I have pretty simple linear optimization problem with two objective functions \[\begin{align} \text{maximize}\, (f_1 &= 4x_1+5 x_2\,,\,f_2 = 1x_1 ) \\ \text{subject to}& \\ 1x_1 + 1x_2 &\leq 200 \\ 1.25x_1 + 0.75x_2 &\leq 200 \\ 1x_2 &\leq 150 \\ x_1,x_2 &\geq 0 \end{align}\] I'm trying to find optimal points to this problem with goal method (matlab) and with normalized objective function, where \(f^*(x) = (950,160)\) are the optimal solutions (Utopia point?) to my objective functions. \[f(x)=\sum_{i=1}^2 (f_i^{*}(x)-f_i (x))/f_i^{*}(x)\] I don't know how to translate this problem into matlab. Any help? |