOP CONSTRAINTS; HOP-INDEXED FLOWS; LAGRANGEAN RELAXATION METHOD; MULTICOMMODITY FLOWS; STEINER TREE;

OPERATIONS RESEARCH;

EID: 0035427762     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(00)00143-0     Document Type: Article

References (17)

1. J. Beasley An algorithm for the Steiner problem in graphs Networks 14 1984 147 159
2. T.G. Crainic A. Frangioni B. Gendron Bundle-based relaxation methods for multicommodity capacitated fixed charge network design Discrete Applied Mathematics 112 1999 73 99
3. G. Dahl The 2-hop spanning tree problem Operations Research Letters 23 1998 21 26
4. M. Fischetti P. Toth An efficient algorithm for the min-sum arborescence problem on complete digraphs ORSA Journal on Computing 5 1993 426 434
5. B. Gendron T.G. Crainic A. Frangioni Multicommodity capacitated network design B. Sansò P. Soriano Telecommunications Network Planning 1999 Kluwer Academic Publishers Dordrecht
6. L. Gouveia Using the Miller–Tucker–Zemlin constraints to formulate a minimal spanning tree problem with hop constraints Computer and Operations Research 22 1995 959 970
7. L. Gouveia Multicommodity flow models for spanning trees with hop constraints European Journal of Operational Research 95 1996 178 190
8. L. Gouveia Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints INFORMS Journal on Computing 10 1998 180 188
9. M. Held P. Wolfe H.P. Crowder Validation of subgradient optimization Mathematical Programming 6 1974 62 88
10. Holmberg, K., Yuan, D., 1996. A Lagrangean heuristic based branch-and-bound approach for the capacitated network design problem. Research Report LiTH-MAT-R-1996-23, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden. Operations Research (accepted)
11. LeBlanc, L., Chifflet, J., Mahey, P., 1998. Packet routing in telecommunication networks with path and flow restrictions. INFORMS Journal on Computing (to appear)
12. Magnanti, T., Wolsey, L., 1995. Optimal trees. In: Ball, M.O., Magnanti, T.L., Monma, C.L., Nemhauser, G.L. (Eds.), Network Models, Handbooks in Operations Research and Management Science, Vol. 7. North-Holland, Amsterdam
13. Manyem, P., Stallmann, M., 1996. Some Approximation Results in Multicasting. Working Paper, North Carolina State University
14. R.K. Martin Generating alternative mixed-integer programming models using variable redefinition Operations Research 35 1987 820 831
15. Vo ß , S., 1999. The Steiner tree problem with hop constraints. In: Sharaiha, Y., Beasley, J. (Eds.), Advances in Combinatorial Optimization. Annals of Operations Research, vol. 86. pp. 271–294
16. K. Woolston S. Albin The design of centralized networks with reliability and availability constraints Computer and Operations Research 15 1988 207 217
17. Yuan, D., 1997. Optimal Synthesis and Multicommodity Routing in Telecommunication Networks. PhD thesis, Division of Optimization, Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden