CONTENTS -- Preface -- List of Contributors -- Chapter 1 Introduction to Optimization Jasbir S. Arora -- 1. Introduction -- 2. Optimization Models -- 2.1. Optimization Models: Continuous Variables -- 2.2. Optimization Models: Mixed Variables -- 3. Optimality Conditions for Problem P -- 3.1. Definitions and General Concepts -- 3.2. Optimality Conditions for the Unconstrained Problem -- 3.3. Optimality Conditions for the Constrained Problem -- 3.4. Global Optimality and Convexity -- 3.5. Lagrange Multipliers -- 3.5.1. Changes in Constraint Limit -- 3.5.2. Scaling of Cost Function. -- 3.5.3. Scaling of Constraints -- 4. Basic Concepts Related to Computational Algorithms -- 4.1. A Basic Gradient-based Algorithm -- 4.2. Constraint Normalization -- 4.3. Potential Constraint Strategy -- 4.4. Descent Function -- 4.5. Convergence of an Algorithm -- 4.6. Attributes of a Good Algorithm -- 5. Overview of Computational Algorithms -- 5.1. Gradient-based Algorithms -- 5.1.1. Linearization and Sequential Linear Programming -- 5.1.2. Sequential Quadratic Programming - SQP -- 5.1.3. Augmented Lagrangian Method -- 5.2. Algorithms for Discrete Variable Problems -- 5.3. Multiobjective Optimization -- 5.3.1. Terminology and Basic Concepts -- 5.3.2. Solution Methods -- 5.4. Algorithms for Global Solution -- 5.4.1. Deterministic Methods -- 5.4.2. Stochastic Methods -- 6. Concluding Remarks -- References -- Chapter 2 Optimization of Large Scale Systems José Herskovits, Evandro Goulart and Miguel Aroztegui -- 1. Introduction -- 2. Quasi-Newton Method for Nonlinear Optimization -- 2.1. Limited Memory Quasi-Newton Method -- 2.2. Sparse Quasi-Newton Matrices -- 2.3. Diagonal Quasi-Newton Matrices -- 3. The Feasible Arc Interior Point Algorithm -- 3.1. BFGS updating rule for constrained optimization -- 4. The Internal Linear Systems in FAIPA.

4.1. Solving the primal-dual systems -- 4.2. Solving the dual systems -- 5. Numerical Experiments -- 5.1. Results with a collection of test problems -- 5.2. Experiments with a structural optimization problem -- 6. Conclusions -- Acknowledgments -- References -- Chapter 3 Structural Optimization Using Evolutionary Computation Christopher M. Foley -- 1. Introduction -- 2. Optimization Problems and Complexity -- 3. Fundamentals of Optimal Design Using Evolutionary Computation -- 3.1. Objective Fitness -- 3.2. Genetic Algorithm -- 3.2.1. Individual Representation -- 3.2.2. Selection -- 3.2.3. Recombination -- 3.2.4. Mutation -- 3.2.5. Elitism -- 3.3. Evolution Strategy -- 3.3.1. Multi-Member Non-Recombinative Evolution Strategy -- 3.3.2. Recombinative Evolution Strategy -- 3.3.3. Self-Adaptive Evolution Strategy -- 4. Applications in Structural Engineering -- 4.1. Bridge Maintenance and Management -- 4.2. Structural System and Component Optimization -- 4.2.1. Deterministic Structural Optimization (DSO) -- 4.2.2. Performance-Based Structural Optimization (PBSO) -- 4.2.3. Reliability-Based Structural Optimization (RBSO) -- 4.2.4. Miscellaneous Applications -- 4.3. Topology Optimization of Truss-Type Structures -- 4.4. Structural Control and Supplemental Damping -- 4.5. Damage Detection -- 4.6. Parameter, Model, or Structure Identification -- 4.7. Conceptual Design of Building Systems -- 4.8. Parallel Processing Applications -- 5. Other Sources of Information -- 6. Concluding Remarks -- Acknowledgments -- References -- Chapter 4 Multiobjective Optimization: Concepts and Methods Achille Messac and Anoop A. Mullur -- 1. Introduction to Multiobjective Optimization -- 1.1. Why Multiobjective Optimization? -- 1.2. Scope of the Chapter -- 2. Concept of Pareto Optimality -- 2.1. Multiobjective Optimization Problem Statement -- 2.2. Pareto Optimal Solutions.

2.3. Local and Global Pareto Optimality -- 2.4. The Pareto Frontier -- 2.5. Pareto Frontier in Multiple Dimensions -- 3. Multiobjective Optimization Solution Techniques -- 3.1. Methods Requiring Designer Preferences -- 3.1.1. Weighted Sum -- 3.1.2. Compromise Programming -- 3.1.3. Weighted Min-Max Method -- 3.1.4. Goal Programming -- 3.1.5. Physical Programming -- 3.2. Pareto Set Generation Methods -- 3.2.1. Weighted Criteria Methods -- 3.2.2. o-Constraint Method -- 3.2.3. Normal Boundary Intersection Method -- 3.2.4. Normal Constraint Method -- 3.2.5. Multiobjective Genetic Algorithms -- 3.3. Choosing an Appropriate Solution Approach -- 4. Multiobjective Optimization in Practice -- 4.1. Decision Making Tools -- 4.1.1. Pareto Filtering Techniques -- 4.1.2. Smart Pareto Representation -- 4.2. Objective Function Normalization -- 4.3. Pareto Set Accuracy Metrics -- 5. Applications and Recent Advances in Multiobjective Optimization -- 5.1. Recent Advances -- 6. Summary and Concluding Remarks -- 7. Problems -- References -- Chapter 5 Shape Optimization Tae Hee Lee -- 1. Introduction -- 2. Definition of Shape Optimization Problem -- 3. Shape Optimization Methods -- 3.1. Element Nodal Coordinate Method -- 3.2. Geometric Boundary Method -- 3.2.1. Definition of Shape Design Variable -- 3.2.2. Shape Optimization -- 4. Concluding Remarks -- References -- Chapter 6 Topology Optimization Martin P. Bendsoe and Ole Sigmund -- 1. Introduction -- 2. Problem Setting -- 2.1. The 0-1 Design Problem -- 2.2. Working with a Grey-scale: Interpolation Models -- 2.3. Interpreting Grey-scale: Material Models -- 3. Solution Methods -- 3.1. Computational Framework -- 3.1.1. FEM -- 3.1.2. Sensitivity Analysis -- 3.1.3. Optimization Algorithm -- 3.2. Finer Points -- 3.2.1. Geometry Control -- 3.2.2. Checkerboards -- 3.2.3. Hinges -- 4. Extensions -- 4.1. Geometrical Nonlinearity.

4.1.1. The Importance of Non-linear Modelling -- 4.1.2. Computational Issues -- 4.2. Design of Supports -- 5. Variations of the Theme -- 5.1. Mathematical Programming Issues -- 5.1.1. SAND Formulation -- 5.1.2. Mixed-integer Format -- 5.1.3. Stress Constraints -- 5.1.4. Other Algorithmic Approaches -- 5.2. Design of Articulated Mechanisms -- 5.3. Level-set Methods -- 6. From Theory to Product -- 6.1. Industrial Use of Topology Design -- 6.2. Nano-photonics -- 6.2.1. Wave Propagation Problems -- 6.2.2. A Z-bend in Photonics -- 7. Challenges in the Field -- 7.1. Multiphysics -- 7.2. Algorithms -- 7.3. Defining the Design -- Acknowledgments -- References -- Chapter 7 Shape Design Sensitivity Analysis of Nonlinear Structural Systems Nam Ho Kim -- 1. Introduction -- 2. Design Sensitivity Analysis of Nonlinear Elastic Problems -- 2.1. Total Lagrangian Formulation -- 2.1.1. Incremental Solution Procedure -- 2.1.2. Shape Sensitivity Formulation -- 2.2. Updated Lagrangian Formulation -- 2.2.1. Incremental Solution Procedure -- 2.2.2. Shape Sensitivity Formulation -- 3. Design Sensitivity Analysis of Elastoplastic Problems -- 3.1. Small Deformation Elastoplasticity -- 3.1.1. Incremental Solution Procedure -- 3.1.2. Shape Sensitivity Formulation -- 3.2. Finite Deformation Elastoplasticity -- 3.2.1. Incremental Solution Procedure -- 3.2.2. Shape Sensitivity Formulation -- 4. Design Sensitivity Analysis of Contact Problems -- 4.1. Contact Problems with the Rigid Surface -- 4.2. Design Sensitivity Analysis for Contact Problems -- 5. Numerical Examples -- 5.1. Shape Design Sensitivity Analysis of the Windshield Wiper Problem24 -- 5.2. Design Sensitivity Analysis of the Deepdrawing Problem54 -- 6. Conclusions and Outlook -- References -- Chapter 8 Optimal Control of Structures Satish Nagarajaiah and Sriram Narasimhan -- 1 Introduction.

2 State Space Representation and Transfer Functions -- 3 Time Domain Methods: LQR and LQG -- 3.1 LQR Method -- 3.2 Optimal Estimation -- 3.3 LQG Method -- 4 Control in the Frequency Domain -- 4.1 H2 and H∞ Norms -- 4.2 Frequency Domain Representation -- 4.3 Equivalence of LQG and H2 Optimal Control -- 5 H∞ Optimal Control -- 6 A Brief note on Robustness of H2 and H∞ Methods -- 7 Concluding Remarks -- 8 Acknowledgments -- References -- Chapter 9 Optimization of Systems for Acoustics Ashok D. Belegundu and Michael D. Grissom -- 1. Introduction -- 2. Definitions and Introductory Concepts -- 3. Optimization Problem Formulation -- 3.1. Objective Function Formulation -- 3.2. Procedure for Optimal Design of Quiet Structures -- 4. Governing Equations and Solution Methods -- 4.1. Vibration Analysis of Base Structure (Without Modifications) -- 4.2. Analysis of Modified Structure by the Impedance Method -- 4.3. A Disadvantage with the Impedance Method For Estimating Broadband Response -- 4.4. Reduced Eigenvalue Reanalysis Method -- 4.5. Sound Power Calculations -- 4.6. Determination of Initial Modal Participation Factors -- 5. Non-gradient Optimizers Used -- 6. Selected Example Problems -- 6.1. Optimization of a Half-Cylindrical Shell -- 6.2. Multicriteria Optimization of a Pressure Vessel -- 6.3. Thin Air Cavity Attached to a Structure -- 7. Summary -- Acknowledgments -- Suggested References -- Chapter 10 Design Optimization Under Uncertainty Sankaran Mahadevan -- 1. Introduction -- 2. Reliability Analysis -- 3. Reliability-Based Optimization -- 4. Multi-objective Optimization -- 5. Concluding Remarks -- Acknowledgments -- References -- Chapter 11 Design Optimization with Uncertainty, Life-cycle Performance and Cost Considerations Dan M. Frangopol, Kurt Maute and Min Liu -- 1. Introduction -- 2. Formulation of RBDO Problems -- 3. Reliability Analysis Methods.

3.1. Probabilistic Measures.