Editing Shape optimization (section)

=== Geometry parametrization ===

Shape optimization can be faced using standard optimization methods if a parametrization of the geometry is defined. Such parametrization is very important in CAE field where goal functions are usually complex functions evaluated using numerical models (CFD, FEA,...). A convenient approach, suitable for a wide class of problems, consists in the parametrization of the CAD model coupled with a full automation of all the process required for function evaluation (meshing, solving and result processing). [[Mesh morphing]] is a valid choice for complex problems that resolves typical issues associated with [[re-meshing]] such as discontinuities in the computed objective and constraint functions.

In this case the parametrization is defined after the meshing stage acting directly on the numerical model used for calculation that is changed using mesh updating methods. 
There are several algorithms available for mesh morphing ([[deforming volume]]s, [[pseudosolid]]s, [[radial basis function]]s).
The selection of the parametrization approach depends mainly on the size of the problem: the CAD approach is preferred for small-to-medium sized models whilst the mesh morphing approach is the best (and sometimes the only feasible one) for large and very large models.
The multi-objective Pareto optimization (NSGA II) could be utilized as a powerful approach for shape optimization. In this regard, the Pareto optimization approach displays useful advantages in design method such as the effect of area constraint that other multi-objective optimization cannot declare it. The approach of using a penalty function is an effective technique which could be used in the first stage of optimization. In this method the constrained shape design problem is adapted to an unconstrained problem with utilizing the constraints in the objective function as a penalty factor. Most of the time penalty factor is dependent to the amount of constraint variation rather than constraint number. The GA real-coded technique is applied in the present optimization problem. Therefore, the calculations are based on real value of variables. <ref name="ssttds">{{cite journal | last1 = Talebitooti | first1 = R.| last2 = shojaeefard | first2 = M.H.| last3 = Yarmohammadisatri | first3 = Sadegh | title = Shape design optimization of cylindrical tank using b-spline curves | journal = Computer & Fluids | volume = 109 | pages = 100–112 | doi= 10.1016/j.compfluid.2014.12.004 | year = 2015}}</ref>