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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

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    How is your specific problem different from the usual, everyday setting? Have you consulted any introductory machine learning text?2011-02-07
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    Also, normally in neural networks there are hidden layers. And you haven't specified how the input is related to the output - what weights are you trying to adjust?2011-02-07
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    The problem is this, I can not define the relation between the input and output as a function. but I can represent it as a neural network. I have tried normal regression on the input data, but the result is not good. a neural network can fit the data fine, but normally it is very difficult to represent the network as formula, because the hidden layer, active function etc....2011-02-07

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