TY - GEN AU - Rao S.S. AU - Kumar N. TI - Engineering Optimization SN - 9789357461238 PY - 2024/// PB - Wiley India N2 - 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 ER -