MSR/ressources/Optimization.md

Often given a problem, the best fitting solution is non-trivial, you need to carefully adjust many parameters to find it.

Multi-Objective Optimization

(Context articles descriptions#Optimization method of composite laminates with a viscoelastic layer)

f(X) = \sum_{i=1}^L \omega_i f_i(X) \tag{1}

\sum_{i=1}^L \omega_i = 1, \omega_i \ge 0 (i=1,2,\dots,L)\tag{2}

Each function should be dimensionless (different dimensions can make weighing really hard). Most common technique :

f_i(X)=\frac{F_i(X)}{\min\limits_{x \in \Omega} F_i(X)} \tag{3}