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Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Generalized Upper Bound Constraints

Brian Keller, Güzin Bayraksan
2012 INFORMS journal on computing  
Then, we examine problems with generalized upper bound constraints in the second stage and exploit this structure to generate cuts. We establish convergence of D 2 variants.  ...  In this paper, we consider two-stage stochastic integer programs with binary first-stage and mixedbinary second-stage decisions and present several computational enhancements to D 2 .  ...  Acknowledgments The authors thank Suvrajeet Sen for valuable discussions and two anonymous referees for helpful comments that significantly improved the presentation of the paper.  ... 
doi:10.1287/ijoc.1100.0442 fatcat:qvtmtgfd5jc5nirgtqe2qqpxba

Decomposition with branch-and-cut approaches for two-stage stochastic mixed-integer programming

Suvrajeet Sen, Hanif D. Sherali
2005 Mathematical programming  
This paper lays the foundation for such decomposition methods for two-stage stochastic integer programs.  ...  A decomposition method with wide applicability is Benders' decomposition, and has been applied to both stochastic programming, as well as integer programming problems.  ...  mixed-integer second stage problems, and these were incorporated within a Benders' decomposition algorithm for a two stage stochastic program having binary first-stage variables.  ... 
doi:10.1007/s10107-005-0592-5 fatcat:imwtn7s7cjhmrgsu6l4jsjihwq

Computations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs

Lewis Ntaimo, Matthew W. Tanner
2007 Journal of Global Optimization  
Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve.  ...  This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP  ...  The authors would like to thank the anonymous referees for their comments which helped improve the presentation of the paper.  ... 
doi:10.1007/s10898-007-9245-y fatcat:qwnqpqkmqvbuvaxmacatkdbyre

A branch-and-cut algorithm for two-stage stochastic mixed-binary programs with continuous first-stage variables

Lewis Ntaimo, Suvrajeet Sen
2007 International Journal of Computational Science and Engineering (IJCSE)  
This paper presents a branch-and-cut method for two-stage stochastic mixed-integer programming (SMIP) problems with continuous firststage variables.  ...  This method is derived based on disjunctive decomposition (D 2 ) for SMIP, an approach in which disjunctive programming is used to derive valid inequalities for SMIP.  ...  Acknowledgments This research was funded by grants from the OR Program (DMII-9978780), and the Next Generation Software Program (CISE-9975050) of the National Science Foundation.  ... 
doi:10.1504/ijcse.2007.017829 fatcat:5wvh5aqarzff5oxwsyxdh5peve

A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints

Yohan Shim, Marte Fodstad, Steven A. Gabriel, Asgeir Tomasgard
2012 Annals of Operations Research  
We present a branch-and-bound algorithm for discretely-constrained mathematical programs with equilibrium constraints (DC-MPEC).  ...  This is a class of bilevel programs with an integer program in the upper-level and a complementarity problem in the lower-level.  ...  For a problem with a two-stage stochastic program in the lower-level, Problem (1) can be written as: min x,y J j=1 p j c x j +ď y j +d jŷ j s.t.  ... 
doi:10.1007/s10479-012-1191-5 fatcat:6vv3kenfuvbyzcxapshlviknlu

Planning With Multiple Transmission and Storage Investment Options Under Uncertainty: A Nested Decomposition Approach

Paola Falugi, Ioannis Konstantelos, Goran Strbac
2018 IEEE Transactions on Power Systems  
However, such an analysis can result in large-scale Mixed Integer Linear Programming (MILP) problems which contain many thousands of continuous and binary variables.  ...  In this manuscript we propose a novel, efficient and highly-generalizable framework for solving large-scale planning problems under uncertainty by using a temporal decomposition scheme based on the principles  ...  In particular, the Disjunctive Programming approach (D 2 ), proposed by Sen and Higle in [39] , aims at two-stage SMIP problems with first stage binary variables and second stage mixed binary-continuous  ... 
doi:10.1109/tpwrs.2017.2774367 fatcat:3desyi2ghzhzhmh3k4ceh52use

Algorithms for Stochastic Mixed-Integer Programming Models [chapter]

Suvrajeet Sen
2005 Handbooks in Operations Research and Management Science  
In this chapter, we will study algorithms for both two-stage as well as multi-stage stochastic mixed-integer programs.  ...  We present stagewise (resource-directive) decomposition methods for two-stage models, and scenario (price-directive) decomposition methods for multi-stage models.  ...  My host, Gautam Mitra, was instrumental in arranging this visit, and I thank him for an invigorating stay. Stochastic Mixed-Integer Programming  ... 
doi:10.1016/s0927-0507(05)12009-x fatcat:ikdaozt5bzc7fadek7ttdvhpi4

A comparative study of decomposition algorithms for stochastic combinatorial optimization

Lewis Ntaimo, Suvrajeet Sen
2007 Computational optimization and applications  
Furthermore, the study shows that convergence of the D 2 methods for stochastic combinatorial optimization (SCO) is in fact attainable since the methods scale well with the number of scenarios.  ...  The computational experience demonstrates the promising potential of the disjunctive decomposition (D 2 ) approach towards solving several large-scale problem instances from the three application areas  ...  Schaefer for providing us with the stochastic matching problem instances, and also for confirming our computational results.  ... 
doi:10.1007/s10589-007-9085-1 fatcat:m46oa2a6ejbwhdkcxuafx4ftnu

A Decomposition Method for Distributionally-Robust Two-stage Stochastic Mixed-integer Cone Programs [article]

Fengqiao Luo, Sanjay Mehrotra
2019 arXiv   pre-print
We develop a decomposition algorithm for distributionally-robust two-stage stochastic mixed-integer convex cone programs, and its important special case of distributionally-robust two-stage stochastic  ...  The second stage problems can be solved using a branch-and-cut algorithm. The decomposition algorithm is illustrated with an example.  ...  The Benders' decomposition algorithms developed for two-stage stochastic mixed integer programs with binary first stage variables can be modified to solve distributionally-robust two-stage stochastic mixed  ... 
arXiv:1911.08713v1 fatcat:bwnczzskrvhnnbk2qiourqnbwi

The C3 Theorem and a D2 Algorithm for Large Scale Stochastic Mixed-Integer Programming: Set Convexification

Suvrajeet Sen, Julia L. Higle
2005 Mathematical programming  
This paper considers the two-stage stochastic integer programming problem, with an emphasis on instances in which integer variables appear in the second stage.  ...  Drawing heavily on the theory of disjunctive programming, we characterize convexifications of the second stage problem and develop a decomposition-based algorithm for the solution of such problems.  ...  The scenario subproblem, (2), is a mixed-integer linear program (MILP) with the variables denoted z capturing the binary restrictions in the second stage.  ... 
doi:10.1007/s10107-004-0566-z fatcat:bc5wkdl2l5adxeybhg5aievady

Recent Progress in Two-stage Mixed-integer Stochastic Programming with Applications to Power Production Planning [chapter]

Werner Römisch, Stefan Vigerske
2010 Energy Systems  
We present recent developments in two-stage mixed-integer stochastic programming with regard to application in power production planning.  ...  In particular, we review structural properties, stability issues, scenario reduction and decomposition algorithms for two-stage models.  ...  For solving a two-stage mixed-integer stochastic program, several decomposition algorithms are reviewed.  ... 
doi:10.1007/978-3-642-02493-1_8 fatcat:a65rmgn3jvadreyzvujlxzdjqy

Decomposition algorithms with parametric Gomory cuts for two-stage stochastic integer programs

Dinakar Gade, Simge Küçükyavuz, Suvrajeet Sen
2012 Mathematical programming  
We consider a class of two-stage stochastic integer programs with binary variables in the first stage and general integer variables in the second stage.  ...  We report computational results using the stochastic server location problem instances which suggest that our decomposition-based approach scales better with increases in the number of scenarios than a  ...  Acknowledgment We thank the two referees for their suggestions that improved the paper.  ... 
doi:10.1007/s10107-012-0615-y fatcat:gawx2h53wffqjbui22q55cntcy

Advances in mathematical programming models for enterprise-wide optimization

Ignacio E. Grossmann
2012 Computers and Chemical Engineering  
We first provide a brief overview of mathematical programming techniques (mixed-integer linear and nonlinear optimization methods), as well as decomposition methods, stochastic programming and modeling  ...  Enterprise-wide optimization (EWO) is an area that lies at the interface of chemical engineering and operations research, and has become a major goal in the process industries due to the increasing pressures for  ...  If there are only two stages then the problem corresponds to a 2-stage stochastic program, while in a multistage stochastic program the uncertainty is revealed sequentially, i.e. in multiple stages (periods  ... 
doi:10.1016/j.compchemeng.2012.06.038 fatcat:jxycpmzmpfa37kp4jh3artwvaa

Large-Scale Stochastic Mixed-Integer Programming Algorithms for Power Generation Scheduling [chapter]

Kibaek Kim, Victor M. Zavala
2016 Alternative Energy Sources and Technologies  
The model is a two-stage stochastic programming problem with first-stage binary variables and second-stage mixed-binary variables.  ...  This chapter presents a stochastic unit commitment model for power systems and revisits parallel decomposition algorithms for these types of models.  ...  We thank Julie Bessac for providing wind speed prediction data.  ... 
doi:10.1007/978-3-319-28752-2_18 fatcat:ytntns2fr5e2bkchp2ftmmpyzq

Disjunctive Decomposition for Two-Stage Stochastic Mixed-Binary Programs with Random Recourse

Lewis Ntaimo
2010 Operations Research  
This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse.  ...  Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem.  ...  The author wishes to thank an anonymous reviewer for their helpful comments on an earlier draft of this paper, and his student Matthew W. Tanner for an initial implementation of the D 2 -R algorithm.  ... 
doi:10.1287/opre.1090.0693 fatcat:2jqxhi3abve2ho2gtgbzit3fmq
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