Cutting plane versus compact formulations for uncertain (integer) linear programs

Mathematical Programming Computation

Volumn 4, Issue 3, 2012, Pages 239-273

  Fischetti, Matteo ^a   Monaci, Michele ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Cutting planes; Optimization under uncertainty; Uncertain connectivity problems; Uncertain set covering

Indexed keywords

COMPUTATIONAL EXPERIMENT; CONNECTIVITY PROBLEMS; CUTTING PLANES; OPTIMIZATION PROBLEMS; OPTIMIZATION UNDER UNCERTAINTY; PROBABILITY OF FAILURE; SET COVERING PROBLEM; SET COVERINGS;

OPTIMIZATION; PROBABILITY; SET THEORY;

INDUCTIVE LOGIC PROGRAMMING (ILP);

EID: 84865770790     PISSN: 18672949     EISSN: 18672957     Source Type: Journal    
DOI: 10.1007/s12532-012-0039-y     Document Type: Article

References (38)

1. Achterberg, T.: Constraint Integer Programming. Ph. D. thesis, ZIB, Technische Universität Berlin (2007).
2. Balas, E.: A class of location, distribution and scheduling problems: modeling and solution methods. In: Proc. Chinese-US Symposium on System Analysis. Wiley, New York (1983).
3. Ben-Tal A., Nemirovski A.: Robust solutions to uncertain linear programs. Oper. Res. Lett. 25, 1-13 (1999).
4. Ben-Tal A., Nemirovski A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Progr. 88, 411-424 (2000).
5. Ben-Tal A., Nemirovski A.: Robust optimization-methodology and applications. Math. Progr. 92, 453-480 (2002).
6. Beraldi P., Ruszczyński A.: The probabilistic set-covering problem. Oper. Res. 50, 956-967 (2002).
7. Bertsimas D., Sim M.: Robust discrete optimization and network flows. Math. Progr. 98, 49-71 (2003).
8. Bertsimas D., Sim M.: The price of robustness. Oper. Res. 52, 35-53 (2004).
9. Caprara A., Fischetti M., Toth P.: Algorithms for the set covering problem. Ann. Oper. Res. 98, 353-371 (2000).
10. Caprara A., Fischetti M., Toth P., Vigo D., Guida P. L.: Algorithms for railway crew management. Math. Progr. 79, 125-141 (1997).
11. Ceria S., Nobili P., Sassano A.: A lagrangian-based heuristic for large-scale set covering problems. Math. Progr. 81, 215-228 (1998).
12. Chen X., Sim M., Sun P.: A robust optimization perspective on stochastic programming. Oper. Res. 55, 1058-1071 (2007).
13. Crowder H., Padberg M. W.: Solving large-scale symmetric travelling salesman problems to optimality. Manag. Sci. 26, 495-509 (1980).
14. Eén, N., Sörensson, N.: An extensible SAT-solver. In International Conference on Theory and Applications of Satisfiability Testing (SAT), LNCS, vol. 6. Springer, Berlin (2003).
15. Fischetti M., Martello S.: A hybrid algorithm for finding the k-th smallest of n elements in O(n) time. In: Simeone, B., Toth, P., Gallo, G., Maffioli, F., Pallottino, S. (eds) FORTRAN Codes for Network Optimization. Annals of Operational Research, vol. 13, pp. 401-419. JC Baltzer AG, Basel (1988).
16. Fischetti, M., Monaci, M.: Light robustness. In: Ahuja, R. K., Moehring, R., Zaroliagis, C. (eds.) Robust and Online Large-Scale Optimization, Lecture Notes in Computer Science, vol. 5868, pp. 61-84. Springer, Berlin (2009).
17. Gamache M., Soumis F., Marquis G., Desrosiers J.: A column generation approach for large-scale aircrew rostering problems. Oper. Res. 47, 247-263 (1999).
18. Garey M., Johnson D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco (1979).
19. Goldberg E., Novikov Y.: Berkmin: a fast and robust sat-solver. Discrete Appl. Math. 155, 1549-1561 (2007).
20. Gomes C.: Complete randomized backtrack search. In: Milano, M. (ed) Constraint and Integer Programming: Toward a Unified Methodology, pp. 233-283. Kluwer, Dordrecht (2003).
21. Gomes, C., Selman, B., Kautz, H.: Boosting combinatorial search through randomization. In: Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98). American Association for Artificial Intelligence (1998).
22. Gomes C., Walsh T.: Randomness and structure. In: Rossi, F., van Beek, P., Walsh, T. (eds) Handbook of Constraint Programming, Elsevier, Amsterdam (2006).
23. Grötschel M., Monma C. L.: Integer polyhedra arising from certain network design problems with connectivity constraints. SIAM J. Discrete Math. 3, 502-523 (1990).
24. Grötschel M., Monma C. L., Stoer M.: Computational results with a cutting plane algorithm for designing communication networks with low-connectivity constraints. Oper. Res. 40, 309-330 (1992).
25. Haight R. G., Revelle C., Snyder S. A.: An integer optimization approach to a probabilistic reserve site selection problem. Oper. Res. 48, 697-708 (2000).
26. IBM ILOG CPLEX Optimizer. http://www-01. ibm. com/software/integration/optimization/cplex-optimizer/.
27. Karzan F. K., Nemhauser G. L., Savelsbergh M. W. P.: Information-based branching schemes for binary linear mixed integer problems. Math. Progr. Comput. 1, 249-293 (2009).
28. Luby M., Sinclair A., Zuckerman D.: Optimal speedup of las vegas algorithms. Inf. Process. Lett. 47, 173-180 (1993).
29. Martello S., Pisinger D., Toth P.: Dynamic programming and strong bounds for the 0-1 knapsack problem. Manag. Sci. 45, 414-424 (1999).
30. Martello S., Toth P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, Chichester (1990).
31. Monma C. L., Munson B. S., Pulleyblank W. R.: Minimum-weight two-connected spanning networks. Math. Progr. 46, 153-171 (1990).
32. Moskewicz, M. W., Madigan, C. F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Annual Design Automation Conference, pp. 530-535. ACM, New York (2001).
33. ORLIB. http://people. brunel. ac. uk/~mastjjb/jeb/info. html.
34. SCIP: Solving Constraint Integer Programs. http://scip. zib. de/.
35. Saxena A., Goyal V., Lejeune M.: MIP reformulations of the probabilistic set covering problem. Math. Progr. 121, 1-31 (2010).
36. Soyster A. L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154-1157 (1973).
37. TSPLIB. http://comopt. ifi. uni-heidelberg. de/software/tsplib95/.
38. Williams, R., Gomes, C. P., Selman, B.: Backdoors to typical case complexity. In: Gottlob, G., Walsh, T. (eds) IJCAI-03, Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence, pp. 1173-1178. Morgan Kaufmann, Waltham (2003).