In the last few years, the development of hybrid algorithms that combine multi-objective evolutionary algorithms (MOEAs) with mathematical programming techniques has significantly increased. Such hybrid algorithms attempt to combine the global search properties of MOEAs with the exploitative power of mathematical programming techniques. Most of these approaches normally rely on the use of gradients and, therefore, their use is limited to certain types of problems. The use of nonlinear direct search techniques-i.e., methods that do not require gradient information-has been less popular in these type of approaches. This paper focuses on the design of a hybrid algorithm between the well-known MOEA/D and one of most popular direct search methods, the Nelder and Mead method. The mathematical programming technique adopted here, acts as a local search engine, whose goal is to exploit promising regions of the search space that have been generated by MOEA/D. Our preliminary results indicate that this sort of hybridization is promising for dealing with multi-objective optimization problems having a moderately high number of decision variables.