Author: Elizabeth Jordan
Date/Time: July 10th, 2025 at 1:00 PM EST
Location: EGR-2164, Glenn Martin Hall
Committee Members:
- Professor Shapour Azarm, Chair
- Professor Vikrant Aute
- Professor Yancy Diaz-Mercado
- Professor Katrina Groth
- Professor Johan Larsson
- Professor P.K. Kannan, Dean’s Representative
Title of Dissertation: Scenario Generation-Based Single- and Multi-Objective Robust Optimization under Fixed and Variable Interval Uncertainty
Abstract: Multi-objective robust optimization is a prominent field of optimization that deals with problems that have multiple, at least partially conflicting objectives, are subject to some constraints, and contain uncertainty. The main goal of these problems is to obtain solutions that are optimal and robust – i.e. relatively insensitive (have uncertainty robustness) to any realization of the uncertain parameters.
This dissertation presents three new methods for solving single- and multi-objective robust optimization (SORO and MORO) problems under fixed and variable uncertainty. The proposed methods share an underlying single-level iterative framework and handle the uncertainty robustness via a scenario generation technique.
The first method is the original sampling-based approach (OSB-MORO) which uses a multi-objective genetic algorithm solver to solve the optimization problem, and then handles the robustness aspect by sampling the fixed uncertainty space to find the worst-case realization and iteratively shrink the feasible domain to find the robust solution. This approach is very general in nature and can be applied to a variety of problems that have fixed interval uncertainty. However, sometimes the computational burden of solving MORO problems can be infeasible, or analyzing the trade-offs between the objectives can be challenging. To address this issue, MORO problems can be reformulated as single-objective problems – namely, via utility functions. The utility-based sampling-based MORO approach (USB-MORO) is an extension of the OSB-MORO approach, where the multiple objectives are converted to a single scalar via a multi-attribute utility function. This makes it possible to apply efficient single-objective optimization techniques, rather than the expensive multi-objective genetic algorithm solver. Although the utility approach can help solve the MORO problem more efficiently, it does not solve the issue of dealing with expensive functions – i.e. functions that are based on computationally costly simulations. The second method (SSB-MORO) aims to improve the computational cost of the OSB-MORO approach by integrating an online surrogate model. A Kriging model is developed for all the functions of the problem, and is updated as the MORO algorithm progresses. The previous methods mentioned can only handle fixed interval uncertainties – i.e. the uncertainty bounds are known a priori and do not change. However, in many real-world applications the uncertainty may be dependent on the decision variables, hence the uncertainty bounds become variable. The third method (SB-SORO-DDU) aims to address this issue by extending the OSB-MORO approach to account for decision-dependent uncertainty for single-objective problems.
The key contributions in this dissertation are:
1) a single-level, sequential sampling-based single- and multi-objective robust optimization method for problems with fixed interval uncertainty (OSB-MORO);
2) a sampling-based multi-objective robust optimization method with integrated online surrogates for problems with fixed interval uncertainty (SSB-MORO); and
3) a sampling-based single-objective robust optimization method for problems with decision-dependent (or variable) interval uncertainty (SB-SORO-DDU).