All ETDs from UAB

Advisory Committee Chair

Murat M Tanik

Advisory Committee Members

Leon Jololian

Karthikeyan Lingasubramanian

Arie Nakhmani

Buren Earl Wells

Document Type


Date of Award


Degree Name by School

Doctor of Philosophy (PhD) School of Engineering


This thesis studies Combinatorial Optimization Problems (COPs) on graphs that integrate uncertainty in the problem definition. We focus on Probabilistic Combinatorial Optimization Problems (PCOPs), where uncertainty is associated with the presence or absence of subsets of vertices that describe the problem. In general, combinatorial optimization problems are formulated as a Mixed Integer Linear Programming (MILP) model. This process aims to convert elements of decision-making into variables considering related constraints and choosing an objective function. In such cases, it is recommended to define an objective function that is a linear function with linear constraints. Also, when practical problems are formulated as combinatorial optimization models, one must often include logical implications. Yet, the Least Action Principle (LAP) of information theory has been exploited to achieve optimization goal using the least amount of resources. Therefore, we approach combinatorial optimization problems on graphs by modeling them with a noisy communication channel using the maximum independent set as a tool of the least action of information theory. Subsequently, we propose an information-theoretic modeling approach for a class of PCOP that transformable into bipartite graphs. Using the a priori approach, we construct a communication channel and obtain any sub-instance solution with the noisy communication model. This communication channel model is used to a portfolio optimization problem as a case study.

Included in

Engineering Commons



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