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Derivatives are an important tool for single-objective optimization. In fact,it is commonly accepted that derivative-based methods present a betterperformance than derivative-free optimization approaches. In this work, we willshow that the same does not apply to multiobjective derivative-basedoptimization, when the goal is to compute an approximation to the completePareto front of a given problem. The competitiveness of Direct MultiSearch(DMS), a robust and efficient derivative-free optimization algorithm, will bestated for derivative-based multiobjective optimization problems. We will thenassess the potential enrichment of adding first-order information to the DMSframework. Derivatives will be used to prune the positive spanning setsconsidered at the poll step of the algorithm, highlighting the role that ascentdirections, that conform to the geometry of the nearby feasible region, canhave. Both variants of DMS show to be competitive against a state-of-artderivative-based algorithm. Moreover, for reasonable small budgets of functionevaluations, the new variant is not only competitive with the derivative-basedsolver but also with the original implementation of DMS.

Using first-order information in Direct Multisearch for multiobjective optimization