We suppose have a multi objective problem, with two objectives subject to minimized,
F=MIN(Sum(w1*F1, w2*F2)).
If I want to resolve this problem with neural network NN, the size of the input layer of NN would be equal to the number of attributes, so I suppose that the output layer should be equal to the number of objectives to minimize? Is this right?
So the important question is how to decide, from the output of the NN that one solution is the chosen one? And the output of the NN will be what exactly? I mean for the forecasting problem we will get a value of the prediction, for a classification purposes we will get an attribution of inputs to a classes and for this problem the result would be what?
It looks like you want to approximate the cost function using NN. But how do you want to find the best solution (input vector) using this model? I have no idea.
No.
1) If your multi-objective (MO) problem has conflicting objectives, then you usually end up with more than one solution. Your NN should be able to give as many solutions.
2) Why do you want to use NN for MO? NN is good for pattern recognition and prediction in data, I dont know how this will benefit MO. It is not impossible, but as Mahboobeh pointed out, there are easier and much more accurate ways to do it.
I think a deeper understanding of MO is required if you really want to implement it using NN or GA techniques. For that, literature by Kalyanmoy Deb might be a good starting point. Here's his article that might help
http://www.cs.bham.ac.uk/~pkl/teaching/2009/ec/lecture_notes/l08-emo-deb-subset.pdf
I guess you have two different problems. First you want to optimize using NN and probably you want to find a Pareto front for it as @Ankita told. Often you use MO for problems were you want the best for both opposite objectives (e.g.max volume and min surface area. How to choice the best? you probably take the max volumen that have a reasonable surface area). There are optimization method based on NN to optimize and you can programming it for MO, but indeed as @Mahboobeh said they are not the best optimizers.
And second, you want forecast using NN. To forecast, you must to optimize your NN; the most popular algorithm to optimize NN is Rprop.
The structure for the NN for both problems are different and there are a lot paradigms with different structures. The weights of the NN for forecast are regularly related with information that you use for do it. The weights of the NN for optimization would depend which method you use.
- Badges
- Science topic