  Derivatives are an important tool for single-objective optimization. In fact,
it is commonly accepted that derivative-based methods present a better
performance than derivative-free optimization approaches. In this work, we will
show that the same does not apply to multiobjective derivative-based
optimization, when the goal is to compute an approximation to the complete
Pareto front of a given problem. The competitiveness of Direct MultiSearch
(DMS), a robust and efficient derivative-free optimization algorithm, will be
stated for derivative-based multiobjective optimization problems. We will then
assess the potential enrichment of adding first-order information to the DMS
framework. Derivatives will be used to prune the positive spanning sets
considered at the poll step of the algorithm, highlighting the role that ascent
directions, that conform to the geometry of the nearby feasible region, can
have. Both variants of DMS show to be competitive against a state-of-art
derivative-based algorithm. Moreover, for reasonable small budgets of function
evaluations, the new variant is not only competitive with the derivative-based
solver but also with the original implementation of DMS.
