Geometric programming - an approach to optimizing engineering design
Author: Theodore S. Glassman
Publisher:
Published: 1968
Total Pages:
ISBN-13:
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Geometric Programming for Design Equation Development and Cost/Profit Optimization (with illustrative case study problems and solutions), Third Edition
Author: Robert Creese
Publisher: Springer Nature
Published: 2022-05-31
Total Pages: 194
ISBN-13: 3031793765
DOWNLOAD EBOOKGeometric Programming is used for cost minimization, profit maximization, obtaining cost ratios, and the development of generalized design equations for the primal variables. The early pioneers of geometric programming—Zener, Duffin, Peterson, Beightler, Wilde, and Phillips—played important roles in its development. Five new case studies have been added to the third edition. There are five major sections: (1) Introduction, History and Theoretical Fundamentals; (2) Cost Minimization Applications with Zero Degrees of Difficulty; (3) Profit Maximization Applications with Zero Degrees of Difficulty; (4) Applications with Positive Degrees of Difficulty; and (5) Summary, Future Directions, and Geometric Programming Theses & Dissertations Titles. The various solution techniques presented are the constrained derivative approach, condensation of terms approach, dimensional analysis approach, and transformed dual approach. A primary goal of this work is to have readers develop more case studies and new solution techniques to further the application of geometric programming.
Optimum Design of Structures
Author: Lahbib Chibani
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 165
ISBN-13: 3642838901
DOWNLOAD EBOOKThis book presents the integrated approach of analysis and optimal design of structures. This approach, which is more convenient than the so-called nested approach, has the difficulty of generating a large optimization problem. To overcome this problem a methodology of decomposition by multilevel is developed. This technique, which is also suitable for implementation on parallel processing computers, has the advantage of reducing the size of the optimization problem generated. The geometric programming for both equality and inequality constraints is used in the optimization.
Structural Optimization,
Author: A. Borkowski
Publisher: Springer Science & Business Media
Published: 1990-01-31
Total Pages: 422
ISBN-13: 9780306418624
DOWNLOAD EBOOKAdvances in Geometric Programming
Author: Mordecai Avriel
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 457
ISBN-13: 1461582857
DOWNLOAD EBOOKIn 1961, C. Zener, then Director of Science at Westinghouse Corpora tion, and a member of the U. S. National Academy of Sciences who has made important contributions to physics and engineering, published a short article in the Proceedings of the National Academy of Sciences entitled" A Mathe matical Aid in Optimizing Engineering Design. " In this article Zener considered the problem of finding an optimal engineering design that can often be expressed as the problem of minimizing a numerical cost function, termed a "generalized polynomial," consisting of a sum of terms, where each term is a product of a positive constant and the design variables, raised to arbitrary powers. He observed that if the number of terms exceeds the number of variables by one, the optimal values of the design variables can be easily found by solving a set of linear equations. Furthermore, certain invariances of the relative contribution of each term to the total cost can be deduced. The mathematical intricacies in Zener's method soon raised the curiosity of R. J. Duffin, the distinguished mathematician from Carnegie Mellon University who joined forces with Zener in laying the rigorous mathematical foundations of optimizing generalized polynomials. Interes tingly, the investigation of optimality conditions and properties of the optimal solutions in such problems were carried out by Duffin and Zener with the aid of inequalities, rather than the more common approach of the Kuhn-Tucker theory.
Geometric Programming for Communication Systems
Author: Mung Chiang
Publisher: Now Publishers Inc
Published: 2005
Total Pages: 172
ISBN-13: 9781933019093
DOWNLOAD EBOOKRecently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results. Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.
Conceptual Engineering Design and Optimization Methodologies Using Geometric Programming
Author: Berk Öztürk
Publisher:
Published: 2018
Total Pages: 68
ISBN-13:
DOWNLOAD EBOOKGeometric programs (GPs) and other forms of convex optimization have recently experienced a resurgence due to the advent of polynomial-time solution algorithms and improvements in computing. Observing the need for fast and stable methods for multidisciplinary design optimization (MDO), previous work has shown that geometric programming can be a powerful framework for MDO by leveraging the mathematical guarantees and speed of convex optimization. However, there are barriers to the implementation of optimization in design. In this work, we formalize how the formulation of non-linear design problems as GPs facilitates design process. Using the principles of pressure and boundedness, we demonstrate the intuitive transformation of physics- and data-based engineering relations into GP-compatible constraints by systematically formulating an aircraft design model. We motivate the difference-of-convex GP extension called signomial programs (SPs) in order to extend the scope and fidelity of the model. We detail the features specific to GPkit, an object-oriented GP formulation framework, which facilitate the modern engineering design process. Using both performance and mission modeling paradigms, we demonstrate the ability to model and design increasingly complex systems in GP, and extract maximal engineering intuition using sensitivities and tradespace exploration methods. Though the methods are applied to an aircraft design problem, they are general to models with continuous, explicit constraints, and lower the barriers to implementing optimization in design.
Geometric Programming for Design and Cost Optimization
Author: Robert C. Creese
Publisher: Morgan & Claypool Publishers
Published: 2009-10-26
Total Pages: 70
ISBN-13: 9781608452620
DOWNLOAD EBOOKThere are numerous techniques of optimization methods such as linear programming, dynamic programming, geometric programming, queuing theory, statistical analysis, risk analysis, Monte Carlo simulation, numerous search techniques, etc. Geometric programming is one of the better tools that can be used to achieve the design requirements and minimal cost objective. Geometric programming can be used not only to provide a specific solution to a problem, but it also can in many instances give a general solution with specific design relationships. These design relationships based upon the design constants can then be used for the optimal solution without having to resolve the original problem. This fascinating characteristic appears to be unique to geometric programming. The purpose of this text is to introduce manufacturing engineers, design engineers, manufacturing technologists, cost engineers, project managers, industrial consultants and finance managers to the topic of geometric programming.
Engineering Design Optimization
Author: Joaquim R. R. A. Martins
Publisher: Cambridge University Press
Published: 2021-11-18
Total Pages: 653
ISBN-13: 110898861X
DOWNLOAD EBOOKBased on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.
Geometric Programming for Design and Cost Optimization 2nd edition
Author: Robert Creese
Publisher: Springer Nature
Published: 2022-05-31
Total Pages: 128
ISBN-13: 3031793307
DOWNLOAD EBOOKGeometric programming is used for design and cost optimization, the development of generalized design relationships, cost ratios for specific problems, and profit maximization. The early pioneers of the process - Zener, Duffin, Peterson, Beightler, Wilde, and Phillips -- played important roles in the development of geometric programming. There are three major areas: 1) Introduction, History, and Theoretical Fundamentals, 2) Applications with Zero Degrees of Difficulty, and 3) Applications with Positive Degrees of Difficulty. The primal-dual relationships are used to illustrate how to determine the primal variables from the dual solution and how to determine additional dual equations when the degrees of difficulty are positive. A new technique for determining additional equations for the dual, Dimensional Analysis, is demonstrated. The various solution techniques of the constrained derivative approach, the condensation of terms, and dimensional analysis are illustrated with example problems. The goal of this work is to have readers develop more case studies to further the application of this exciting tool. Table of Contents: Introduction / Brief History of Geometric Programming / Theoretical Considerations / The Optimal Box Design Case Study / Trash Can Case Study / The Open Cargo Shipping Box Case Study / Metal Casting Cylindrical Riser Case Study / Inventory Model Case Study / Process Furnace Design Case Study / Gas Transmission Pipeline Case Study / Profit Maximization Case Study / Material Removal/Metal Cutting Economics Case Study / Journal Bearing Design Case Study / Metal Casting Hemispherical Top Cylindrical Side Riser\\Case Study / Liquefied Petroleum Gas (LPG) Cylinders Case Study / Material Removal/Metal Cutting Economics with Two Constraints / The Open Cargo Shipping Box with Skids / Profit Maximization Considering Decreasing Cost Functions of Inventory Policy / Summary and Future Directions / Thesis and Dissertations on Geometric Programming
