This paper is concerned with the definition of new derivative-free methods for box constrained multiobjective optimization. The method that we propose is a non-trivial extension of the well-known implicit filtering algorithm to the multiobjective case. Global convergence results are stated under smooth assumptions on the objective functions. We also show how the proposed method can be used as a tool to enhance the performance of the Direct MultiSearch (DMS) algorithm. Numerical results on a set of test problems show the efficiency of the implicit filtering algorithm when used to find a single Pareto solution of the problem. Furthermore, we also show through numerical experience that the proposed algorithm improves the performance of DMS alone when used to reconstruct the entire Pareto front.

An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints / Cocchi, G.; Liuzzi, G.; Papini, A.; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 69:2(2018), pp. 267-296. [10.1007/s10589-017-9953-2]

An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints

Cocchi G.;Liuzzi G.
;
Sciandrone M.
2018

Abstract

This paper is concerned with the definition of new derivative-free methods for box constrained multiobjective optimization. The method that we propose is a non-trivial extension of the well-known implicit filtering algorithm to the multiobjective case. Global convergence results are stated under smooth assumptions on the objective functions. We also show how the proposed method can be used as a tool to enhance the performance of the Direct MultiSearch (DMS) algorithm. Numerical results on a set of test problems show the efficiency of the implicit filtering algorithm when used to find a single Pareto solution of the problem. Furthermore, we also show through numerical experience that the proposed algorithm improves the performance of DMS alone when used to reconstruct the entire Pareto front.
2018
Derivative-free optimization; Implicit filtering; Multiobjective nonlinear programming
01 Pubblicazione su rivista::01a Articolo in rivista
An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints / Cocchi, G.; Liuzzi, G.; Papini, A.; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 69:2(2018), pp. 267-296. [10.1007/s10589-017-9953-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1433994
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