Committee Chair
Weerasena, Lakmali
Committee Member
Ebiefung, Aniekan; Bandara, Damitha; Ma, Ziwei
College
College of Engineering and Computer Science
Publisher
University of Tennessee at Chattanooga
Place of Publication
Chattanooga (Tenn.)
Abstract
This dissertation investigates decision-making methods in Uncertain Discrete Multi-objective Optimization Problems (UDMOPs), where uncertainty arises in both objective function and constraint coefficients. The study pursues three main goals: (1) constructing sensitivity regions in the objective space to handle objective-wise uncertainty, (2) constructing sensitivity regions in the decision space to handle feasibility uncertainties, and (3) developing methods to sort, group, and prune uncertain solutions based on their similarity. Each goal proposes a method to explore uncertain solutions and quantify their level of uncertainty. Based on this, solutions are classified as low and high-risk solutions, according to the Decision-Maker (DM)'s preferences and risk tolerance. The proposed approaches employ stochastic optimization techniques to identify low and high-risk solutions, enabling risk-averse decision-making. Numerical experiments, including a real-world application, and benchmark comparisons, show that low or high-risk solutions under uncertainty can outperform the efficient solutions from deterministic model. Overall, the methods provide a more consistent and informative decision support system for DMs under uncertainty.
Acknowledgments
I would like to thank the Department of Mathematics and the Graduate School at UTC for providing me with the opportunity to pursue my Ph.D. I sincerely appreciate the support from the Departments of Mathematics and Computer Science, as well as the National Science Foundation (LEAPS-MPS) under Grant #2137622, for funding my assistantship. I am especially thankful to my advisor, Dr. Lakmali Weerasena, for her invaluable knowledge, encouragement, and continuous guidance throughout this research. I am grateful to mycommittee members, Dr. Aniekan Ebiefung, Dr. Damitha Bandara, and Dr. Ziwei Ma, for their insightful feedback and support. In addition, I would like to thank all my teachers, and especially to Dr. W.B. Daundasekera, Dr. Christopher L. Cox and Dr. Francesco Barioli for their contributions and encouragement during this journey. Last but not least, I extend my heartfelt appreciation to my family, my late father, K. G. B. Aththanayake, whose greatest wish was to see this accomplishment; my mother Anula Ranaraja; my siblings Janaka and Nadeesha; my husband Rukman; and my beloved son Sasiru, who stood by me through every challenge. Their unwavering love, support and belief in me have been my greatest source of strength and motivation.
Degree
Ph. D.; A dissertation submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Doctor of Philosophy.
Date
8-2025
Subject
Decision making--Mathematical models; Sensitivity theory (Mathematics); Stochastic programming; Uncertainty--Mathematical models
Document Type
Doctoral dissertations
DCMI Type
Text
Extent
xv, 214 leaves
Language
English
Rights
http://rightsstatements.org/vocab/InC/1.0/
License
http://creativecommons.org/licenses/by/4.0/
Date Available
8-31-2026
Recommended Citation
Aththanayake, Chathuri Malee, "Decision-making methods under Uncertainty in Discrete Multi-objective Optimization" (2025). Masters Theses and Doctoral Dissertations.
https://scholar.utc.edu/theses/1016
Department
Dept. of Mathematics