How to do multi-objective optimization using neural networks?
There are many methods, but the easiest way is "linear scalarization".
You can add objectives to make single objective.
While doing this, you can weight objectives considering priority.
(Making linear combination of multiple objectives)
See examples:
Variational AE loss (regularization loss + reconstruction loss)
Associative DA loss (classification loss + walker loss + visit loss)
I have five decision variables, each having a specific range. I need to find a combination of these variables so as to maximize one of my objectives while minimizing the other at the same time. I have prepared a datasheet of randomly generated variables with respective values of the 2 objective functions. Please suggest me how to approach the solution using neural networks. 
My objective function involves thermodynamic calculations. If interested you can have a look at the objective functions here :