In recent years, the development of multi-objective evolutionary algorithms (MOEAs) hybridized with mathematical programming techniques has significantly increased. However, most of these hybrid approaches are gradient-based, and tend to require a high number of extra objective function evaluations to estimate the gradient information required. The use of direct search methods—i.e., methods that do not require gradient information—has been, however, less popular in the specialized literature (although such approaches have been used with single-objective evolutionary algorithms). This paper precisely focuses on the design of a hybrid between the wellknownMOEA/ D and Nelder and Mead's algorithm. Clearly, the mathematical programming technique adopted here, acts as a local search mechanism, whose goal is to improve the search performed by MOEA/D. Because of its nature, the proposed local search mechanism can be easily coupled to any other decomposition-based MOEA. Our preliminary results indicate that this sort of hybridization is quite promising for dealing with multi-objective optimization problems (MOPs) having high dimensionality (in decision variable space).