Date of Award
5-2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
School of Mathematical and Statistical Sciences
Committee Chair/Advisor
Dr. Margaret M. Wiecek, Dr. Herve Kerivin
Committee Member
Dr. Matthew Saltzman
Committee Member
Dr. Cameron Turner
Abstract
This dissertation addresses decision-making under multiple conflicting objectives and uncertainty by studying two-stage robust multiobjective optimization problems. Such problems arise naturally in many real-world applications where decisions must be made before and after uncertain parameters are revealed, and where trade-offs between competing objectives must be carefully balanced.
A new class of problems, termed Two-Stage Robust Multiobjective Linear Problems (TSRMOLPs), is introduced along with appropriate solution concepts, including first-stage robust efficient solutions and two-stage robust Pareto outcomes. To enable tractable analysis, a scalarization framework based on scalarizing support functions is developed. Among various approaches, the weighted-sum scalarization is identified as the most suitable for preserving the two-stage structure, although it yields sub-robust efficient solutions. This leads to reformulating the original problem as a parametric single-objective optimization problem, which facilitates the generation of a set of sub-robust solutions.
To solve the resulting problem, a novel algorithmic framework, termed Parametric Benders Decomposition (pBD), is proposed. This method integrates parametric optimization with Benders, decomposition and extends classical approaches to handle multiobjective and robust features. Theoretical properties of the method are established, including the construction of parametric master and subproblems, generation of optimality and feasibility cuts, and finite convergence.
The effectiveness of the proposed methodology is demonstrated through numerical experiments, in which approximate first-stage sub-robust efficient sets and corresponding second-stage Pareto sets are computed and closely match the analytical solutions when available. The approach is further applied to a vehicle drivetrain and design optimization problem, illustrating its practical relevance. In addition, simulated data is used to identify second-best Pareto solutions, highlighting the importance of practical alternatives in engineering applications.
Finally, the dissertation develops theoretical insights into multiobjective optimization under uncertainty by introducing Pareto and efficient envelopes for collections of parametric problems. Their structural properties are analyzed, particularly in the linear case, and alternative formulations are explored, revealing complex geometric characteristics.
Overall, this work provides a unified theoretical and computational framework for two-stage robust multiobjective optimization, along with practical algorithms and applications, and opens several directions for future research.
Recommended Citation
Goswami, Rakhi, "On Solving Two-Stage Robust Multiobjective Linear Programs with Uncertainties" (2026). All Dissertations. 4278.
https://open.clemson.edu/all_dissertations/4278