A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization

We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of...

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Veröffentlicht in:arXiv.org 2021-04
Hauptverfasser: Bolusani, Suresh, Coniglio, Stefano, Ralphs, Ted K, Tahernejad, Sahar
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Sprache:eng
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Bending machines
Computer Science - Computer Science and Game Theory
Mathematics - Optimization and Control
Mixed integer
Optimization
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creator Bolusani, Suresh
Coniglio, Stefano
Ralphs, Ted K
Tahernejad, Sahar
description We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, the nature of the value function of the second-stage problem, highlighting its connection to dual functions and the theory of duality for mixed integer linear optimization problems, and summarize different reformulations. We then present two main solution techniques, one based on a Benders-like decomposition to approximate either the risk function or the value function, and the other one based on cutting plane generation.
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subjects Bending machines
Computer Science - Computer Science and Game Theory
Mathematics - Optimization and Control
Mixed integer
Optimization
title A Unified Framework for Multistage and Multilevel Mixed Integer Linear Optimization
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