An assessment of Direct MultiSearch when enriched with first-order information for multiobjective optimization

Direct MultiSearch (DMS) is a robust and efficient derivative-free optimization algorithm, able to generate approximations to the complete Pareto front of a given multiobjective optimization (MOO) problem. When first (or higher) order derivatives of the different components of the objective function are available, typical approaches for MOO problems are based on generating a single sequence of iterates that converges to a point with corresponding image lying on the Pareto front (one at a time). The purpose of this work is to asses the potential enrichment of adding first-order information, when derivatives are available, to the DMS framework. For that, we describe and analyze several different combined techniques that maintain the search/poll paradigm of DMS, while adding in a suitable way gradient information to the poll step. To properly evaluate the new proposed schemes, we provide numerical results for a set of benchmark MOO problems, in the form of performance profiles, where common performance metrics considered in the MOO community are reported. The proposed schemes are compared with the original DMS and also with the recently developed MOSQP approach that approximates the entire Pareto front at once, using first and second order information.