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Direct Multisearch (DMS) is a well-established class of methods formultiobjective derivative-free optimization, where constraints are addressed byan extreme barrier approach, only evaluating feasible points. In this work, wepropose a filter approach, combined with an inexact feasibility restorationstep, to address constraints in the DMS framework. The filter approach treatsfeasibility as an additional component of the objective function, avoiding thecomputation of penalty parameters or Lagrange multipliers. The inexactrestoration step attempts to generate new feasible points, contributing toprioritize feasibility, a requirement for the good performance of any filterapproach. Theoretical results are provided, analyzing the different types ofsequences of points generated by the new algorithm, and numerical experimentson a set of nonlinearly constrained biobjective problems are reported, statingthe good algorithmic performance of the proposed approach.

An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization