A BSTRACT  
1 Introduction  
2 Shape Optimization Problem Formulation  
3 Tackling the Curse of Dimensionality  
3.1 Literature Overview  
4 Space Reduction Methods  
4.1 Bounds Narrowing  
4.2 Geometric Filtering  
5 Indirect Dimensionality Reduction Methods  
6 Direct Dimensionality Reduction Methods: Representation Learning  
6.1 Linear Dimensionality Reduction Methods  
6.2 Nonlinear Dimensionality Reduction Methods  
7 Discussion and Conclusions