Introduction to Optimum Design

5th Edition - November 15, 2023
Author: Jasbir Singh Arora
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 1 8 3 2 0 - 5
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 1 8 3 2 1 - 2

Introduction to Optimum Design, Fifth Edition is the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course… Read more

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Introduction to Optimum Design, Fifth Edition is the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level within engineering departments of all disciplines, but primarily within mechanical, aerospace and civil engineering. The basic approach of the text presents an organized approach to engineering design optimization in a rigorous yet simplified manner, illustrating various concepts and procedures with simple examples and demonstrating their applicability to engineering design problems. Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text. Excel and MATLAB are featured as learning and teaching aids. This new edition has been enhanced with new or expanded content in such areas as reliability‐based optimization, metamodeling, design of experiments, robust design, nature-inspired metaheuristic search methods, and combinatorial optimizaton.

Cover image
Title page
Table of Contents
Copyright
Dedication
Preface to Fifth Edition
Acknowledgments
Key symbols and abbreviations
Section I. The Basic Concepts
Chapter 1. Introduction to design optimization
1.1. The design process
1.2. Engineering design versus engineering analysis
1.3. Conventional versus optimum design process
1.4. Optimum design versus optimal control
1.5. Basic terminology and notation
Chapter 2. Optimum design problem formulation
2.1. The problem formulation process
2.2. Design of a can
2.3. Design of an insulated spherical tank
2.4. Design of sawmill operation
2.5. Design of a two-bar bracket
2.6. Design of a cabinet—three formulations
2.7. Minimum-weight tubular column design—two formulations
2.8. Minimum-cost cylindrical tank design
2.9. Design of coil springs
2.10. Minimum-weight design of a symmetric three-bar truss
2.11. A general mathematical model for optimum design
2.12. Development of problem formulation for practical applications
Exercises for Chapter 2
Chapter 3. Graphical solution method and basic optimization concepts
3.1. Graphical solution process
3.2. Use of Mathematica® for graphical optimization
3.3. Use of MATLAB® for graphical optimization
3.4. Design problem with multiple solutions
3.5. Design problem with unbounded solutions
3.6. Infeasible design problem
3.7. Graphical solution for the minimum-weight tubular column
3.8. Graphical solution for a beam design problem
Exercises for Chapter 3
Chapter 4. Optimum design concepts: optimality conditions
4.1. Definitions of global and local minima
4.2. Review of some basic calculus concepts
4.3. Concepts of necessary and sufficient conditions
4.4. Optimality conditions: unconstrained problem
4.5. Necessary conditions: equality-constrained problem
4.6. Necessary conditions: general constrained problem
4.7. Postoptimality analysis: physical meaning of Lagrange multipliers
4.8. Global optimality
4.9. Engineering design examples
Exercises for Chapter 4
Chapter 5. More on optimum design concepts: optimality conditions
5.1. Karush–Kuhn–Tucker (KKT) necessary conditions: an alternate form
5.2. Irregular points
5.3. Second-order conditions for constrained optimization
5.4. Second-order conditions for rectangular beam design problem
5.5. Duality in nonlinear programming
Exercises for Chapter 5
Section II. Numerical Methods for Continuous Variable Optimization
Chapter 6. Optimum design: numerical solution process and Excel Solver
6.1. Introduction to numerical search methods
6.2. Optimum design: numerical aspects of problem formulation
6.3. Numerical solution process for optimum design
6.4. Excel Solver: an introduction
6.5. Excel Solver for unconstrained optimization problems
6.6. Excel Solver for linear programming problems
6.7. Excel Solver for nonlinear programming: optimum design of springs
6.8. Optimum design of plate girders using Excel Solver
Exercises for Chapter 6
Chapter 7. Optimum design with MATLAB®
7.1. Introduction to Optimization Toolbox
7.2. Unconstrained optimum design problems
7.3. Constrained optimum design problems
7.4. Optimum design examples with MATLAB®
Exercises for Chapter 7∗
Chapter 8. Linear programming methods for optimum design
8.1. Linear functions
8.2. Definition of a standard linear programming (LP) problem
8.3. Basic concepts related to linear programming (LP) problems
8.4. Calculation of basic solutions of linear system of equations Ax = b
8.5. Simplex method for linear programming (LP) problems
8.6. Two-phase Simplex method for linear programming (LP) problems—artificial variables
8.7. Postoptimality analysis of linear programming (LP) problem
Exercises for Chapter 8
Chapter 9. More on linear programming (LP) methods for optimum design
9.1. Simplex method: derivation
9.2. An alternate Simplex method of linear programming (LP)
9.3. Duality in linear programming
9.4. Simplex method and Karush–Kuhn–Tucker (KKT) optimality conditions
9.5. Quadratic programming (QP) problems
Exercises for Chapter 9
Chapter 10. Numerical methods for unconstrained optimum design
10.1. Optimum design: general concepts of search methods
10.2. Optimum design: a general iterative algorithm
10.3. Descent direction and convergence of algorithms for optimum design
10.4. Step size determination: reduction to function of one variable
10.5. Numerical methods to compute step size
10.6. Search direction determination: steepest-descent method
10.7. Search direction determination: conjugate gradient method
10.8. Other conjugate gradient methods
Exercises for Chapter 10
Chapter 11. More on numerical methods for unconstrained optimum design
11.1. More on step size determination: inexact line search
11.2. More on the steepest-descent method
11.3. Scaling of design variables
11.4. Search direction determination: Newton method
11.5. Search direction determination: quasi-Newton methods
11.6. Engineering applications of unconstrained methods
11.7. Solution of constrained problem using unconstrained optimization methods
11.8. Rate of convergence of algorithms
11.9. Direct search methods—no need for gradients
Exercises for Chapter 11
Chapter 12. Numerical methods for constrained optimum design
12.1. Basic concepts related to numerical methods
12.2. Linearization of constrained problem
12.3. Sequential linear programming (SLP) algorithm
12.4. Sequential quadratic programming (SQP)
12.5. Search direction calculation: quadratic programming (QP) subproblem
12.6. Subproblem definition for step size calculation
12.7. Constrained steepest-descent (CSD) method
Exercises for Chapter 12
Chapter 13. More on numerical methods for constrained optimum design
13.1. Potential constraint strategy
13.2. Inexact step size calculation
13.3. Bound-constrained optimization
13.4. Sequential quadratic programming (SQP) methods
13.5. Other numerical optimization methods
13.6. Solution of quadratic programming (QP) subproblem
Exercises for Chapter 13
Chapter 14. Practical engineering design optimization applications
14.1. Formulation of practical design optimization problems
14.2. Gradient evaluation of implicit functions
14.3. Issues in practical design optimization
14.4. Use of general-purpose software
14.5. Optimum design: two-member frame with out-of-plane loads
14.6. Optimum design: three-bar structure for multiple performance requirements
14.7. Optimal control of systems by nonlinear programming
14.8. Optimum design of steel tension members
14.9. Optimum design of steel compression members
14.10. Optimum design of steel members for flexure
14.11. Optimum design of telecommunication poles
14.12. Alternative formulations for structural optimization problems
14.13. Alternative formulations for time-dependent problems
Exercises for Chapter 14∗
Section III. Advanced and Modern Topics on Optimum Design
Chapter 15. Discrete variable optimum design: concepts and methods
15.1. Basic concepts and definitions
15.2. Branch-and-bound methods (BBM)
15.3. Integer programming (IP)
15.4. Sequential linearization methods
15.5. Simulated annealing (SA)
15.6. Dynamic rounding-off method
15.7. Neighborhood search method
15.8. Methods for linked discrete variables
15.9. Selection of a method
15.10. Adaptive numerical method for discrete variable optimization
Exercises for Chapter 15
Chapter 16. Global optimization: concepts and methods
16.1. Fundamentals of global optimization
16.2. Deterministic global optimization methods: an introduction
16.3. Stochastic global optimization methods: an introduction
16.4. Two local-global stochastic optimization methods
16.5. Numerical performance of global optimization methods
Exercises for Chapter 16
Chapter 17. Nature-inspired metaheuristic search methods
17.1. Nature-inspired metaheuristic search methods: an overview
17.2. Genetic algorithms (GAs) for optimum design
17.3. Differential evolution algorithm (DEA)
17.4. Ant colony optimization (ACO)
17.5. Particle swarm optimization (PSO)
17.6. Harmony search (HS) algorithm
17.7. Colliding bodies optimization (CBO)
Exercises for Chapter 17∗
Chapter 18. Multiobjective optimum design: concepts and methods
18.1. Problem definition
18.2. Terminology and basic concepts
18.3. Multiobjective genetic algorithms
18.4. Weighted sum method
18.5. Weighted min-max method
18.6. Weighted global criterion method
18.7. Lexicographic method
18.8. Bounded objective function method
18.9. Goal programming
18.10. Selection of methods
Exercises for Chapter 18
Chapter 19. Design under uncertainty: introduction to reliability-based design optimization
19.1. Reliability-based design optimization (RBDO): basic concept
19.2. Reliability-based design optimization (RBDO): background material
19.3. Reliability index for a limit state constraint
19.4. Linear constraint function: probability of failure
19.5. Nonlinear constraint function: probability of failure—first-order second-moment (FOSM) method
19.6. Advanced first-order second-moment (AFOSM) method
19.7. A formulation for reliability-based design optimization (RBDO)
19.8. Reliability-based design optimization (RBDO): literature overview
Chapter 20. Metamodels for design optimization: response surface method
20.1. What are metamodels?
20.2. Response surface method
20.3. Quadratic response surface approximations
20.4. Selection of sample points using orthogonal arrays
20.5. Discrete variable design with orthogonal arrays
Chapter 21. Robust design and optimization: an introduction
21.1. What is a robust design?
21.2. Robust design and optimization: preliminaries
21.3. Robust design: optimization formulation
21.4. Robust design optimization: formulation summary
21.5. Robust design: Taguchi method
Chapter 22. Design of experiments: an introduction
22.1. What is design of experiments (DOE)?
22.2. Design of experiments (DOE): terminology
22.3. Design of experiments (DOE): full factorial design
22.4. Design of experiments (DOE): fractional factorial design
22.5. Design of experiments (DOE): central composite design (CCD)
22.6. Design of experiments (DOE): Box–Behnken design (BBD)
22.7. Design of experiments (DOE): Latin hypercube design (LHD)
22.8. Design of experiments (DOE): concluding remarks
Appendix A. Vector and matrix algebra
Appendix B. Sample computer programs
References
Answers to selected exercises
Index

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Introduction to Optimum Design

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Jasbir Singh Arora