Optimization is known as the process of finding the best possible solution to a problem given a set of constraints. The problem becomes challenging when dealing with conflicting objectives, which leads to a multiplicity of solutions. Evolutionary algorithms, which use a population approach in their search procedures, are advised to suitably solve the problem. In this article, we present an approach for an evolutionary combinatorial multi-objective optimization of business process designs using a variation of NSGAII, baptized MA-NSGAII. The variants of NSGAII are numerous. In fact, the vast majority deals either with the crossover operator or with the crowding distance. We discuss an optimization Framework that uses (i) a proposal of effective Fitness function, (ii) 02 contradictory criteria to optimize and (iii) an original selection technique. We test the proposed Framework with a real life case of multi-objective optimization of business process designs. The obtained results clearly indicate that an effectual Fitness function combined with the appropriate selection operator affects undeniably quality and quantity of solutions.