BA, Oberlin College, 2013, Computer Science

This honors thesis describes the algorithmic abstraction of a problem modeling a swarm of Mars rovers, where many "agents" must together achieve a goal. The algorithmic formulation of this problem is based on the traveling salesman problem (TSP), and so in this thesis I offer a review of the mathematical technique of linear programming in the context of its application to the TSP, an overview of some variations of the TSP and algorithms for approximating and solving them, and formulations without solutions of two novel TSP variations which are useful for modeling the original problem.

Committee: Tom Wexler (Advisor) Subjects: Computer Science; Mathematics

Master of Science, The Ohio State University, 1966, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1965, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1969, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1963, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1963, Graduate School

Committee: Not Provided (Other) Subjects:

Master of Science, The Ohio State University, 1968, Graduate School

Committee: Not Provided (Other) Subjects:

Undergraduate Honors Program, Malone University, 2024, Honors Thesis

Objectives: University course timetabling is a complex task involving the allocation of instructors, timeslots, and rooms to courses while adhering to various constraints. Our objective is to develop a decision-support system that can streamline and optimize the course timetabling process at Malone University. Methods: We present a novel three-stage binary integer linear programming model designed to address the specific timetabling challenges faced by the Department of Natural Sciences at Malone University. This model is implemented in Excel and solved using OpenSolver, an Excel add-in for linear programming. Results: Utilizing real data from Malone University's Department of Natural Sciences for the Fall 2024 semester, our proposed model demonstrates efficient and effective automation of course timetabling through successful generation of a timetable.

Committee: Kyle Calderhead (Advisor); Adam Klemann (Committee Member); Shawn Campbell (Committee Member) Subjects: Applied Mathematics; Operations Research

Master of Engineering, Case Western Reserve University, 2024, EECS - Computer and Information Sciences

As Quantum Computers continue to increase in size, throughput has not increased proportionally. Researchers have begun exploring ways of parallelizing circuit execution. Due to the noisiness of quantum computers, this requires new algorithms for efficient resource allocation, qubit mapping, and scheduling. We improve on existing greedy algorithms by formulating the mapping search as a Binary Integer Non-Linear Programming (BINLP) problem. We model practical constraints and propose new heuristics for determining the goodness of a mapping. We observe similar fidelity compared to Qiskit's transpiler for circuit cutting and throughput benchmarks. We observe greater fidelity over Qiskit's transpiler for dense QAOA ansatzes. We find that parallel circuit cutting provides greater fidelity than full-circuit execution. We also propose a scheduling algorithm for parallelizing circuits of different lengths and shot counts. Our algorithm achieves a lower makespan for time and number-of-shots for diverse workloads as well as lower per-job runtimes in all cases.

Committee: Vipin Chaudhary (Committee Chair); Mehmet Koyutürk (Committee Member); Shuai Xu (Committee Member) Subjects: Computer Science

Master of Science (MS), Ohio University, 2023, Industrial and Systems Engineering (Engineering and Technology)

Human trafficking (HT) is a form of contemporary slavery that affects individuals in every state of the United States. Despite the existence of government and non-profit rehabilitation services, HT-affected individuals often miss out due to improper resource allocation. To address this issue, we propose an optimization model that efficiently allocates resources to rehabilitate and reintegrate HT-affected individuals where they are most needed. Our strategy uses a Mixed Integer Linear Programming model to optimize the net societal value (NSV) gained from offering support services while considering the three stages of HT-affected people's healing path, including victim, survivor, and thriver. This model determines the optimal type, quantity, and location of services while also integrating HT risk scores that account for the risk of HT in those areas. Our model's efficacy is demonstrated in an Ohio case study, allocating housing, detoxification, and food services across the state's eighty-eight counties and three stages of the healing path of HT-affected individuals. Through Monte Carlo Simulation in the solution approach, uncertain demand is accounted for, leading to improved NSV under such conditions. Moreover, we illustrate the impact of an increased budget, showcasing extended service reach and allocation possibilities. Our work aims to support decision-makers in efficiently allocating resources to rehabilitate and reintegrate HT-affected individuals effectively.

Committee: Felipe Aros-Vera Dr. (Advisor); Vardges Melkonian Dr. (Committee Member); Omar Ibrahim Alhawari Dr. (Committee Member); Tao Yuan Dr. (Committee Member) Subjects: Industrial Engineering; Operations Research; Rehabilitation

Bachelor of Science (BS), Ohio University, 2021, Mathematics

Historically, redistricting has been a process ridden with political manipulation in which politicians “gerrymander” districts to achieve a competitive advantage in future elections. However, the process of redistricting can be aided significantly by mathematical models that prioritize key characteristics of a “fair” district. This paper details one such integer linear programming model implemented in AMPL that ensures just that—a fair district. To ensure fairness, the model produces districts that reflect the political distribution of the state, with no party favored to win more districts than their share of the statewide vote. At the same time, the model prioritizes even population distribution while constraining for contiguous and compact districts. This model is tested and evaluated on data from the state of Ohio and details some possible variations and future directions that allow the model to adapt to other states and goals.

Committee: Vardges Melkonian (Advisor) Subjects: Computer Science; Mathematics; Operations Research; Political Science

Master of Science, The Ohio State University, 2020, Animal Sciences

Careful management of P balance on farms is multi-faceted and necessary to reduce the environmental burden caused by P pollution. Dairy operations are uniquely poised to closely control dietary inputs as well as grow a portion of feed dietary inputs, offering opportunities for efficiency in P cycling through the operation. We developed a mathematical programming model capable of simultaneously optimizing diets with different weights for least cost and least on farm P-balance. Using OpenSolver (v.2.9.0, opensolver.org), three objective functions were individually optimized to: i) minimize the diet cost; ii) minimize the excess of P balance in the system, computed as the difference between P excreted and P uptake by forage production on-farm; and iii) minimize the weighted deviations from the values of the two previously optimized objective functions. The trade-offs between the two goals set by a weighting scheme allowed the identification of a set of diets that all met the NRC (2001) requirements while having different costs and determining different P balances on the farm. Initial reductions in P were generally accompanied by increased forage fed, increased on-farm corn silage production, and decreased legume hay production. These optimizations suggest a potential use of weighted goal programming as a technique to identify diets that allow a reduction in on-farm P balance with limited effects on whole farm feed cost.

Committee: Luis Moraes (Advisor); William Weiss (Committee Member); Maurice Eastridge (Committee Member) Subjects: Animal Sciences

Master of Science (M.S.), University of Dayton, 2020, Mechanical Engineering

This thesis presents an investigation of the suitability of tensegrity aircraft wing concepts and compares their simulated structural performance to a baseline conventional wing structure. Tensegrity systems, which consist of arrangements of struts and cables, are appealing for their structural efficiency, enabling lightweight structures with each member loaded in tension or compression. Of specific interest, tensegrity systems may provide a pathway to morphing aircraft structures through the actuation of cables. The present study compares two tensegrity-based wing designs to the aluminum Van's RV-4 aircraft rib/spar wing structure, chosen as the baseline performance case. Aerodynamic loading conditions are derived which simulate a 2g pullup maneuver and a 1g pushover, intended to interrogate the structures under characteristic positive and negative loading. The first tensegrity concept, developed with design judgment, is configured by merging known unit cells and is shown to yield deflections and strain energies comparable to the conventional wing at a fraction of its weight. The second tensegrity design, in contrast, is developed by application of a topology optimization algorithm, intended to minimize the weight with maximum stress and strain energy constraints. The topology-optimized wing has similar structural performance at slightly less weight than the designer-developed tensegrity wing. Additionally, a scaled down physical prototype of the designer-developed tensegrity wing was designed and fabricated, providing valuable insight into practical hurdles of tensegrity construction.

Committee: David Myszka (Committee Chair); Andrew Murray (Committee Member); James Joo (Committee Member) Subjects: Aerospace Engineering; Engineering; Mechanical Engineering

MS, University of Cincinnati, 2019, Engineering and Applied Science: Computer Science

As the applications of Unmanned Aerial Vehicles (UAVs) are becoming more and more common, it is necessary to address their inherent technological challenges so as to make them safe and more useful. Designing an eective UAV path planning algorithm is essential in all UAV missions. The UAV path planning strategy depends on its application eld. The application specic constraints also need to be satised along with UAV mobility aspects for a successful UAV mission. This thesis aims to solve the UAV Path planning problem for the scenarios when the UAVs are used for remote sensing and data communication applications. The thesis consists of two pieces of work. The rst piece of work addresses and solves a UAV path planning problem when time windows and data ooading constraints are involved, which is very typical in a data communication application scenario. A Genetic Algorithm based approach is used to solve the problem in realistic time limits. In the second piece of work, an evaluation of the capabilities of currently available robotics and network simulators is conducted to determine their suitability to be used as a simulator for multimedia data communication over UAV networks. An ideal simulator for this purpose should have simulation capabilities for image/video capture, image processing, encoding/decoding and quality measurement along with flight and network simulation. A new simulation framework is proposed and tested by combining X-Plane, M3WSN and EvalVid simulator platforms to achieve an end to end simulation of a UAV multimedia data communication scenario.

Committee: Rui Dai Ph.D. (Committee Chair); Dharma Agrawal D.Sc. (Committee Member); Manish Kumar Ph.D. (Committee Member) Subjects: Computer Science

Master of Science, University of Toledo, 2017, Civil Engineering

In the United States, aging of the transportation infrastructures increased the need of M&R activities significantly. Further, as the consequence of economic and population growth, increasing travel demand accelerated the rate of deterioration along with the congestion and poor safety. At most of the highway agencies, budget allocation decisions are often based on the historical proportions or empirical relations. However, the public awareness and involvement in the sustainable development demand the accountability of such decision- making. Compounded with the budget constraints and rise in the highway improvement costs, highway agencies have a need of efficient and most cost-effective decision-making. Thus, development of a data-driven tool as a senior decision support system is essential for short-term as well as long-term planning, specifically, in a limited available resource scenario such as of now. This thesis presents the development and implementation of a trade-off analysis tool in Transportation Asset Management (TAM). The tool is capable of budget allocation and optimal treatment policy determination, based on the budget versus asset performance plots. For a given budget level, the corresponding performance of the asset network is determined using the linear programming optimization with the objective of average network condition maximization. The optimization model essentially consists of an asset deterioration model. The deterioration rates are predicted based on the historical condition data using the Markov model. At the network level, the macroscopic model is adopted where each decision variables represents a specific proportion of the asset network. For each decision variable, future condition prediction models are developed. An annual budget scenario can be analyzed with the flexibility to vary the treatment unit costs, allowable treatments, treatment average life, the budget allocation between asset types, and the span of the analysis period. (open full item for complete abstract)

Committee: Eddie Chou Dr. (Committee Chair); Liangbo Hu Dr. (Committee Member); Habib Kaake Dr. (Committee Member) Subjects: Civil Engineering

PhD, University of Cincinnati, 2017, Business: Business Administration

In the electric utility industry, it could be challenging to adjust supply to match demand due to large generator ramp up times, high generation costs and insufficient in-house generation capacity. Demand response (DR) is a technique for adjusting the demand for electric power instead of the supply. Direct Load Control (DLC) is one of the ways to implement DR. DLC program participants sign up for power interruption contracts and are given financial incentives for curtailing electricity usage during peak demand time periods. This dissertation studies a DLC program for residential air conditioners using mathematical optimization models. First, we develop a model that determines what contract parameters to use in designing contracts between the provider and residential customers, when to turn which power unit on or off and how much power to cut during peak demand hours. The model uses information on customer preferences for choice of contract parameters such as DLC financial incentives and energy usage curtailment. In numerical experiments, the proposed model leads to projected cost savings of the order of 20%, compared to a current benchmark model used in practice. We also quantify the impact of factors leading to cost savings and study characteristics of customers picked by different contracts. Second, we study a DLC program in a macro economic environment using a Computable General Equilibrium (CGE) model. A CGE model is used to study the impact of external factors such as policy and technology changes on different economic sectors. Here we differentiate customers based on their preference for DLC programs by using different values for price elasticity of demand for electricity commodity. Consequently, DLC program customers could substitute demand for electricity commodity with other commodities such as transportation sector. Price elasticity of demand is calculated using a novel methodology that incorporates customer preferences for DLC contracts from the first m (open full item for complete abstract)

Committee: Uday Rao Ph.D. (Committee Chair); Debashis Pal Ph.D. (Committee Member); R. Kenneth Skinner Ph.D. (Committee Member); Yan Yu Ph.D. (Committee Member); Jeffrey Camm Ph.D. (Committee Member) Subjects: Operations Research

Master of Science, University of Akron, 2017, Applied Mathematics

Combinatorial methods have proved to be useful in generating relaxations of polytopes in various areas of mathematical programming. In this work, we propose a discrete-integer linear programming model for a recent version of the Phylogeny Estimation Problem (PEP), known as the Balanced Minimal Evolution Method (BME). We begin by examining an object known as the Balanced Minimal Evolution Polytope and several classes of geometric constraints that result in its relaxation. We use this information to develop the linear program and propose two Branch and Bound algorithms to solve the model. The second algorithm takes advantage of a heuristic known as a large neighborhood search. We provide experimental results for both algorithms, using perfect and noisy data, as well as suggestions for further improvement.

Committee: Stefan Forcey Dr. (Advisor); Malena Espanol Dr. (Committee Member); Patrick Wilber Dr. (Committee Member) Subjects: Applied Mathematics; Biology

Doctor of Philosophy, The Ohio State University, 1975, Graduate School

Committee: Not Provided (Other) Subjects: Business Administration

Doctor of Philosophy, The Ohio State University, 1971, Graduate School

Committee: Not Provided (Other) Subjects: Geography

Doctor of Philosophy, The Ohio State University, 1971, Graduate School

Committee: Not Provided (Other) Subjects: Economics