I'm currently working on an optimization problem with 4 different objective functions and need an algorithm to compute the pareto frontier from several "solutions" to that problem.
I already found algorithms that compute the pareto frontier for 2 objective functions (like cost & value) very efficiently but are (i.m.o.) not that easy to generalize to work with n objectives.
So what i basically want is an algorithm, that takes a set of 4-dimensional vectors and sorts out all the ones, that are dominated.
Of course it can be done with brute-force by checking any vector against every other one, but that would have exponential complexity and wouldn't be applicable with realistic problems since it would take forever to terminate.
I think, that there has to be an algorithm which works in (at least) O(n^m), with m = number of objective functions.
I really appreciate any suggestions/ideas.