A cross-decomposition scheme with integrated primal–dual multi-cuts for two-stage stochastic programming investment planning problems

Mathematical Programming

Volumn 157, Issue 1, 2016, Pages 95-119

  Mitra, Sumit ^a   Garcia Herreros, Pablo ^a   Grossmann, Ignacio E ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Cross decomposition; Investment planning; Two stage stochastic programming

Indexed keywords

INTEGER PROGRAMMING; STAGES; STOCHASTIC PROGRAMMING; STOCHASTIC SYSTEMS;

BENDERS DECOMPOSITION; CROSS DECOMPOSITIONS; DECOMPOSITION METHODS; FACILITY LOCATION PROBLEM; INVESTMENT PLANNING; LARGE-SCALE PROBLEM; NUMERICAL EXPERIMENTS; TWO-STAGE STOCHASTIC PROGRAMMING;

INVESTMENTS;

EID: 84962007167     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-016-1001-y     Document Type: Article

References (46)

1. Balas, E., Jeroslow, R.G.: Canonical cuts on the unit hypercube. SIAM J. Appl. Math. 23, 61–69 (1972)
2. Barahona, F., Anbil, R.: The volume algorithm: producing primal solutions with a subgradient method. Math. Program. 87, 385–399 (2000)
3. Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252 (1962)
4. Birge, J.R., Louveaux, F.: A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. 34, 384–392 (1988)
5. Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer Series in Operations Research. Springer, New York (2011)
6. Bixby, R., Rothberg, E.: Progress in computational mixed integer programming—a look back from the other side of the tipping point. Ann. Oper. Res. 49, 37–41 (2007)
7. Brooke, A., Kendrick, D., Meeraus, A.: GAMS: A Users Guide, Release 24.2.1. The Scientific Press, South San Francisco (2013)
8. Bussieck, M.R., Ferris, M.C., Meeraus, A.: Grid-enabled optimization with GAMS. INFORMS J. Comput. 21, 349–362 (2009)
9. Caroe, C.C., Schultz, R.: Dual decomposition in stochastic integer programming. Oper. Res. Lett. 24, 37–45 (1999)
10. Cerisola, S., Baillo, A., Fernandez-Lopez, J.M., Ramos, A., Gollmer, R.: Stochastic power generation unit commitment in electricity markets: a novel formulation and a comparison of solution methods. Oper. Res. 57, 32–46 (2009)
11. Cheney, E.W., Goldstein, A.A.: Newton’s method for convex programming and Tchebycheff approximation. Numer. Math. 1, 253–268 (1959)
12. Daskin, M.S.: Network and Discrete Location: Models, Algorithms, and Applications. Wiley, New York (1995). Chap. Appendix H. Longitudes, Latitudes, Demands, and Fixed Cost for SORTCAP.GRT: A 49-Node Problem Defined on the Continental United States
13. Fisher, M.L.: The Lagrangian relaxation method for solving integer programming problems. Manag. Sci. 27, 1–18 (1981)
14. Frangioni, A.: Generalized bundle methods. SIAM J. Optim. 13, 117–156 (2002)
15. Frangioni, A.: About Langrangian methods in integer optimization. Ann. Oper. Res. 139, 163–193 (2005)
16. Garcia-Herreros, P., Wassick, J., Grossmann, I.E.: Design of resilient supply chains with risk of facility disruptions. Ind. Eng. Chem. Res. 53, 17,240–17,251 (2014)
17. Geoffrion, A.M.: Generalized Benders decomposition. J. Optim. Theory Appl. 10, 237–260 (1972)
18. Goffin, J.L., Haurie, A., Vial, J.P.: Decomposition and nondifferentiable optimization with the projective algorithm. Manag. Sci. 38, 284–302 (1992)
19. Guignard, M.: Lagrangean relaxation. Top 11, 151–228 (2003)
20. Guignard, M., Kim, S.: Lagrangean decomposition—a model yielding stronger Lagrangean bounds. Math. Program. 39, 215–228 (1987)
21. Gupta, V.: Modeling and computational strategies for optimal oilfield development planning under fiscal rules and endogenous uncertainties. PhD thesis, Carnegie Mellon University, Pittsburgh (2013)
22. Heitsch, H., Romisch, W.: Scenario reduction algorithms in stochastic programming. Comput. Optim. Appl. 24, 187–206 (2003)
23. Held, M., Karp, R.M.: The traveling-salesman problem and minimum spanning trees: part ii. Math. Program. 1, 6–25 (1971)
24. Held, M., Wolfe, P., Crowder, H.P.: Validation of subgradient optimization. Math. Program. 6, 62–88 (1974)
25. Holmberg, K.: On the convergence of cross decomposition. Math. Program. 47, 269–296 (1990)
26. Holmberg, K.: Linear mean value cross decomposition: a generalization of the Kornai–Liptak method. Eur. J. Oper. Res. 62, 55–73 (1992)
27. Holmberg, K.: A convergence proof for linear mean value cross decomposition. Zeitschrift für Op. Res. 39(2), 157–186 (1994)
28. Holmberg, K.: Mean value cross decomposition applied to integer programming problems. Eur. J. Oper. Res. 97, 124–138 (1997)
29. Karuppiah, R., Grossmann, I.E.: A Lagrangean based branch-and-cut algorithm for global optimization of nonconvex mixed-integer nonlinear programs with decomposable structures. J. Glob. Optim. 41, 163–186 (2008)
30. Kelley, J.E.: The cutting-plane method for solving convex programs. J. Soc. Ind. Appl. Math. 8, 703–712 (1960)
31. Kiwiel, K.C.: Proximity control in bundle methods for convex nondifferentiable minimization. Math. Program. 46, 105–122 (1990)
32. Lemarechal, C.: An algorithm for minimizing convex functions. In: Rosenfeld, J.L. (ed.) Proceedings IFIP74, pp. 552–556, Stockholm (1974)
33. Lima, R., Grossmann, I.E.: Computational advances in solving mixed integer linear programming problems. In: Chemical engineering greetings to Prof. Sauro Pierucci. AIDAC, Milano, Italy, pp. 151–160 (2011)
34. Linderoth, J., Shapiro, A., Wright, S.: The empirical behavior of sampling methods for stochastic programming. Ann. Oper. Res. 142, 215–241 (2006)
35. Magnanti, T.L., Wong, R.T.: Accelerating Benders decomposition: algorithmic enhancement and model selection criteria. Oper. Res. 29, 464–484 (1981)
36. Mouret, S., Grossmann, I.E., Pestiaux, P.: A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling. Comput. Chem. Eng. 35, 2750–2766 (2011)
37. Oliveira, F., Gupta, V., Hamacher, S., Grossmann, I.E.: A Lagrangean decomposition approach for oil supply chain investment planning under uncertainty with risk considerations. Comput. Chem. Eng. 50, 184–195 (2013)
38. Saharidis, G.K.D., Minoux, M., Ierapetritou, M.G.: Accelerating Benders method using covering cut bundle generation. Int. Trans. Oper. Res. 17, 221–237 (2010)
39. Sahinidis, N.V., Grossmann, I.E.: Convergence properties of generalized Benders decomposition. Comput. Chem. Eng. 15, 481–491 (1991)
40. Snyder, L.V., Daskin, M.S.: Reliability models for facility location: the expected failure cost case. Transp. Sci. 39(3), 400–416 (2005)
41. Sohn, H.S., Bricker, D.L., Tseng, T.L.: Mean value cross decomposition for two-stage stochastic linear programming with recourse. Open Oper. Res. J. 5, 30–38 (2011)
42. Tarhan, B.: Stochastic programming approaches for decision-dependent uncertainty and gradual uncertainty resolution. Ph.D thesis, Carnegie Mellon University, Pittsburgh (2009)
43. Van Roy, T.J.: Cross decomposition for mixed integer programming. Math. Program. 25, 46–63 (1983)
44. Van Slyke, R., Wets, R.J.B.: L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. 17, 638–663 (1969)
45. You, F., Grossmann, I.E.: Multicut Benders decomposition algorithm for process supply chain planning under uncertainty. Ann. Oper. Res. 210, 191–211 (2011)
46. Zowe, J.: Nondifferentiable optimization. In: Schittkowski, K. (ed.) Computational Mathematical Program, NATO ASI Series F: Computer and Systems Science, vol. 15, pp. 323–356 (1985)