Suppose I have a neural network, with input variables $a,b,c,d,f,g$ and output variables $m,n,o,p,q$.
Given different input values, the neural network will output corresponding $m,n,o,p,q$.
Now I want find out the best input values which can maxmize m,n, while minimize $o,p,q$ with different weights as well. So how can I find the best $a,b,c,d,f,g$?
Currently I use a simple way, which calculate $x=w_1m+w_2n+\frac{w_3}{o}+\frac{w_4}{p}+\frac{w_5}{q}$, then simply search all the possible inputs to find the input to get maxmization of x. However this simple method is not efficient and it also assume m,n,o,p,q are independent, which is not the case.
Meanwhile, normally Neural network will not give you a formula how the output related to the input, all the optimization approach I known all need a specific function how the output related to input. Even for genetic algorithm, I need a fitness function like $x=w_1m+w_2n+\frac{w_3}{o}+\frac{w_4}{p}+\frac{w_5}{q}$, but in this case, x has to related to inputs $a,b,c,d,f,g$ instead of outputs.
Any suggestions? Many thanks