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We propose a technique for incorporating robustness as part of the search process of evolutionary multiobjective optimization algorithms. The proposed approach calculates the sensitivity of candidate solutions by solving a linear programming subproblem, defined by regression models fitted using points in the neighborhood of each candidate solution. This sensitivity information is then used as part of the selection process, to drive the search towards solutions that comply with robustness requirements defined a priori by the decision-maker. Preliminary results suggest that this approach is capable of correctly converging to the desired robust fronts.