Download or read book Conceptual Engineering Design and Optimization Methodologies Using Geometric Programming written by Berk Öztürk and published by . This book was released on 2018 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric 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.
Download or read book Optimization Concepts and Applications in Engineering written by Ashok D. Belegundu and published by Cambridge University Press. This book was released on 2019-06-06 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Organizations and businesses strive toward excellence, and solutions to problems are based mostly on judgment and experience. However, increased competition and consumer demands require that the solutions be optimum and not just feasible. Theory leads to algorithms. Algorithms need to be translated into computer codes. Engineering problems need to be modeled. Optimum solutions are obtained using theory and computers, and then interpreted. Revised and expanded in its third edition, this textbook integrates theory, modeling, development of numerical methods, and problem solving, thus preparing students to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multi-objective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate courses in optimization design and for practicing engineers.
Download or read book Structural Optimization written by A. Borkowski and published by Springer Science & Business Media. This book was released on 1990-01-31 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Geometric Programming written by Mordecai Avriel and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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.
Download or read book Geometric Programming for Design Equation Development and Cost Profit Optimization with illustrative case study problems and solutions Third Edition written by Robert Creese and published by Springer Nature. This book was released on 2022-05-31 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric 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.
Download or read book Design Optimization written by John Gero and published by Elsevier. This book was released on 2012-12-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design Optimization deals with the application of the ideas of optimization to design, taking as its central theme the notion that design can be treated as a goal-seeking, decision-making activity. Emphasis is on design optimization rather than on optimization techniques. This book consists of nine chapters, each focusing on a particular class of design optimization and demonstrating how design optimization problems are formulated and solved. The applications range from architecture and structural engineering to mechanical engineering, chemical engineering, building design and layout, and siting policy. The first five chapters are all concerned with design problems where it is convenient to express the goals in a single objective or criterion to be optimized. In particular, optimal space planning and shape optimization of structures are discussed, along with approximation concepts for optimum structural design; application of nonlinear programming to design; and generalized Steiner network problems in engineering design. The last four chapters focus on multicriteria programming; multicriteria optimization for engineering and architectural design; and a system for integrated optimal design. This monograph will be of interest to designers and others concerned with the use of optimization concepts and tools in design optimization.
Download or read book Geometric Programming for Design and Cost Optimization written by Robert C. Creese and published by Morgan & Claypool Publishers. This book was released on 2009-10-26 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: There 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.
Download or read book Global and Robust O for Engineering Design written by Berk Öztürk and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In anticipation of future aerospace design problems becoming increasingly coupled, complex and risky, this thesis provides a new perspective for dealing with design challenges using structured mathematical optimization. The proposed methods inject mathematical rigor into engineering design methods while keeping practical concerns for conceptual design in focus.
Download or read book Principles of Optimal Design written by Panos Y. Papalambros and published by Cambridge University Press. This book was released on 2017-01-09 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design optimization is a standard concept in engineering design, and in other disciplines which utilize mathematical decision-making methods. This textbook focuses on the close relationship between a design problem's mathematical model and the solution-driven methods which optimize it. Along with extensive material on modeling problems, this book also features useful techniques for checking whether a model is suitable for computational treatment. Throughout, key concepts are discussed in the context of why and when a particular algorithm may be successful, and a large number of examples demonstrate the theory or method right after it is presented. This book also contains step-by-step instructions for executing a design optimization project - from building the problem statement to interpreting the computer results. All chapters contain exercises from which instructors can easily build quizzes, and a chapter on 'principles and practice' offers the reader tips and guidance based on the authors' vast research and instruction experience.
Download or read book Optimization Concepts and Applications in Engineering written by Ashok D. Belegundu and published by Cambridge University Press. This book was released on 2011-03-28 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this revised and enhanced second edition of Optimization Concepts and Applications in Engineering, the already robust pedagogy has been enhanced with more detailed explanations, an increased number of solved examples and end-of-chapter problems. The source codes are now available free on multiple platforms. It is vitally important to meet or exceed previous quality and reliability standards while at the same time reducing resource consumption. This textbook addresses this critical imperative integrating theory, modeling, the development of numerical methods, and problem solving, thus preparing the student to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multiobjective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. It is ideal for advanced undergraduate or graduate courses and for practising engineers in all engineering disciplines, as well as in applied mathematics.
Download or read book Optimization for Engineering Systems written by Ralph W. Pike and published by Van Nostrand Reinhold Company. This book was released on 1986 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization Methods for Engineering Design written by Richard L. Fox and published by . This book was released on 1971 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Engineering Design Optimization written by Joaquim R. R. A. Martins and published by Cambridge University Press. This book was released on 2021-11-18 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based 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.
Download or read book Global and Robust Optimization for Engineering Design written by Berk Öztürk and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a need to adapt and improve conceptual design methods through better optimization, in order to address the challenge of designing future engineered systems. Aerospace design problems are tightly-coupled optimization problems, and require all-at-once solution methods for design consensus and global optimality. Although the literature on design optimization has been growing, it has generally focused on the use of gradient-based and heuristic methods, which are limited to local and low-dimensional optimization respectively. There are significant benefits to leveraging structured mathematical optimization instead. Mathematical optimization provides guarantees of solution quality, and is fast, scalable, and compatible with using physics-based models in design. More importantly perhaps, there has been a wave of research in optimization and machine learning that provides new opportunities to improve the engineering design process. This thesis capitalizes on two such opportunities. The first opportunity is to enable efficient all-at-once optimization over constraints and objectives that use arbitrary mathematical primitives. This work proposes a constraint sampling and learning approach for global optimization, leveraging developments in machine learning and mixed-integer optimization. More specifically, the feasible space of intractable constraints is sampled using existing and novel design of experiments methods, and learned using optimal classification trees with hyperplanes (OCT-Hs). OCT-Hs describe union-of-polyhedra approximations of intractable constraints, which are solved efficiently using commercial solvers to find near-feasible and near-optimal solutions to the global optimization problem. The constraints are then checked and the solution is repaired using projected gradient methods, ensuring feasibility and local optimality. The method is first tested on synthetic examples, where it finds the global optima for 9 out of 11 benchmarks, and high-performing solutions otherwise. Then it is applied to two real-world problems from the aerospace literature, and especially to a satellite on-orbit servicing problem that cannot be addressed via other global optimization methods. These applications demonstrate that decision tree driven optimization provides efficient, practical and optimal solutions to difficult global optimization problems present in aerospace design as well as other domains, regardless of the form of the underlying constraints. The second opportunity is to optimize designs affected by parametric uncertainty in a tractable and deterministic manner, while providing guarantees of constraint satisfaction. Inspired by the wealth of literature on robust optimization, and specifically on robust geometric programming, this thesis proposes and implements robust signomial programming to solve engineering design problems under uncertainty. The methods are tested on a conceptual aircraft design problem, demonstrating that robust signomial programs are sufficiently general to address engineering design problems, solved efficiently by commercial solvers, and result in designs that protect deterministically against uncertain parameter outcomes from predefined sets. In addition, robust designs are found to be less conservative than designs with margins; robust aircraft demonstrate 9% better average performance than aircraft designed with margins over the same scenarios, while providing guarantees of constraint feasibility. In anticipation of future aerospace design problems becoming increasingly coupled, complex and risky, this thesis provides a new perspective for dealing with design challenges using structured mathematical optimization. The proposed methods inject mathematical rigor into engineering design methods while keeping practical concerns for conceptual design in focus.
Download or read book Criteria and Methods of Structural Optimization written by Andrzej M Brandt and published by Springer Science & Business Media. This book was released on 1987-06-30 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve all those who are interested in structural opti mization, whether they work in this field or study it for other purposes. Rapid growth of interest in the cognitive aspects of optimization and the increas ing demands that the present day engineer has to meet in modern design have created the need of a monographic treatment of the subject. The vast number and wide range of structural optimization problems formulated and investigated in the last twenty years call for an attempt to sum up the pres ent state of knowledge in this domain and to outline the directions of its further development. The present authors undertook this task, hoping that the result would stimulate further work towards finding new methods and solutions and increasing the range of applications of the optimization methods to structural design. The immediate aim of the book is to present the basic criteria and methods of optimization and to provide a reference guide to the most important publications in the field. 'The book consists of fourteen chapters. Chapter 1 introduces the basic concepts, definitions and assumptions relating to structural optimization. Chapter 2 gives the foundations of optimization for minimum elastic strain potential or maximum rigidity, and sets a basis for optimization of bar, plate and lattice structures. Chapter 3 presents criteria of strength design and their applications to plane structures.
Download or read book Engineering Design by Geometric Programming written by Clarence Zener and published by John Wiley & Sons. This book was released on 1971 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multidisciplinary Design Optimization Supported by Knowledge Based Engineering written by Jaroslaw Sobieszczanski-Sobieski and published by John Wiley & Sons. This book was released on 2017-05-08 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multidisciplinary Design Optimization supported by Knowledge Based Engineering supports engineers confronting this daunting and new design paradigm. It describes methodology for conducting a system design in a systematic and rigorous manner that supports human creativity to optimize the design objective(s) subject to constraints and uncertainties. The material presented builds on decades of experience in Multidisciplinary Design Optimization (MDO) methods, progress in concurrent computing, and Knowledge Based Engineering (KBE) tools. Key features: Comprehensively covers MDO and is the only book to directly link this with KBE methods Provides a pathway through basic optimization methods to MDO methods Directly links design optimization methods to the massively concurrent computing technology Emphasizes real world engineering design practice in the application of optimization methods Multidisciplinary Design Optimization supported by Knowledge Based Engineering is a one-stop-shop guide to the state-of-the-art tools in the MDO and KBE disciplines for systems design engineers and managers. Graduate or post-graduate students can use it to support their design courses, and researchers or developers of computer-aided design methods will find it useful as a wide-ranging reference.
