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A Study on Multilevel Optimization Subject to Uncertainty

Xu, Liang (2023) A Study on Multilevel Optimization Subject to Uncertainty. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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Status: Unpublished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:
CreatorsEmailPitt UsernameORCID
Xu, Lianglix21@pitt.edulix210000-0003-2890-4872
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairZeng, Bobzeng@pitt.edu
Committee MemberJiang, Danieldrjiang@pitt.edu
Committee MemberBidkhori, Hodabidkhori@pitt.edu
Committee MemberMao, Zhi-Hongzhm4@pitt.edu
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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