A mesh adaptive direct search algorithm for multiobjective optimization

Abstract

This work studies multiobjective optimization ( MOP ) of nonsmooth functions subject to general constraints. We first present definitions and optimality conditions as well as some single-objective formulations of MOP, parameterized with respect to some reference point in the space of objective functions. Next, we propose a new algorithm called M ultiM ads (multiobjective mesh adaptive direct search) for MOP. M ultiM ads generates an approximation of the Pareto front by solving a series of single-objective formulations of MOP generated using the NBI (natural boundary intersection) framework. These single-objective problems are solved using the M ads (mesh adaptive direct search) algorithm for constrained nonsmooth optimization. The Pareto front approximation is shown to satisfy some first-order necessary optimality conditions based on the Clarke calculus. M ultiM ads is then tested on problems from the literature with different Pareto front landscapes and on a styrene production process simulation problem from chemical engineering.