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Advances in Discrete Optimization: F...

Fakhimi, Ramin.

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Advances in Discrete Optimization: From Truss Design Optimization to Quantum Computing Optimization.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Advances in Discrete Optimization: From Truss Design Optimization to Quantum Computing Optimization./
作者:	Fakhimi, Ramin.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2024,
面頁冊數:	178 p.
附註:	Source: Dissertations Abstracts International, Volume: 85-07, Section: B.
Contained By:	Dissertations Abstracts International85-07B.
標題:	Engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30688660
ISBN:	9798381376753

Advances in Discrete Optimization: From Truss Design Optimization to Quantum Computing Optimization.
Fakhimi, Ramin.

Advances in Discrete Optimization: From Truss Design Optimization to Quantum Computing Optimization. - Ann Arbor : ProQuest Dissertations & Theses, 2024 - 178 p.

Source: Dissertations Abstracts International, Volume: 85-07, Section: B.

Thesis (Ph.D.)--Lehigh University, 2024.

This item must not be sold to any third party vendors.

This manuscript explores optimization problems and spans two distinct but interconnected parts. The first part delves into the practical application of mathematical optimization techniques with a particular focus on discrete structural design optimization problems, notorious for their combinatorial, nonlinear, and non-convex nature. The second part focuses on quantum computing, examining its potential for solving optimization problems.Chapter 3 presents two mathematical formulations for structural design optimization. These formulations are designed to handle discrete cross-sectional areas. The chapter proposes rigorous mathematical approaches to address the stability of structural configurations. We leverage the linear and bilinear nature of these problems to exploit the rescaling properties of both the design and auxiliary variables, while also extending the superposition principle to accommodate nonlinear stress constraints.In Chapter 4, we introduce the neighborhood search mixed-integer linear optimization (NS-MILO) method. This method is developed based on the insights gained from the preceding chapter, leveraging the specific characteristics of the optimization problems discussed. This chapter comprises a comprehensive set of experiments designed to provide compelling empirical evidence regarding the effectiveness of the proposed solution methodologies.In Chapter 5, our focus shifts to a challenging problem known as the max k-cut problem, a problem of considerable complexity within combinatorial optimization. Within this chapter, we undertake a systematic examination of various optimization formulations tailored to address this problem while rigorously assessing their practical efficacy. Additionally, the chapter extends its exploration beyond traditional optimization formulations, delving into the domain of binary quadratic optimization (BQO) formulations and quantum-inspired methodologies. These novel approaches represent an intriguing avenue for addressing the max k-cut problem, harnessing insights from quantum computing principles without making any claims of surpassing classical methods.Finally, Chapter 6 delves into inexact interior-point methods for linear optimization problems, considering the potential integration of quantum linear system solvers. It highlights the advantages and challenges posed by quantum solvers and investigates iterative refinement techniques to enhance their performance. 

ISBN: 9798381376753Subjects--Topical Terms:

586835
Engineering.
Subjects--Index Terms:

Discrete optimization

Advances in Discrete Optimization: From Truss Design Optimization to Quantum Computing Optimization.
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