Xu, Liang
(2023)
A Study on Multilevel Optimization Subject to Uncertainty.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
Multilevel, including bilevel, optimization has been widely applied in real world hierarchical systems, such as power systems and transportation systems. However, this optimization scheme is complex and its extension to handle uncertainty is very limited. In this dissertation, we explore the mathematical structure and develop efficient solution methods for two types of such optimization problem: bilevel mixed-integer nonlinear programming and robust bilevel optimization. Two applications, wind farm capacity expansion problem and optimal decision tree problem, are investigated using the proposed methods.
In our first study, we consider general bilevel mixed-integer nonlinear programming problems. By analyzing the structure of the problem, we provide optimality conditions based reformulation and computing scheme for both optimistic and pessimistic cases.
Our second study focuses on bilevel optimization with uncertainty and develops robust bilevel optimization (RBO) models along with solution methods. We first study single-stage RBO problems and provide solution methods to deal with different types of uncertainties. For single-stage RBO with discrete uncertainty set, we develop a novel cut-and-branch algorithm. We then study two-stage RBO problems, which involve wait-and-see decisions. We provide two basic models and their variations, as well as column-and-constraint generation algorithms to exactly handle uncertainties.
Finally, we apply our proposed methods to wind farm capacity expansion problem and optimal decision tree problem. In the first application, we formulate the wind farm investment problem into a two-stage RBO model and solve it by a proposed column-and-constraint generation algorithm. In the second application, we develop a new mixed-integer programming (MIP) based formulation to construct an optimal classification tree. We improve the generalizability of the model through a data-driven hyperparameter tuning approach in the bilevel optimization framework.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
13 June 2023 |
| Date Type: |
Publication |
| Defense Date: |
13 December 2022 |
| Approval Date: |
13 June 2023 |
| Submission Date: |
5 April 2023 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
143 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Swanson School of Engineering > Industrial Engineering |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
bilevel optimization, robust optimization, sustainable energy, interpretable artificial intelligence |
| Date Deposited: |
13 Jun 2023 14:11 |
| Last Modified: |
13 Jun 2024 05:00 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/44427 |
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