Cost Optimization of Structures

Contents
Preface xi
Acknowledgments xiii
About the Authors xv
1 Introduction 1
1.1 The Case for Cost Optimization 1
1.2 Cost Optimization of Concrete Structures 2
1.2.1 Concrete Beams and Slabs 3
1.2.2 Concrete Columns 11
1.2.3 Concrete Frame Structures 12
1.2.4 Bridge Structures 14
1.2.5 Water Tanks 16
1.2.6 Folded Plates and Shear Walls 17
1.2.7 Concrete Pipes 17
1.2.8 Concrete Tensile Members 17
1.2.9 Cost Optimization Using the Reliability Theory 18
1.2.10 Concluding Comments 20
1.3 Cost Optimization of Steel Structures 20
1.3.1 Deterministic Cost Optimization 20
1.3.2 Cost Optimization Using the Reliability Theory 31
1.3.3 Fuzzy Optimization 33
1.3.4 Concluding Comments 35
2 Evolutionary Computing and the Genetic Algorithm 37
2.1 Overview and Basic Operations 37
2.2 Coding and Decoding 39viii Contents
2.3 Basic Operations in Genetic Algorithms 40
2.4 GA with the Penalty Function Method 43
2.4.1 Problem Formulation for Axial Force (Truss)
Structures 43
2.4.2 Genetic Algorithm with the Penalty Function
Method 45
2.5 Augmented Lagrangian Method 47
2.6 GA with the Augmented Lagrangian Method 48
2.6.1 Problem Formulation for Axial Force (Truss)
Structures 48
2.6.2 Genetic Algorithm with the Augmented Lagrangian
Method 49
3 Cost Optimization of Composite Floors 53
3.1 Introduction 53
3.2 Minimum Cost Design of Composite Beams 54
3.2.1 Cost Function 54
3.2.2 Constraints 55
3.2.3 Problem Formulation as a Mixed Integer–Discrete
Nonlinear Programming Problem 61
3.3 Solution by the Floating-Point Genetic Algorithm 62
3.3.1 Binary Versus Floating-Point GA 62
3.3.2 Crossover Operation for the Floating-Point GA 62
3.3.3 Mutation Operation for the Floating-Point GA 63
3.3.4 Floating-Point GA for Cost Optimization
of Composite Floors 63
3.4 Solution by the Neural Dynamics Method 65
3.5 Counter Propagation Neural (CPN) Network for Function
Approximations 68
3.6 Examples 71
3.6.1 Example 1 71
3.6.2 Example 2 72
4 Fuzzy Genetic Algorithm for Optimization of Steel Structures 77
4.1 Introduction 77
4.2 Fuzzy Set Theory and Structural Optimization 79
4.3 Minimum Weight Design of Axially Loaded Space
Structures 82
4.4 Fuzzy Membership Functions 85
4.5 Fuzzy Augmented Lagrangian Genetic Algorithm 87Contents ix
4.6 Implementation and Examples 92
4.6.1 Example 1 93
4.6.2 Example 2 93
4.7 Conclusion 98
5 Fuzzy Discrete Multi-criteria Cost Optimization of Steel
Structures 101
5.1 Cost of a Steel Structure 101
5.2 Primary Contributing Factors to the Cost of a Steel
Structure 102
5.3 Fuzzy Discrete Multi-criteria Cost Optimization 105
5.4 Membership Functions 110
5.4.1 Membership Function for Minimum Cost 110
5.4.2 Membership Function for Minimum Weight 110
5.4.3 Membership Function for Minimum Number of
Section Types 110
5.5 Fuzzy Membership Functions for Criteria with Unequal
Imortance 112
5.6 Pareto Optimality 112
5.7 Selection of Commercially Available Discrete Shapes 114
5.8 Implementation and a Parametric Study 117
5.9 Application to High-Rise Steel Structures 118
5.9.1 Example 1 118
5.9.2 Example 2 119
5.10 Concluding Comments 123
6 Parallel Computing 125
6.1 Multiprocessor Computing Environment 125
6.2 Parallel Processing Implementation Environment 128
6.2.1 OpenMP Data Parallel Application Programming
Interface (API) 128
6.2.2 Message Passing Interface (MPI) 130
6.3 Performance Optimization of Parallel Programs 130
7 Parallel Fuzzy Genetic Algorithms for Cost Optimization of
Large Steel Structures 133
7.1 Genetic Algorithm and Parallel Processing 133
7.2 Cost Optimization of Moment-Resisting Steel Space
Structures 135
7.3 Data Parallel Fuzzy Genetic Algorithm for Optimization
of Steel Structures Using OpenMP 136
7.4 Distributed Parallel Fuzzy Genetic Algorithm for
Optimization of Steel Structures Using MPI 138
7.4.1 Processor Farming Scheme 138
7.4.2 Migration Scheme 140
7.5 Bilevel Parallel Fuzzy GA for Optimization of Steel
Structures Using OpenMP and MPI 142
7.5.1 Bilevel Parallel Fuzzy GA with the Processor
Farming Scheme 145
7.5.2 Bilevel Parallel Fuzzy GA with the Migration Scheme 146
7.6 Application to High-Rise Building Steel Structures 147
7.6.1 Example 1 147
7.6.2 Example 2 149
7.7 Parallel Processing Performance Evaluation 155
7.7.1 Data Parallel Fuzzy GA Using OpenMP 155
7.7.2 Distributed Parallel Fuzzy GA Using MPI 157
7.7.3 Bilevel Parallel Fuzzy GA Using OpenMP and MPI 160
7.8 Concluding Comments 164
8 Life-Cycle Cost Optimization of Steel Structures 165
8.1 Introduction 165
8.2 Life-Cycle Cost of a Steel Structure and the Primary
Contributing Factors 167
8.3 Formulation of the Total Life-Cycle Cost 170
8.4 Fuzzy Discrete Multi-criteria Life-Cycle Cost Optimization 171
8.5 Application to a High-Rise Building Steel Structure 174
Appendix A 177
Appendix B 181
References 185
Index 201


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