ADVANCES IN METAHEURISTIC ALGORITHMS FOR OPTIMAL DESIGN OF STRUCTURES

Preface
Contents
1 Introduction
	1.1 Metaheuristic Algorithms for Optimization
	1.2 Optimal Design of Structures and Goals of the Present Book
	1.3 Organization of the Present Book
	References
2 Particle Swarm Optimization
	2.1 Introduction
	2.2 PSO Algorithm
		2.2.1 Development
		2.2.2 PSO Algorithm
		2.2.3 Parameters
		2.2.4 Premature Convergence
		2.2.5 Topology
		2.2.6 Biases
	2.3 Hybrid Algorithms
	2.4 Discrete PSO
	2.5 Democratic PSO for Structural Optimization
		2.5.1 Description of the Democratic PSO
		2.5.2 Truss Layout and Size Optimization with Frequency Constraints
		2.5.3 Numerical Examples
	References
3 Charged System Search Algorithm
	3.1 Introduction
	3.2 Charged System Search
		3.2.1 Background
		3.2.2 Presentation of Charged Search System
	3.3 Validation of CSS
		3.3.1 Description of the Examples
		3.3.2 Results
	3.4 Charged System Search for Structural Optimization
		3.4.1 Statement of the Optimization Design Problem
		3.4.2 CSS Algorithm-Based Structural Optimization Procedure
	3.5 Numerical Examples
		3.5.1 A Benchmark Truss
		3.5.2 The 120-Bar Dome Truss
		3.5.3 The 26-Story-Tower Space Truss
		3.5.4 An Unbraced Space Frame
		3.5.5 A Braced Space Frame
	3.6 Discussion
		3.6.1 Efficiency of the CSS Rules
		3.6.2 Comparison of the PSO and CSS
		3.6.3 Efficiency of the CSS
	References
4 Magnetic Charged System Search
	4.1 Introduction
	4.2 Magnetic Charged System Search Method
		4.2.1 Magnetic Laws
		4.2.2 A Brief Introduction to Charged System Search Algorithm
		4.2.3 Magnetic Charged System Search Algorithm
		4.2.4 Numerical Examples
		4.2.5 Engineering Examples
	4.3 Improved Magnetic Charged System Search
		4.3.1 A Discrete IMCSS
		4.3.2 An Improved Magnetic Charged System Search for Optimization of Truss Structures with Continuous and Discrete Variables
	References
5 Field of Forces Optimization
	5.1 Introduction
	5.2 Formulation of the Configuration Optimization Problems
	5.3 Fundamental Concepts of the Fields of Forces
	5.4 Necessary Definitions for a FOF-Based Model
	5.5 A FOF-Based General Method
	5.6 An Enhanced Charged System Search Algorithm for Configuration Optimization
		5.6.1 Review of the Charged System Search Algorithm
		5.6.2 An Enhanced Charged System Search Algorithm
	5.7 Design Examples
		5.7.1 The 18-Bar Planar Truss
		5.7.2 The 25-Bar Spatial Truss
		5.7.3 The 120-Bar Dome Truss
	5.8 Discussion
	References
6 Dolphin Echolocation Optimization
	6.1 Introduction
	6.2 Dolphin Echolocation in Nature
	6.3 Dolphin Echolocation Optimization
		6.3.1 Introduction to Dolphin Echolocation
		6.3.2 Dolphin Echolocation Algorithm
	6.4 Structural Optimization
	6.5 Numerical Examples
		6.5.1 Truss Structures
	References
7 Colliding Bodies Optimization
	7.1 Introduction
	7.2 Colliding Bodies Optimization
		7.2.1 The Collision Between Two Bodies
		7.2.2 The CBO Algorithm
		7.2.3 Test Problems and Optimization Results
	7.3 CBO for Optimum Design of Truss Structures with Continuous Variables
		7.3.1 Flowchart of the CBO Algorithm
		7.3.2 Numerical Examples
		7.3.3 Discussion
	References
8 Ray Optimization Algorithm
	8.1 Introduction
	8.2 Ray Optimization for Continuous Variables
		8.2.1 Definitions and Concepts from Ray Theory
		8.2.2 Ray Optimization Method
		8.2.3 Validation of the Ray Optimization
	8.3 Ray Optimization for Size and Shape Optimization of Truss Structures
		8.3.1 Formulation
		8.3.2 Design Examples
	8.4 Improved Ray Optimization Algorithm for Design of Truss Structures
		8.4.1 Introduction
		8.4.2 Improved Ray Optimization Algorithm
		8.4.3 Mathematical and Structural Design Examples
	References
9 Modified Big Bang-Big Crunch Algorithm
	9.1 Introduction
	9.2 MBB–BC Method
		9.2.1 Introduction to BB–BC Method
		9.2.2 A Modified BB–BC Algorithm
	9.3 Size Optimization of Space Trusses Using a MBB-BC Algorithm
		9.3.1 Formulation
		9.3.2 Design Examples
	9.4 Optimal Design of Schwedler and Ribbed Domes Using MBB-BC Algorithm
		9.4.1 Introduction
		9.4.2 Dome Structure Optimization Problems
		9.4.3 Psudo-Code of the Modified Big Bang-Big Crunch Algorithm
		9.4.4 Elastic Critical Load Analysis of Spatial Structures
		9.4.5 Configuration of Schwedler and Ribbed Domes
		9.4.6 Results and Discussion
		9.4.7 Discussion
	References
10 Cuckoo Search Optimization
	10.1 Introduction
	10.2 Optimum Design of Truss Structures Using Cuckoo Search Algorithm with Lévy Flights
		10.2.1 Formulation
		10.2.2 Lévy Flights as Random Walks
		10.2.3 Cuckoo Search Algorithm
		10.2.4 Optimum Design of Truss Structures Using Cuckoo Search Algorithm
		10.2.5 Design Examples
		10.2.6 Discussions
	10.3 Optimum Design of Steel Frames
		10.3.1 Optimum Design of Planar Frames
		10.3.2 Optimum Design of Steel Frames Using Cuckoo Search Algorithm
		10.3.3 Design Examples
		10.3.4 Discussions
	References
11 Imperialist Competitive Algorithm
	11.1 Introduction
	11.2 Optimum Design of Skeletal Structures
		11.2.1 Constraint Conditions for Truss Structures
		11.2.2 Constraints Conditions for Steel Frames
	11.3 Imperialist Competitive Algorithm
	11.4 Design Examples
		11.4.1 Design of the 120-Bar Dome Shaped Truss
		11.4.2 Design of the 72-Bar Spatial Truss
		11.4.3 Design of the 3-Bay, 15-Story Frame
		11.4.4 Design of the 3-Bay 24-Story Frame
	11.5 Discussions
	References
12 Chaos Embedded Metaheuristic Algorithms
	12.1 Introduction
	12.2 An Overview of Chaotic Systems
		12.2.1 Logistic Map
		12.2.2 Tent Map
		12.2.3 Sinusoidal Map
		12.2.4 Gauss Map
		12.2.5 Circle Map
		12.2.6 Sinus Map
		12.2.7 Henon Map
		12.2.8 Ikeda Map
		12.2.9 Zaslavskii Map
	12.3 Use of Chaotic Systems in Metaheuristics
	12.4 Chaotic Update of Internal Parameters for Metaheuristics
	12.5 Chaotic Search Strategy in Metaheuristics
	12.6 A New Combination of Metaheuristics and Chaos Theory
		12.6.1 The Original PSO
		12.6.2 The CPVPSO Phase
		12.6.3 The CLSPSO Phase
		12.6.4 Design Examples
	12.7 Concluding Remarks
	References
13 Enhanced Colliding Bodies Optimization
	13.1 Introduction
	13.2 Structural Optimization
	13.3 An Enhanced Colliding Bodies Optimization (ECBO)
		13.3.1 A Brief Explanation of the CBO Algorithm
		13.3.2 The ECBO Algorithm
	13.4 Mathematical Optimization Problems
	13.5 Design Examples
		13.5.1 The 25-Bar Space Truss
		13.5.2 The 72-Bar Space Truss
		13.5.3 The 582-Bar Tower Truss
		13.5.4 The 3-Bay 15-Story Frame
		13.5.5 The 3-Bay 24-Story Frame
	13.6 Concluding Remarks
	References
14 Global Sensitivity Analysis-Based Optimization Algorithm
	14.1 Introduction
	14.2 Background Study
		14.2.1 Variance-Based Sensitivity Indices
		14.2.2 The Variance-Based Sensitivity Analysis Using Space-Partition Method
	14.3 Global Sensitivity Analysis Based Algorithm
		14.3.1 Methodology
	14.4 Numerical Examples
		14.4.1 Design of a Tension/Compression Spring
		14.4.2 A Constraint Function
		14.4.3 The 17-Bar Planar Truss Problem
		14.4.4 The 72-Bar Spatial Truss Structure
		14.4.5 The 120-Bar Truss Dome
	14.5 Concluding Remarks
	References
15 Tug of War Optimization
	15.1 Introduction
	15.2 Tug of War Optimization Method
		15.2.1 Idealized Tug of War Framework
		15.2.2 Tug of War Optimization Algorithm
	15.3 Mathematical and Engineering Design Problems
		15.3.1 Mathematical Optimization Problems
		15.3.2 Engineering Design Problems
	15.4 Structural Optimization Problems
		15.4.1 Truss Weight Optimization with Static Constraints
		15.4.2 Truss Weight Optimization with Dynamic Constraints
	15.5 Concluding Remarks
	References
16 Water Evaporation Optimization Algorithm
	16.1 Introduction
	16.2 Basic Water Evaporation Optimization Algorithm
	16.3 Water Evaporation Optimization with Mixed Phases
	16.4 Test Problems and Optimization Results
		16.4.1 The 25-Bar Special Tower Truss
		16.4.2 The 72-Bar Special Truss
		16.4.3 The 3-Bay 15-Story Frame
		16.4.4 The 3-Bay 24-Story Frame
	16.5 Concluding Remarks
	References
17 Vibrating Particles System Algorithm
	17.1 Introduction
	17.2 Formulation of the Structural Optimization Problems
	17.3 The Damped Free Vibration
	17.4 A New Metaheuristic Algorithm Based on the Vibrating Particles System
	17.5 Search Behavior of the Vibrating Particles System Algorithm
	17.6 Test Problems and Optimization Results
		17.6.1 The 120-Bar Spatial Dome Shaped Truss
		17.6.2 The 200-Bar Planar Truss
		17.6.3 The 3-Bay 15-Story Frame Problem
		17.6.4 The 3-Bay 24-Story Frame Problem
	17.7 Concluding Remarks
	References
18 Cyclical Parthenogenesis Optimization Algorithm
	18.1 Introduction
	18.2 Cyclical Parthenogenesis Algorithm
		18.2.1 Aphids and Cyclical Parthenogenesis
		18.2.2 Description of Cyclical Parthenogenesis Algorithm
	18.3 Sensitivity Analysis of CPA
	18.4 Test Problems and Optimization Results
		18.4.1 Mathematical Optimization Problems
		18.4.2 Truss Design Problems
	18.5 Concluding Remarks
	References
19 Optimal Design of Large-Scale Frame Structures
	19.1 Introduction
	19.2 Code Based Design Optimization of Steel Frames
	19.3 Cascade Sizing Optimization Utilizing Series of Design Variable Configurations
		19.3.1 Cascade Optimization Strategy
		19.3.2 Multi-DVC Cascade Optimization
	19.4 Colliding Body Optimization and Its Enhanced Version
		19.4.1 A Brief Explanation of the CBO Algorithm
		19.4.2 The ECBO Algorithm
	19.5 Numerical Examples
		19.5.1 The 1860-Member Steel Space Frame
		19.5.2 The 3590-Member Steel Space Frame
		19.5.3 The 3328-Member Steel Space Frame
	19.6 Concluding Remarks
	References
20 Shuffled Shepherd Optimization Algorithm
	20.1 Introduction
	20.2 Shuffle Shepherd Optimization Algorithm
		20.2.1 Inspiration
		20.2.2 Mathematical Model
		20.2.3 Steps of the Optimization Algorithm
	20.3 Validation of the SSOA
		20.3.1 Mathematical Optimization Problems
		20.3.2 Engineering Optimization Problems
	20.4 Numerical Examples
		20.4.1 The 72-Bar Spatial Truss
		20.4.2 The 200-Bar Planar Truss
		20.4.3 The 272-Bar Transmission Tower
		20.4.4 The 582-Bar Tower Truss
		20.4.5 The 1016-Bar Double-Layer Grid
	20.5 Concluding Remarks
	References
21 Set Theoretical Shuffled Shepherd Optimization Algorithm
	21.1 Introduction
	21.2 Shuffled Shepherd Optimization Algorithm
	21.3 Set Theoretical Shuffled Shepherd Optimization Algorithm (ST-SSOA)
	21.4 Definition of the Optimization Problem
	21.5 Analysis of Reinforced Concrete Cantilever Retaining Wall Structures
		21.5.1 Active and Passive Earth Pressures
		21.5.2 Stability Control
	21.6 Results and Discussion
	21.7 Concluding Remarks
	References
22 Set Theoretical Teaching-Learning-Based Optimization Algorithm
	22.1 Introduction
	22.2 Teaching-Learning-Based Optimization (TLBO) Algorithm
	22.3 Set Theoretical Variants of Teaching-Learning-Based Optimization Algorithm
		22.3.1 Ordered Set Theoretical Teaching-Learning-Based Optimization (OST-TLBO) Algorithm
		22.3.2 Set Theoretical Multi-phase Teaching-Learning-Based Optimization (STMP-TLBO) Algorithm
	22.4 Formulation of Truss Optimization Problems with Frequency Constraints
	22.5 Numerical Examples
		22.5.1 The 37-Bar Planar Truss
		22.5.2 The 52-Bar Dome-like Truss
		22.5.3 The 120-Bar Dome-like Truss
		22.5.4 The 200-Bar Planar Truss
	22.6 Concluding Remarks
	References
23 Thermal Exchange Metaheuristic Optimization Algorithm
	23.1 Introduction
	23.2 Thermal Exchange Optimization
		23.2.1 Background
		23.2.2 Presentation of Thermal Exchange Optimization
	23.3 Verification of the Algorithm
		23.3.1 Exploration and Exploitation
		23.3.2 Sensitivity Analysis
		23.3.3 Convergence Curves
		23.3.4 Verification of the Search History
	23.4 Benchmark Functions
		23.4.1 Mathematical Optimization Problems
		23.4.2 Engineering Optimization Problems
	23.5 Concluding Remarks
	23.6 Improved Thermal Exchange Optimization
		23.6.1 Improvement on t Parameter
		23.6.2 Improvement on β Parameter
		23.6.3 Improvement on Thermal Updating Equation
		23.6.4 Pseudo-Code of the ITEO
		23.6.5 Constraint Handling
	23.7 Numerical Examples
		23.7.1 The Spatial 25-Bar Truss
		23.7.2 The Spatial 72-Bar Truss
		23.7.3 The Three-Bay Fifteen-Story Frame
		23.7.4 The Three-Bay Twenty Four-Story Frame
	23.8 Concluding Remarks
	References
24 Water Strider Optimization Algorithm and Its Enhancement
	24.1 Introduction
	24.2 Water Strider Optimizer
		24.2.1 Inspiration
		24.2.2 Mathematical Model and Algorithm
		24.2.3 Computational Complexity of the WSA
	24.3 Numerical Experiments
		24.3.1 Phase I: Exploration and Exploitation Behavior of WSA
		24.3.2 Phase I: Convergence Rate
		24.3.3 Phase I: Monitoring the Position of WSs
		24.3.4 Phase II: Verification Against Possible Biases
	24.4 Engineering Design Problems
		24.4.1 Welded Beam Design Problem
		24.4.2 Three-Bar Truss Design Problem
		24.4.3 Compound Gear Design Problem
		24.4.4 Cantilever Beam Design Problem
		24.4.5 Application of WSA in Structural Health Monitoring
		24.4.6 Application of WSA in Optimal Design of Double-Layer Barrel Vaults
	24.5 Discussion on the Results and Conclusions
	24.6 Dynamic Water Strider Algorithm
		24.6.1 Dynamic Number of Territories
		24.6.2 Dynamic Approaching Distance
		24.6.3 Numerical Experiments
		24.6.4 The 25-Bar Spatial Transmission Tower
		24.6.5 The 72-Bar Spatial Truss
		24.6.6 The 3-Bay 15-Story Frame Example
	24.7 Concluding Remarks
	References
25 Multi-objective Optimization of Truss Structures
	25.1 Introduction
	25.2 Multi-objective Optimization Concepts
	25.3 Charged System Search Algorithm
	25.4 Multi-objective Charged System Search Optimization Algorithm
		25.4.1 Algorithm
	25.5 Multi-criteria Decision Making
	25.6 Numerical Examples
		25.6.1 Design of a 2-Bar Truss Design
		25.6.2 Design of an I-Beam
		25.6.3 Design of a Welded Beam
		25.6.4 Design of a 25-Bar Truss
		25.6.5 Design of a 56-Bar
		25.6.6 Design of a 272-Bar Transmission Tower
	25.7 Concluding Remarks
	References
Index