GAs are popular for multi-objective optimization because there are not many alternatives, at least in terms of accessible implementations. This lack of alternatives is due to the fact that multi-objective optimization is mathematically ill-defined, and that it is thus much harder to develop algorithms with solid theoretical foundations.
There's ample evidence, including work by myself and collaborators, that GAs are not very effective on single-objective, derivative-free problems, for example in building energy optimization. It thus seems save to assume that they are not very effective on multi-objective, derivative-free problems either.
Why not try to implement a multi-objective scheme based on a branch-and-bound technique for the subproblems? It makes more sense to use a methodology that has a known theory (namely B&B), than a genetic algorithm that has a more shallow theory behind it.
The only one benefit is the speed. Possible disadvantage is you can find suboptimal solution (local min/ max, not global one). This could be important/ applicable for real-time control.
I daresay that genetic algorithm is most wide and almost unlimited approach due to his natural evolution basis, which gives you huge opportunities to develope high effective solving tool. For example, the algorithm of ant colony will be high effective for solving some problems of optimal route finding, because the algorithm simulate the mechanism of route finding by ants.