  Direct Multisearch (DMS) is a well-established class of methods for
multiobjective derivative-free optimization, where constraints are addressed by
an extreme barrier approach, only evaluating feasible points. In this work, we
propose a filter approach, combined with an inexact feasibility restoration
step, to address constraints in the DMS framework. The filter approach treats
feasibility as an additional component of the objective function, avoiding the
computation of penalty parameters or Lagrange multipliers. The inexact
restoration step attempts to generate new feasible points, contributing to
prioritize feasibility, a requirement for the good performance of any filter
approach. Theoretical results are provided, analyzing the different types of
sequences of points generated by the new algorithm, and numerical experiments
on a set of nonlinearly constrained biobjective problems are reported, stating
the good algorithmic performance of the proposed approach.
