I understand that solving Traveling Salesperson-style problems is a topic of open research, but I'm wondering what the architecture of such a neural network would look like.
Specifically, it's not clear to me how to configure neural networks to solve a non-categorization problem, without any training data.
Here is a concrete problem I am trying to solve:
- The input into the system is the maximum amount of money the customer is willing to spend.
- The desired output is a list of cities that the customer will travel to.
- Our goal is to minimize the cost of the overall trip.
- Note that the cost function we are trying to minimize is not a direct consequence of the output value. We need to look up the cost of traveling between each origin-destination pair using an external system, and minimize that cost. Further, the cost will never reach zero and we don't know what the target cost looks like (we just know that the lower, the better).
How would the above constraints change the neural network architecture? Is this even solvable using neural networks (if not, what is a better approach)?