I have been trying to optimize Optimal Power Flow Objectives using weighted sum method. For few objectives, I am in a position to obtain pareto front but for few (for e.g. Fuel Cost and Voltage Stability Index), I am getting number of solutions spread scatter. Can anybody help me realize/interpret such outcome?
When there are integer variables, the Pareto optimal (or trade-off) curve can have a crooked shape, because the solution set is non-convex. It is called the "integer gap". What also happens is, you not necessarily find all Pareto optimal solutions when using the weighted sum of the objectives. If you really need all solutions, you should use the "constraint" method, as described in a nice book by Jared Cohon (https://www.amazon.com/Multiobjective-Programming-Planning-Computer-Science/dp/0486432637)
I am not saying that this is THE answer, but it could be.
Good luck!
Vlad
I would suggest using GAMS for solving your optimization problem
academic discount code is here
https://www.udemy.com/powersystemopt/?couponCode=GAMSPSO2019
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