Integer set reduction for stochastic mixed-integer programming

Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a subset of the convex hull of feasible integer points of the second-stage subproblem wh...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 85; no. 1; pp. 181 - 211
Main Authors: Venkatachalam, Saravanan, Ntaimo, Lewis
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2023
Springer Nature B.V
Subjects:
Algorithms
Computational geometry
Convex and Discrete Geometry
Convexity
Decomposition
Integer programming
Linear programming
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Operations Research
Operations Research/Decision Theory
Optimization
Reduction
Statistics
Integer programming
Multidimensional knapsack
Cutting planes
Integer set reduction
Fenchel decomposition
Stochastic programming
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:Two-stage stochastic mixed-integer programs (SMIPs) with general integer variables in the second-stage are generally difficult to solve. This paper develops the theory of integer set reduction for characterizing a subset of the convex hull of feasible integer points of the second-stage subproblem which can be used for solving the SMIP with pure integer recourse. The basic idea is to use the smallest possible subset of the subproblem feasible integer set to generate a valid inequality like Fenchel decomposition cuts with a goal of reducing computation time. An algorithm for obtaining such a subset based on the solution of the subproblem linear programming relaxation is devised and incorporated into a decomposition method for SMIP. To demonstrate the performance of the new integer set reduction methodology, a computational study based on randomly generated knapsack test instances was performed. The results of the study show that integer set reduction aids in speeding up cut generation, leading to better bounds in solving SMIPs with pure integer recourse than using a direct solver.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00457-4