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

TL;DR

This paper introduces a derivative-free, linesearch-based method for solving complex multiobjective mixed-integer constrained optimization problems with black-box functions, demonstrating promising numerical results.

Contribution

It presents a novel linesearch approach that handles mixed-integer variables and nonlinear constraints in a multiobjective black-box setting, with proven convergence.

Findings

Method converges to stationary points.

Effective estimation of Pareto frontiers.

Numerical results show efficiency and viability.

Abstract

In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. Furthermore, we consider the case where a subset of the variables can only take integer values. We propose a new linesearch-based solution method and show that it converges to a set of stationary points for the problem. For what concerns the continuous variables, we employ a strategy for the estimation of the Pareto frontier recently proposed in the literature and which takes advantage of dense sequences of search directions. The subset of variables that must assume discrete values are dealt with using primitive directions appropriately modified to take into account the presence of more than one objective functions. Numerical results obtained with the proposed method on a set of test problems and comparison with other solution methods show the viability and efficiency of the proposed approach.