scholarly journals Two‐stage stochastic minimum s  −  t cut problems: Formulations, complexity and decomposition algorithms

Networks ◽  
2019 ◽  
Vol 75 (3) ◽  
pp. 235-258
Author(s):  
Steffen Rebennack ◽  
Oleg A. Prokopyev ◽  
Bismark Singh
Keyword(s):  
Decomposition Algorithms ◽  
Two Stage ◽  
Cut Problems

Decomposition algorithms for two-stage chance-constrained programs

2014 ◽  
Vol 157 (1) ◽  
pp. 219-243 ◽  
Author(s):  
Xiao Liu ◽  
Simge Küçükyavuz ◽  
James Luedtke
Keyword(s):  
Decomposition Algorithms ◽  
Two Stage

Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

2014 ◽  
Vol 26 (4) ◽  
pp. 825-847 ◽  
Author(s):  
Dimitri J. Papageorgiou ◽  
Ahmet B. Keha ◽  
George L. Nemhauser ◽  
Joel Sokol
Keyword(s):  
Decomposition Algorithms ◽  
Inventory Routing ◽  
Two Stage ◽  
Single Product ◽  
Maritime Inventory Routing

scholarly journals Optimization-Driven Scenario Grouping

2020 ◽  
Vol 32 (3) ◽  
pp. 805-821
Author(s):  
Kevin Ryan ◽  
Shabbir Ahmed ◽  
Santanu S. Dey ◽  
Deepak Rajan ◽  
Amelia Musselman ◽  
...  
Keyword(s):  
Large Scale ◽  
Unit Commitment ◽  
Standard Test ◽  
Mixed Integer ◽  
Feasible Region ◽  
Decomposition Algorithms ◽  
Two Stage ◽  
Stochastic Programs ◽  
Stochastic Unit Commitment ◽  
Nonanticipativity Constraints

Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. We develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

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