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Table of contents
Acknowledgements
Résumé
Abstract
Contents
Introduction
Background
Topology optimization
Defination
Mathematical description
Key issues
Approaches
Thesis organization
1. State of the art
1.1 Homogenization method
1.2 Density based method
1.3 ON/OFF method
1.4 Boundary based methods
1.4.1 Level-set method
1.4.2 Phase-field method
1.5 Hard-kill methods
1.5.1 Evolutionary structure optimization
1.5.2 Heuristic searching algorithms
1.6 Multi-objective topology optimization methods
1.7 Applications
1.8 Chapter summary
2. Methodologies of single-objective topology optimization on electromagnetic devices
2.1 ON/OFF and finite-difference method
2.1.1 ON/OFF method
2.1.2 An improved ON/OFF method
2.2 A combined Tabu-ON/OFF methodology
2.2.1 Tabu searching algorihtm
2.2.2 The proposed topology optimization methodololgy
2.3 A revised quantum-inspired evolutionary algorithm
2.3.1 Quantum-iuspired evolutionary algorihtm
2.3.2 Improvements
2.3.3 Algorithm flowchart
2.4 A revised genetic algorithm
2.4.1 Revised GA
2.4.2 The proposed topology optimization methodology
2.5 A combined SIMP-RBF method
2.5.1 SIMP model and RBF post-processor
2.5.2 The proposed topology optimization methodology
2.6 A combined LSM-RBF method
2.6.1 Level set method
2.6.2 Material interpolation and RBF post-processor
2.7 Chapter summary
3. Methodology of multi-objective topology optimization
3.1 Multi-objective optimization method
3.1.1 Classical MOO method
3.1.2 Evolutionary MOO method
3.2 Basic concepts of the multi-objective optimization
3.2.1 Feasible solution and feasible solution set
3.2.2 Dominance relation and Pareto frontier
3.2.3 Performance metrics for multi-objective algorithms
3.3 A new hybrid multi-objective optimization algorithm
3.3.1 Improved NSGA
3.3.2 Binary DE algorithm
3.3.3 Flowchart of the proposed algorithm
3.4 Algorithm performance analysis and validation
3.4.1 Test functions
3.4.2 Algorithm verification
3.5 A multi-objective topology optimization methodology
3.6 Chapter summary
4. Numerical applications
4.1 Case study 1 : single-objective topology optimization
4.1.1 Solid model
4.1.2 Mathematical formulation
4.1.3 Numerical results
4.2 Case study 2 : single-objective topology optimization
4.2.1 Solid model
4.2.2 Mathematical formulation
4.2.3 Numerical results
4.3 Case study 3 : multi-objective topology optimization
4.3.1 Mathematical formulation
4.3.2 Numerical results
4.4 Comparatively remarks
4.4.1 Single-objective topology optimization method
4.4.2 Multi-objective topology optimization method
4.5 Chapter summary
Conclusions and perspectives
Bibliographie
