A mesh adaptive direct search algorithm for multiobjective optimization

Charles Audet, Gilles Savard and Walid Zghal

European Journal of Operational Research, 2010, vol. 204, issue 3, 545-556

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 MultiMads (multiobjective mesh adaptive direct search) for MOP. MultiMads 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 Mads (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. MultiMads is then tested on problems from the literature with different Pareto front landscapes and on a styrene production process simulation problem from chemical engineering.

Keywords: Multiobjective; optimization; Mesh; adaptive; direct; search; (Mads); Convergence; analysis (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:204:y:2010:i:3:p:545-556

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