On Circuit-Based Optimization Methods
Guardado en:
| Publicado en: | ProQuest Dissertations and Theses (2025) |
|---|---|
| Autor principal: | |
| Publicado: |
ProQuest Dissertations & Theses
|
| Materias: | |
| Acceso en línea: | Citation/Abstract Full Text - PDF |
| Etiquetas: |
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
MARC
| LEADER | 00000nab a2200000uu 4500 | ||
|---|---|---|---|
| 001 | 3204181577 | ||
| 003 | UK-CbPIL | ||
| 020 | |a 9798314889114 | ||
| 035 | |a 3204181577 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 66569 |2 nlm | ||
| 100 | 1 | |a Morrison, Angela Rose | |
| 245 | 1 | |a On Circuit-Based Optimization Methods | |
| 260 | |b ProQuest Dissertations & Theses |c 2025 | ||
| 513 | |a Dissertation/Thesis | ||
| 520 | 3 | |a Our motivation for studying optimization, and in particular linear programming, stems from a desire for efficient problem-solving methods. Over the years, this desire has led to the development of tailored combinatorial algorithms for specific problem instances such as the min-mean cycle canceling algorithm for min-cost flow problems as well as general solvers such as the primal Simplex method and interior point methods. These algorithms utilize underlying structures of the problem instance such as the traversal of edges in primal Simplex or identifying cycles in a network. In an effort to expand the use of such techniques in problem-solving methods, we study the effect and integration of circuits or elementary vectors in optimization methods. Circuits are generalizations of edge directions which enables them to serve as justification for lower bounds on many edge results. This fact lends itself to our interest in research areas such as circuit diameters and circuit augmentation schemes. Each of these relates to a generalization of edge results and methods such as combinatorial diameters and edge walks performed during primal Simplex. In this thesis, we explore circuits from various angles to expand the current connections between network flow problems, polyhedral theory, and circuit augmentation scheme implementation. In the network flows setting, we characterize the circuits of the so-called pseudoflow polyhedron and the type of circuit walks performed by three combinatorial algorithms. For polyhedral theory, we determine the circuit diameter of a generalized parking-function polytope as well as the circuit imbalance of the polytope constructed from rank inequality constraints which appear in many graph theoretical problems. Further, we study refinements to the so-called polyhedral model, which is the backbone of the current best steepest-descent circuit augmentation scheme implementation. Finally, we look at a real-world application of network flows and combinatorial algorithms through our development of an algorithm for evacuation planning. In this work, we modify a time-expanded network based on hazard information and use it to create an evacuation plan for the affected community. | |
| 653 | |a Applied mathematics | ||
| 653 | |a Mathematics | ||
| 653 | |a Operations research | ||
| 773 | 0 | |t ProQuest Dissertations and Theses |g (2025) | |
| 786 | 0 | |d ProQuest |t ProQuest Dissertations & Theses Global | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3204181577/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3204181577/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |