An adaptive partition-based approach for solving two-stage stochastic programs with fixed recourse

SIAM Journal on Optimization

Volumn 25, Issue 3, 2015, Pages 1344-1367

  Song, Yongjia ^a   Luedtke, James ^b  

^a VIRGINIA COMMONWEALTH UNIVERSITY   (United States)

^b Wisconsin Electric Machines and Power Electronics Consortium   (United States)

Author keywords

Scenario partitions; Simple recourse; Two stage stochastic programming

Indexed keywords

LINEAR PROGRAMMING; OPTIMAL SYSTEMS; STOCHASTIC PROGRAMMING;

ADAPTIVE PARTITIONS; BENDERS DECOMPOSITION; COMPUTATIONAL RESULTS; REFINEMENT STRATEGY; SIMPLE RECOURSE; STATE-OF-ART METHODS; TWO-STAGE STOCHASTIC PROGRAMMING; TWO-STAGE STOCHASTIC PROGRAMS;

STOCHASTIC SYSTEMS;

EID: 84944594372     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/140967337     Document Type: Article

References (41)

1. K.A. Ariyawansa and A.J. Felt, On a new collection of stochastic linear programming test problems, INFORMS J. Comput., 16 (2004), pp. 291-299.
2. J.C. Bean, J. Birge, and R.L. Smith, Aggregation in dynamic programming, Oper. Res., 35 (1987), pp. 215-220.
3. J.E. Beasley, OR-library: Distributing test problems by electronic mail, J. Oper. Res. Soc., 41 (1990), pp. 1069-1072.
4. P. Beraldi and A. Ruszczyński, A branch and bound method for stochastic integer programs under probabilistic constraints, Optim. Methods Softw., 17 (2002), pp. 359-382.
5. D. Bienstock and M. Zuckerberg, Solving LP relaxations of large-scale precedence constrained problems, in Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 6080, 2010, pp. 1-14.
6. J. Birge, Aggregation bounds in stochastic linear programming, Math. Program., 31 (1985), pp. 25-41.
7. J.R. Birge and F.V. Louveaux, Introduction to Stochastic Programming, 2nd ed., Springer, New York, 2011.
8. J. Birge and R. Wets, Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse, Math. Program. Study, 27 (1986), pp. 54-102.
9. M.S. Casey and S. Sen, The scenario generation algorithm for multistage stochastic linear programming, Math. Oper. Res., 30 (2005), pp. 615-631.
10. K.J. Cormican, D.P. Morton, and R.K. Wood, Stochastic network interdiction, Oper. Res., 46 (1998), pp. 184-197.
11. B. Denton and D. Gupta, A sequential bounding approach for optimal appointment scheduling, IIE Trans., 35 (2003), pp. 1003-1016.
12. N.C.P. Edirisinghe and W.T. Ziemba, Tight bounds for stochastic convex programs, Oper. Res., 40 (1992), pp. 660-677.
13. D. Espinoza and E. Moreno, A primal-dual aggregation algorithm for minimizing conditional-value-at-risk in linear programs, Comput. Optim. Appl., 59 (2014), pp. 617-638.
14. C. Fábián and Z. Szöke, Solving two-stage stochastic programming problems with level decomposition, Comput. Manage. Sci., 4 (2007), pp. 313-353.
15. C. Fábián, C. Wolf, A. Koberstein, and L. Suhl, Risk-averse optimization in two-stage stochastic models: Computational aspects and a study, SIAM J. Optim., 25 (2015), pp. 28-52.
16. G. Guennebaud, B. Jacob, et al., Eigen v3, http://eigen.tuxfamily.org, 2010.
17. A. Hallefjord and S. Storoy, Aggregation and disaggregation in integer programming problems, Oper. Res., 38 (1990), pp. 619-623.
18. D.B. Hausch and W.T. Ziemba, Bounds on the value of information in uncertain decision problems: Two, Stochastics, 10 (1983), pp. 181-217.
19. C.C. Huang, W.T. Ziemba, and A. Ben-Tal, Bounds on the expectation of a convex function of a random variable, Oper. Res., 25 (1977), pp. 315-325.
20. K. Jornsten, R. Leisten, and S. Storoy, Convergence aspects of adaptive clustering in variable aggregation, Comput. Oper. Res., 26 (1999), pp. 955-966.
21. P. Kall and J. Mayer, Stochastic Linear Programming: Models, Theory and Computation, Springer, New York, 2011.
22. C. Lemaŕechal, A. Nemirovskii, and Y. Nesterov, New variants of bundle methods, Math. Program., 69 (1995), pp. 111-147.
23. J. Linderoth, A. Shapiro, and S. Wright, The empirical behavior of sampling methods for stochastic programming, Ann. Oper. Res., 142 (2006), pp. 215-241.
24. W. Oliveira, C. Sagastizábal, and S. Scheimberg, Inexact bundle methods for two-stage stochastic programming, SIAM J. Optim., 21 (2011), pp. 517-544.
25. W. Oliveira and C. Sagastizábal, Level bundle methods for oracles with on-demand accuracy, Optim. Methods Softw., 29 (2014), pp. 1180-1209.
26. P. Pierre-Louis, G. Bayraksan, and D.P. Morton, A combined deterministic and sampling-based sequential bounding method for stochastic programming, in Proceedings of the Winter Simulation Conference, S. Jain, R.R. Creasey, J. Himmelspach, K.P. White, and M. Fu, eds., 2011, pp. 4172-4183.
27. F. Qiu, S. Ahmed, S.S. Dey, and L.A. Wolsey, Covering linear programming with violations, INFORMS J. Comput., 26 (2014), pp. 531-546.
28. D.F. Rogers, R.D. Plante, R.T. Wong, and J.R. Evans, Aggregation and disaggregation techniques and methodology in optimization, Oper. Res., 39 (1991), pp. 553-582.
29. C.H. Rosa and S. Takriti, Improving aggregation bounds for two-stage stochastic programs, Oper. Res. Lett., 24 (1999), pp. 127-137.
30. A. Ruszczyński, A regularized decomposition method for minimizing a sum of polyhedral functions, Math. Program., 35 (1986), pp. 309-333.
31. A. Ruszczyński and A. Swiętanowski, Accelerating the regularized decomposition method for two stage stochastic linear problems, European J. Oper. Res., 101 (1997), pp. 328-342.
32. B. Sandikçi, N. Kong, and A.J. Schaefer, A hierarchy of bounds for stochastic mixed-integer programs, Math. Program., 138 (2013), pp. 253-272.
33. Y. Song, Structure-exploiting Algorithms for Chance-constrained and Integer Stochastic Programs, Ph.D. thesis, University of Wisconsin-Madison, Madison, WI, 2013.
34. Y. Song, J. Luedtke, and S. Küçükyavuz, Chance-constrained binary packing problems, INFORMS J. Comput., 26 (2014), pp. 735-747.
35. S. Trukhanov, L. Ntaimo, and A. Schaefer, Adaptive multicut aggregation for two-stage stochastic linear programs with recourse, European J. Oper. Res., 206 (2010), pp. 395-406.
36. R. Van Slyke and R.J.-B. Wets, L-shaped linear programs with applications to optimal control and stochastic programming, SIAM J. Appl. Math., 17 (1969), pp. 638-663.
37. C. Wolf, C.I. Fábián, A. Koberstein, and L. Suhl, Applying oracles of on-demand accuracy in two-stage stochastic programming-a computational study, European J. Oper. Res., 239 (2014), pp. 437-448.
38. C. Wolf and A. Koberstein, Dynamic sequencing and cut consolidation for the parallel hybrid-cut nested l-shaped method, European J. Oper. Res., 230 (2013), pp. 143-156.
39. S.E. Wright, Primal-dual aggregation and disaggregation for stochastic linear programs, Math. Oper. Res., 19 (1994), pp. 893-908.
40. P.H. Zipkin, Bounds for row-aggregation in linear programming, Oper. Res., 28 (1980), pp. 903-916.
41. P.H. Zipkin, Bounds on the effect of aggregating variables in linear programming, Oper. Res., 28 (1980), pp. 403-418.