Accelerating Benders method using covering cut bundle generation

International Transactions in Operational Research

Volumn 17, Issue 2, 2010, Pages 221-237

  Saharidis, Georgios K D ^a   Minoux, Michel ^b   Ierapetritou, Marianthi G ^a  

^a The State University of New Jersey   (United States)

^b UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

Benders decomposition; Covering cut bundle; Mixed integer programming; Multi generation of cuts

Indexed keywords

EID: 85040409511     PISSN: 09696016     EISSN: 14753995     Source Type: Journal    
DOI: 10.1111/j.1475-3995.2009.00706.x     Document Type: Article

References (23)

1. Benders, J.F., 1962. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252.
2. Conejo, A.J., Castillo, E., Minguez, R., Garcia-Bertrand, R., 2006. Decomposition Techniques in Mathematical Programming. Engineering and Science Applications Vol. XVI. Springer, Berlin.
3. Cote, G., Laughton, M., 1984. Large-scale mixed integer programming: Benders-type heuristics. European Journal of Operational Research 16, 327–333.
4. Farkas, J., 1902. Uber die Theorie der einfachen Ungleichungen. Journal of Mathematics 124, 1–24.
5. Gabrel, V., Knippel, A., Minoux, M., 1999. Exact solution of multicommodity network optimization problems with general step cost functions. Operational Research Letters 25, 15–23.
6. Ierapetritou, M., Floudas, C., 1998. Effective continuous-time formulation for short-term scheduling: I. Multipurpose batch processes. Industrial and Engineering Chemistry Research 37, 11, 4341–4359.
7. Magnanti, T., Wong, R., 1981. Accelerating Benders decomposition algorithmic enhancement and model selection criteria. Operational Research 29, 464–484.
8. McDaniel, D., Devine, M., 1977. A modified Benders partitioning algorithm for mixed integer programming. Management Science 24, 312–319.
9. Minkowski, H., 1910. Geometri der Zahlen. Teubner, Leipzig.
10. Minkowski, H., 1911. Theorie der Konvexen Korper, Insbesondere Begrundung ihres Oberflachenbegriffs. Gesammelte Abhandlungen II, Teubner, Leipzig.
11. Minoux, M., 1986. Mathematical Programming Theory and Algorithms. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley-Interscience, New York.
12. Minoux, M., 2001. Discrete cost multicommodity network optimization problems and exact solution methods. Annals of Operations Research 106, 19–46.
13. Rei, W., Gendreau, M., Cordeau, J.-F., Soriano, P., 2008. Accelerating Benders decomposition by local branching. INFORMS Journal on Computing. doi: DOI: 10.1287/ijoc.1080.0296.
14. Rekik, M., Cordeau, J.F., Soumis, F., 2008. Solution approaches to large shift scheduling problems. RAIRO – Operations Research 42, 2, 229–258.
15. Saharidis, G., 2006. Pilotage de production à moyen terme et à court terme: contribution aux problématique d'optimisation globale vc locale et à l'ordonnancement dans les raffineries. PhD Ecole Centrale Paris France.
16. Saharidis, G.K., Ierapetritou, M.G., 2008a. Resolution method for mixed integer bi-level linear problems based on decomposition technique. Journal of Global Optimization Online: doi: DOI: 10.1007/s10898-008-9291-0.
17. Saharidis, G.K.D., Ierapetritou, M.G., 2008b. Scheduling of loading and unloading of crude oil in a refinery with optimal mixture preparation. Industrial Engineering and Chemistry Research 48, 5, 2624–2633.
18. Saharidis, G.K.D., Minoux, M., Dallery, Y., 2009. Scheduling of crude oil using event-based discrete time formulation. Computer and Chemical Engineering, forthcoming.
19. Smith, R.A., Villegas, A.M., 1997. A comparative analysis of various optimization models for electricity capacity expansion. International Transactions in Operational Research 4, 1, 35–44.
20. Watkins, D.W., McKinney, D.C., Lasdon, L.S., Nielsen, S.S., Martin, Q.W., 2000. A scenario-based stochastic programming model for water supplies from the highland lakes. International Transactions in Operational Research 7, 3, 211–230.
21. Zakeri, G., Philpott, A.B., Ryan, D.M., 1999. Inexact cuts in benders decomposition. SIAM Journal of Optimization 10, 3, 643–657.
22. Zhang, J.L., Ponnambalam, K., 2006. Hydro energy management optimization in a deregulated electricity market. Journal Optimization and Engineering 7, 1, 47–61.
23. Zhu, Y., Kuno, T., 2003. Global optimization of nonconvex MINLP by a hybrid branch-and-bound and revised general Benders decomposition approach. Industrial and Engineering Chemistry Research 42, 3, 528–539.