Engineering Optimization: Theory and Practice, 5ed (An Indian Adaptation)

Preface to the Adapted Edition

Preface

Acknowledgment

About the Author

1 Introduction to Optimization

1.1 Introduction

1.2 Historical Development

1.3 Optimization in Engineering Practices

1.4 Defining an Optimization Problem

1.5 Classification of Optimization Problems

1.6 Tools and Techniques for Optimization

1.7 Engineering Optimization Literature

1.8 Challenges in Solving Optimization Problems

1.9 Solutions Using MATLAB

2 Classical Optimization Techniques

2.1 Introduction

2.2 Single-Variable Optimization

2.3 Multivariable Optimization with No Constraints

2.4 Multivariable Optimization with Equality Constraints

2.5 Multivariable Optimization with Inequality Constraints

2.6 Convex Programming Problem

3 Linear Programming I: Graphical and Simplex Method

3.1 Introduction

3.2 Applications of Linear Programming

3.3 Standard Form of a Linear Programming Problem

3.4 Geometry of Linear Programming Problems

3.5 Definitions and Theorems

3.6 Solution of a System of Linear Simultaneous Equations

3.7 Pivotal Reduction of a General System of Equations

3.8 Motivation of the Simplex Method

3.9 Simplex Algorithm

3.10 Two Phases of the Simplex Method

3.11 Big M Method

3.12 Solutions Using MATLAB

4 Linear Programming II: Additional Topics and Extensions

4.1 Introduction

4.2 Revised Simplex Method

4.3 Duality in Linear Programming

4.4 Decomposition Principle

4.5 Sensitivity or Postoptimality Analysis

4.6 Transportation Problem

4.7 Karmarkar’s Interior Method

4.8 Quadratic Programming

4.9 Solutions Using MATLAB

5 Nonlinear Programming I: One-Dimensional Minimization Methods

5.1 Introduction

5.2 Unimodal Function

5.3 Unrestricted Search

5.4 Exhaustive Search

5.5 Dichotomous Search

5.6 Interval Halving Method

5.7 Fibonacci Method

5.8 Golden Section Method

5.9 Comparison of Elimination Methods

5.10 Quadratic Interpolation Method

5.11 Cubic Interpolation Method

5.12 Direct Root Methods

5.13 Practical Considerations

5.14 Solutions Using MATLAB

6 Nonlinear Programming II: Unconstrained Optimization Techniques

6.1 Introduction

6.2 Random Search Methods

6.3 Grid Search Method

6.4 Univariate Method

6.5 Pattern Directions

6.6 Hooke and Jeeves’ Method

6.7 Powell’s Method

6.8 Simplex Method

6.9 Gradient of a Function

6.10 Steepest Descent (Cauchy) Method

6.11 Conjugate Gradient (Fletcher–Reeves) Method

6.12 Newton’s Method

6.13 Marquardt Method

6.14 Quasi-Newton Methods

6.15 Davidon–Fletcher–Powell Method

6.16 Broyden–Fletcher–Goldfarb–Shanno Method

6.17 Test Functions

6.18 Solutions Using MATLAB

7 Nonlinear Programming III: Constrained Optimization Techniques

7.1 Introduction

7.2 Characteristics of a Constrained Problem

7.3 Random Search Methods

7.4 Complex Method

7.5 Sequential Linear Programming

7.6 Basic Approach in the Methods of Feasible Directions

7.7 Zoutendijk’s Method of Feasible Directions

7.8 Rosen’s Gradient Projection Method

7.9 Generalized Reduced Gradient Method

7.10 Sequential Quadratic Programming

7.11 Transformation Techniques

7.12 Basic Approach of the Penalty Function Method

7.13 Interior Penalty Function Method

7.14 Convex Programming Problem

7.15 Exterior Penalty Function Method

7.16 Extrapolation Techniques in the Interior Penalty Function Method

7.17 Extended Interior Penalty Function Methods

7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints

7.19 Penalty Function Method for Parametric Constraints

7.20 Augmented Lagrange Multiplier Method

7.21 Checking the Convergence of Constrained Optimization Problems

7.22 Test Problems

7.23 Solutions Using MATLAB

8 Geometric Programming

8.1 Introduction

8.2 Posynomial

8.3 Unconstrained Minimization Problem

8.4 Solution of an Unconstrained Geometric Programming Program using Differential Calculus

8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic–Geometric Inequality

8.6 Primal–dual Relationship and Sufficiency Conditions in the Unconstrained Case

8.7 Constrained Minimization

8.8 Solution of a Constrained Geometric Programming Problem

8.9 Primal and Dual Programs in the Case of Less-than Inequalities

8.10 Geometric Programming with Mixed Inequality Constraints

8.11 Applications of Geometric Programming

9 Dynamic Programming

9.1 Introduction

9.2 Multistage Decision Processes

9.3 Concept of Suboptimization and Principle of Optimality

9.4 Computational Procedure in Dynamic Programming

9.5 Example Illustrating the Calculus Method of Solution

9.6 Example Illustrating the Tabular Method of Solution

9.7 Conversion of a Final Value Problem into an Initial Value Problem

9.8 Linear Programming as a Case of Dynamic Programming

9.9 Continuous Dynamic Programming

9.10 Engineering Applications

10 Integer Programming

10.1 Introduction

10.2 Graphical Representation

10.3 Gomory’s Cutting Plane Method

10.4 Balas’ Algorithm for Zero–One Programming Problems

10.5 Integer Polynomial Programming

10.6 Branch-and-Bound Method

10.7 Sequential Linear Discrete Programming

10.8 Generalized Penalty Function Method

11 Stochastic Programming

11.1 Introduction

11.2 Basic Concepts of Probability Theory

11.3 Formulating Stochastic Optimization Problems

11.4 Stochastic Linear Programming

11.5 Stochastic Nonlinear Programming

11.6 Stochastic Geometric Programming

11.7 Applications and Examples of Stochastic Programming

12 Optimal Control and Optimality Criteria Methods

12.1 Introduction

12.2 Calculus of Variations

12.3 Optimal Control Theory

12.4 Optimality Criteria Methods

13 Methods of Optimization using Algorithm

13.1 Introduction

13.2 Genetic Algorithms

13.3 Simulated Annealing

13.4 Particle Swarm Optimization

13.5 Ant Colony Optimization

13.6 Optimization of Fuzzy Systems

13.7 Neural-Network-Based Optimization

14 Metaheuristic Optimization Methods

14.1 Definitions

14.2 Metaphors Associated with Metaheuristic Optimization Methods

14.3 Details of Representative Metaheuristic Algorithms

15 Practical Aspects of Optimization

15.1 Introduction

15.2 Reduction of Size of an Optimization Problem

15.3 Fast Reanalysis Techniques

15.4 Derivatives of Static Displacements and Stresses

15.5 Derivatives of Eigenvalues and Eigenvectors

15.6 Derivatives of Transient Response

15.7 Sensitivity of Optimum Solution to Problem Parameters

16 Multilevel and Multiobjective Optimization

16.1 Introduction

16.2 Multilevel Optimization

16.3 Parallel Processing

16.4 Multi Objective Optimization

16.5 Solutions Using MATLAB

17 Solution of Optimization Problems Using MATLAB

17.1 Introduction

17.2 Solution of General Nonlinear Programming Problems

17.3 Solution of Linear Programming Problems

17.4 Solution of LP Problems Using Interior Point Method

17.5 Solution of Quadratic Programming Problems

17.6 Solution of One-Dimensional Minimization Problems

17.7 Solution of Unconstrained Optimization Problems

17.8 Solution of Constrained Optimization Problems

17.9 Solution of Binary Programming Problems

17.10 Solution of Multiobjective Problems

References and Bibliography

Problems

A Convex and Concave Functions

B Some Computational Aspects of Optimization

B.1 Choice of Method

B.2 Comparison of Unconstrained Methods

B.3 Comparison of Constrained Methods

B.4 Availability of Computer Programs

B.5 Scaling of Design Variables and Constraints

B.6 Computer Programs for Modern Methods of Optimization

C Introduction to MATLAB®

C.1 Features and Special Characters

C.2 Defining Matrices in MATLAB

C.3 Creating m-Files

C.4 Optimization Toolbox

D Simulation

D.1 Definition

D.2 Types of Simulation

D.3 Steps in the Simulation Process

D.4 Advantages and Disadvantages of Simulation

D.5 Stochastic Simulation and Random Numbers

D.6 Simulation of Inventory Problems

D.7 Simulation of Queueing Problems

D.8 Simulation of Maintenance Problems

D.9 Applications of Simulation

E Network Analysis and Methods

E.1 Introduction

E.2 Minimum Spanning Tree

E.3 Shortest Path Problem