I need to publish solved multi-objective optimization problem after i had build the system, and i must use the best  method. 

Actually, that is a really hard question because everything depends on the properties of the search space and the objective function as well. As a result, method which is the best  in all possible cases does not exists.  Moreover, in general  all methods both heuristic and analytic are able to calculate  an approximation of the Pareto  set that follows from computational reasons.   Therefore, the best solution is to  choose  an optimization method which in the best way takes into account the specific nature of the problem

you can use for example the SPEA-2 algorithm or NSGA-2

Hi Abdallah,

If you are not sure that an heuristic method achieves the Pareto optimal set, you can apply it on a toy example, where the solutions can be derived analytically. The reference below provides such examples. If you want to know to have an idea the best configuration of your algorithm to approximate the Pareto front of your problem in the case where it cannot be derived analytically (most of the time when you deal of dataset of normal size), then you can try to build a problem with analytic solutions that looks similar. 

I hope this late answer could still help you. 

Article On the analytical derivation of the Pareto-optimal set with ...