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We describe a local search procedure for multiobjective genetic algorithms that employs quadratic approximations for all nonlinear functions involved in the optimization problem. The samples obtained by the algorithm during the evolutionary process are used to fit these quadratic approximations in the neighborhood of the point selected for local search, implying that no extra cost of function evaluations is required. After that, a locally improved solution is easily estimated from the associated quadratic problem. We demonstrate the hybridization of our procedure with the well-known multiobjective genetic algorithm. This methodology can also be coupled with other multiobjective evolutionary algorithms. The results show that the proposed procedure is suitable for time-demanding black-box optimization problems.