I use the weighted sum approach for a multiobjective optimization problem that is formulated as a MILP. This means that the objective function is linear. I read quite often that the weighted sum approach can't find certain pareto-optimal solutions in case of non-convex objective spaces (see for example slide 12 in this presentation https://engineering.purdue.edu/~sudhoff/ee630/Lecture09.pdf).
Now, having a MILP problem, can I deduce that basically the weighted sum approach can find all pareto optimal solutions if I just vary the weights? Of course the number of pareto-optimal solutions might be infinite, but I'd like to know whether there is the risk of missing some areas of the pareto-front. My gut feeling is that in a MILP the weighted sum approach can in fact find all pareto-optimal solutions.
Can anyone tell me more about this issue? I'd really appreciate every comment.