Chaotic Meta-heuristic Algorithms for Optimal Design of Structures

✍ Scribed by Ali Kaveh, Hossein Yousefpoor

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 349
• Series: Studies in Computational Intelligence; 1129
• Category: Library

✦ Synopsis

In this book, various chaos maps are embedded in eleven efficient and well-known metaheuristics and a significant improvement in the optimization results is achieved. The two basic steps of metaheuristic algorithms consist of exploration and exploitation. The imbalance between these stages causes serious problems for metaheuristic algorithms, which are immature convergence and stopping in local optima. Chaos maps with chaotic jumps can save algorithms from being trapped in local optima and lead to convergence toward global optima. Embedding these maps in the exploration phase, exploitation phase, or both simultaneously corresponds to three efficient and useful scenarios. By creating competition between different modes and increasing diversity in the search space and creating sudden jumps in the search phase, improvements are achieved for chaotic algorithms. Four Chaotic Algorithms, including Chaotic Cyclical Parthenogenesis Algorithm, Chaotic Water Evaporation Optimization, Chaotic Tug-of-War Optimization, and Chaotic Thermal Exchange Optimization are developed.

✦ Table of Contents

Preface
Contents
1 Introduction
1.1 Introduction
1.2 Traditional Optimization and Meta-heuristic Optimization
1.3 Chaotically Enhanced Meta-heuristic Algorithms
1.4 Chaos Embedded Meta-heuristic Algorithms for Optimal Design and Goals of This Book
1.5 Organization of the Present Book
References
2 Chaotic Maps and Meta-heuristic Algorithms
2.1 Introduction
2.2 Chaotic Systems
2.2.1 Scientific History of Chaos Theory
2.2.2 Characteristics of Chaotic System
2.2.3 Bifurcation on Chaotic System
2.2.4 Attractor on Chaotic System
2.3 Introduction Chaos Maps and Forming Chaos Series
2.3.1 Logistic Map
2.3.2 Tent Map
2.3.3 Gauss Map
2.3.4 Liebovitch Map
2.3.5 Chebyshev Map
2.3.6 Sinusoidal Map
2.3.7 Piecewise Map
2.3.8 Lorens Attractor System
2.4 Chaos Series and Alternative Scenarios
2.5 Meta-heuristic Algorithms and Chaos Map
2.6 Concluding Remarks
References
3 Chaotic Cyclical Parthenogenesis Algorithm
3.1 Introduction
3.2 Standard Cyclical Parthenogenesis Algorithm (CPA)
3.3 Basic Steps of Cyclical Parthenogenesis Algorithm
3.4 Chaos Enhanced Cyclical Parthenogenesis Algorithm (CCPA)
3.5 Constructive Role of Chaos Functions in Sensitivity Analysis
3.6 Truss Weight Optimization with Static Constraints
3.6.1 Formulation of the Structural Optimization Problems
3.6.2 Introduction of Selected Chaos Map
3.6.3 Numerical Examples of Optimal Truss Design
3.7 Truss Weight Optimization with Multiple Frequency Constraints
3.7.1 Formulation of the Structural Optimization with Frequency Constraints
3.7.2 Introduction of Selected Chaos Map
3.7.3 Numerical Examples of Optimal Truss Design
3.8 Concluding Remarks
References
4 Chaotic Teaching Learning Based Optimization
4.1 Introduction
4.2 Standard Teaching–Learning-Based Optimization (TLBO)
4.3 Basic Steps in Standard Teaching–Learning-Based Optimization
4.4 Chaos Enhanced Teaching–Learning-Based Optimization (CTLBO)
4.5 Truss Weight Optimization with Static Constraints
4.5.1 Formation of the Objective Function and Constraint Conditions
4.5.2 Introduction of Selected Chaos Map
4.5.3 Numerical Examples of Optimal Truss Design
4.6 Truss Weight Optimization with Multiple Frequency Constraints
4.6.1 Truss Size and Layout Optimization with Multi Frequency Constraints
4.6.2 Introduction of Selected Chaos Map
4.6.3 Numerical Examples of Optimal Truss Design
4.7 Concluding Remarks
References
5 Chaotic Biogeography Based Optimization
5.1 Introduction
5.2 Standard Biogeography-Based Optimization (BBO)
5.3 Basic Steps of Biogeography-Based Optimization
5.4 Chaos Enhanced Biogeography-Based Optimization (CBBO)
5.5 Truss Weight Optimization with Static Constraints
5.5.1 Formulation of the Structural Optimization Problems
5.5.2 Introduction of Selected Chaos Map
5.5.3 Numerical Examples of Optimal Truss Design
5.6 Truss Weight Optimization with Multiple Frequency Constraints
5.6.1 Formulation of the Structural Optimization with Multi-frequency Constraints
5.6.2 Numerical Examples of Optimal Truss Design
5.7 Concluding Remarks
References
6 Chaotic Differential Evolution
6.1 Introduction
6.2 Standard Differential Evolution (DE)
6.3 Basic Steps of Differential Evolution
6.4 Chaos Differential Evolution (CDE)
6.5 Truss Weight Optimization with Static Constraints
6.5.1 Formulation of the Structural Optimization Problem
6.5.2 Numerical Examples
6.6 Concluding Remarks
References
7 Chaotic Water Evaporation Optimization
7.1 Introduction
7.2 Standard Water Evaporation Optimization (WEO)
7.3 Basic Steps in Standard Water Evaporation Optimization (WEO)
7.4 Chaos Enhanced Water Evaporation Optimization (CWEO)
7.5 Truss Weight Optimization with Static Constraints
7.5.1 Statement of the Structural Optimization Problems
7.5.2 Introduction of Selected Chaos Map
7.5.3 Numerical Examples of Optimal Truss Design
7.6 Truss Weight Optimization with Multiple Frequency Constraints
7.6.1 Coincidently Size and Topology Optimization of Skeletal Structures
7.6.2 Numerical Examples of Optimal Truss Design
7.7 Concluding Remarks
References
8 Chaotic Artificial Bees Colony
8.1 Introduction
8.2 Standard Artificial Bees Colony (ABC)
8.3 Basic Steps in Artificial Bees Colony
8.4 Chaos Enhanced Artificial Bees Colony (CABC)
8.5 Truss Weight Optimization with Static Constraints
8.5.1 Formulation for Optimal Design of Skeletal Structures
8.5.2 Introduction of Selected Chaos Map
8.5.3 Numerical Examples of Optimal Truss Design
8.6 Truss Weight Optimization with Multiple Frequency Constraints
8.6.1 Formulation of the Structural Optimization with Frequency Constraints
8.6.2 Numerical Examples of Optimal Truss Design
8.7 Concluding Remarks
References
9 Chaotic Imperialist Competitive Algorithm
9.1 Introduction
9.2 Standard Imperialist Competitive Algorithm (ICA)
9.3 Basic Steps in Imperialist Competitive Algorithm
9.4 Chaos-Embedded Imperialist Competitive Algorithm (CICA)
9.5 Truss Weight Optimization with Static Constraints
9.5.1 Formulation of the Structural Optimization Problems
9.5.2 Introduction of Selected Chaos Map
9.5.3 Numerical Examples of Optimal Truss Design
9.6 Truss Weight Optimization with Multiple Frequency Constraints
9.6.1 Formulation of the Structural Size and Layout Optimization with Frequency Constraints
9.6.2 Numerical Examples of Optimal Truss Design
9.7 Concluding Remarks
References
10 Chaotic Shuffled Frog Leaping Algorithm
10.1 Introduction
10.2 Standard Shuffled Frog-Leaping Algorithm (SFLA)
10.3 Basic Steps in Shuffled Frog-Leaping Algorithm
10.4 Chaos-Embedded Shuffled Frog-Leaping Algorithm (CSFLA)
10.5 Truss Weight Optimization with Static Constraints
10.5.1 Formulation of the Structural Optimization Problems
10.5.2 Introduction of Selected Chaos Map
10.5.3 Numerical Examples of Optimal Truss Design
10.6 Truss Weight Optimization with Multiple Frequency Constraints
10.6.1 Formulation of the Structural Optimization with Frequency Constraints
10.6.2 Numerical Examples of Optimal Truss Design
10.7 Concluding Remarks
References
11 Chaotic Particle Swarm Optimization
11.1 Introduction
11.2 Standard Particle Swarm Optimization (PSO)
11.3 Basic Steps in Particle Swarm Optimization
11.4 Chaos-Embedded Particle Swarm Optimization (CPSO)
11.5 Truss Weight Optimization with Multiple Frequency Constraints
11.5.1 Gaussian Map
11.5.2 Liebovitch Map
11.5.3 Piecewise Map
11.6 Formulation of Coincidently Size and Layout Optimization of Truss Structures
11.7 Numerical Examples of Optimal Truss Design
11.7.1 A Planar 10-Bar Truss
11.7.2 A Simply Supported 37-Bar Planar Truss
11.7.3 A 120-Bar Spatial Dome
11.7.4 A 200-Bar Planar Truss Structure
11.8 Concluding Remarks
References
12 Chaotic Tug-of-War Optimization
12.1 Introduction
12.2 Standard Tug of War Optimization (TWO)
12.3 Basic Steps in Tug of War Optimization
12.4 Chaos-Embedded Tug of War Optimization (CTWO)
12.5 Truss Weight Optimization with Multiple Frequency Constraints
12.5.1 Logistics Map
12.5.2 Gauss Map
12.6 Formulation of the Structural Optimization with Frequency Constraints
12.6.1 Numerical Examples of Optimal Truss Design
12.7 Concluding Remarks
References
13 Chaotic Thermal Exchange Optimization
13.1 Introduction
13.2 Standard Thermal Exchange Optimization (TEO)
13.3 Basic Steps in Thermal Exchange Optimization
13.4 Chaos-Embedded Thermal Exchange Optimization (CTEO)
13.5 Truss Weight Optimization with Multiple Frequency Constraints
13.6 Formulation of the Optimization Problems
13.6.1 Free Vibration and Natural Frequencies
13.6.2 Formulation Size and Layout Optimization with Multi Frequency Constraints
13.7 Numerical Examples of Optimal Truss Design
13.7.1 A Simply Supported 37-Bar Planar Truss
13.7.2 A 72-Bar Spatial Truss
13.7.3 A 120-Bar Spatial Dome
13.7.4 A 200-Bar Planar Truss Structure
13.8 Concluding Remarks
References