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In this work, we consider multiobjective optimization problems with bothbound constraints on the variables and general nonlinear constraints, whereobjective and constraint function values can only be obtained by querying ablack box. Furthermore, we consider the case where a subset of the variablescan only take integer values. We propose a new linesearch-based solution methodand show that it converges to a set of stationary points for the problem. Forwhat concerns the continuous variables, we employ a strategy for the estimationof the Pareto frontier recently proposed in the literature and which takesadvantage of dense sequences of search directions. The subset of variables thatmust assume discrete values are dealt with using primitive directionsappropriately modified to take into account the presence of more than oneobjective functions. Numerical results obtained with the proposed method on aset of test problems and comparison with other solution methods show theviability and efficiency of the proposed approach.

A derivative-free approach to mixed integer constrained multiobjective nonsmooth optimization