First, I am not sure if this is the right question to ask in this forum. But I have been looking for answers for a long time and I have been also asking my university's "engineering" professors but I don't seem to get a mathematical answer.
I am trying solve a complex optimization problem involving network and short path optimization and at the same time solve for non-linear pressure, flows and diameter. I can apply one of the following methods:
The first method is to use a Mixed Integer Linear Programming method (MILP) only and linearize the pressure, flows and diameter using piece-wise linear approximation. The linearization is done since the MILP only takes linear equations and look for an optimal solution.
The second method is to use a combined local optimization and global optimization method. The local optimization would use MILP first to find solution to sub-problems where continuous optimization would be costly to use (e.g. allocation of production ). Then, I would use a global optimization method using derivative-free genetic algorithm to perturb the system (e.g. the network path) and find a better global solution. Every time the system is perturbed, the local MILP optimization is repeated.
I am after any recommendations, heads-up and things to watch out for if I implement one of these two methods. Is the second method mathematically acceptable compared to the first method?
