In countries like the US, public school systems function through school districts, which are geographical areas where schools share the same administrative structure and are often coterminous with the boundary of a city or a county. School districts play an important role in the functioning of society. In a well-run school district with safe and well-functioning schools, graduating enough students can enhance the quality of life in its area. Conversely, a poorly run district may cause growth in the area to be far less than surrounding areas, or even a decline in population over time. To promote the efficient functioning of the school district, the boundaries of public schools are redrawn from time to time by the school board/planning officials. In the majority of the cases, this process of redrawing the school boundaries, also called school redistricting or school boundary formation, is done manually by the planners and involves hand-drawn maps. Given the rapid advancements in GIS made in the last decade and the availability of high-quality geospatial data, we opine that an objective treatment of the school redistricting problem by a data-driven model can assist the school board/ decision-makers by providing them with automated plans. These automated plans may serve as possible suggestions to the planners, who can adapt them to prepare their own plans in the way they see fit based on their subjective knowledge and expertise. In this dissertation, we propose algorithmic techniques for solving the problem of (school) redistricting, which is an NP-hard problem. We primarily investigate optimization-based algorithms for solving the problem. Our approaches include (i) clustering, (ii) local search, and (iii) memetic algorithms. We also propose ways of solving the problem using exact methods and fair redistricting techniques based on ethical considerations. The techniques developed here are generic enough to be applied to other redistricting problems with some degree of modification in the objective function and constraint-handling techniques. The source code and corresponding datasets are available at https://github.com/subhodipbiswas/schoolredistricting. / Doctor of Philosophy / In many countries, public school systems function through school districts, which are geographical areas where schools share the same administrative structure and are often coterminous with the boundary of a city or a county. To promote efficient functioning of the school district, the boundaries of public schools are redrawn from time to time by the school board/planning officials. In the majority of the cases, this process of redrawing the school boundaries, also called school redistricting, is done manually by the planners and involves hand-drawn maps. Given the rapid advancements in GIS made in the last decade and the availability of high-quality geospatial data, we opine that an objective treatment of the school redistricting problem by a data-driven model can assist the school board/ decision-makers by providing them with automated plans. In this presentation, we propose algorithmic techniques for solving the school redistricting problem. Our approaches include (i) clustering, (ii) local search, and (iii) memetic algorithms. We also show that MCMC-based techniques can aid in enabling exact methods to operate on this problem. Lastly, we briefly highlight ethical considerations involved in the process of school redistricting and throw light on some ways to devise more ethically-aware strategies for doing school redistricting. The results indicate that the proposed methods could be a valuable decision-making tool for school officials.

<p> A solution to an industrial problem of designing a hydrostatic drive system for logging vehicles is presented. A computer program using Land and Doig's method of Branch and Bound Mixed Integer Programming is used to obtain an optimal solution to the problem. A comprehensive users guide to allow the use of the program by unsophisticated users is provided. </p> <p> An attempted alternate method of solution using the Gomory method of Integer Programming is presented and reasons for its failure discussed. </p> / Thesis / Master of Engineering (MEngr)

The digital transformation of engineering design processes is essential for the aerospace industry to remain competitive in the global market. Multidisciplinary design optimization (MDO) frameworks play a crucial role in this transformation by integrating various engineering disciplines and enabling the optimization of complex spacecraft structures. Since the design team consists of multiple entities from different domains working together to build the final product, the design and analysis tools must be readily available and compatible. An integrated approach is required to handle the problem's complexity efficiently. Additionally, most aerospace structures are made from composite panels. It is challenging to optimize such panels as they require the satisfaction of constraints where the design ply thicknesses and orientations can only take discrete values prescribed by the manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient because they provide sub-optimal solutions when the number of design variables is large. They also are computationally expensive in handling the combinatorial nature of the problem. To overcome these challenges, this work proposes a two-fold solution that integrates multiple disciplines and efficiently optimizes composite spacecraft structures by building a rapid design framework. The proposed model-based design framework for spacecraft structures integrates commercially available software from Siemens packages such as NX and HEEDS and open-source Python libraries. The framework can handle multiple objectives, constraint non-linearities, and discrete design variables efficiently using a combination of black-box global optimization algorithms and Mixed Integer Programming (MIP)-based optimization techniques developed in this work. Lamination parameters and MIP are adopted to optimize composite panels efficiently. The framework integrates structural, thermal and acoustic analysis to optimize the spacecraft's overall performance while satisfying multiple design constraints. Its capabilities are demonstrated in optimizing a small spacecraft structure for required structural performance under various static and dynamic loading conditions when the spacecraft is inside the launch vehicle or operating in orbit. / Doctor of Philosophy / The design of new spacecraft takes several years and requires significant resources. The primary design objective is to minimize spacecraft mass/cost while satisfying the mission requirements. This is done by altering the structure's geometric and material properties. Most spacecraft panels are made from composite materials where the orientations of fiber paths and the thickness of the panel determine its strength and stiffness. Finding the best values for these parameters cannot be done efficiently using existing optimization algorithms, as several combinations of orientations can give a similar performance which can be subpar. In this dissertation, mathematical programming is adopted for fast evaluation of optimum panel properties, thereby saving a significant amount of resources compared to conventional techniques. Moreover, the requirements that govern the design process are handled one at a time in an organization. This leads to discrepancies in the various teams' designs that satisfy all requirements. A framework is built to integrate all requirements to account for their conflicting nature and quickly give the best possible spacecraft structural design configuration.

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