Constrained optimization is one of the popular research areas since constraints are usually present in most real world optimization problems. The purpose of this work is to develop a gradient free constrained global optimization methodology to solve this type of problems. In the methodology proposed, the single objective constrained optimization problem is solved using a Multi-Objective Evolutionary Algorithm (MOEA) by considering two objectives simultaneously, the original objective function and a measure of constraint violation. The MOEA incorporates a penalty function where the penalty parameter is estimated adaptively. The use of penalty function method will enable to further improve the current best solution by decreasing the level of constraint violation, which is made using a gradient free local search method. The performance of the proposed methodology was assessed on a set of benchmark test problems. The results obtained allowed to conclude that the present approach is competitive when compared with other methods available.