Computational Optimization and Applications

, Volume 69, Issue 2, pp 267–296 | Cite as

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

  • G. Cocchi
  • G. LiuzziEmail author
  • A. Papini
  • M. Sciandrone


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.


Multiobjective nonlinear programming Derivative-free optimization Implicit filtering 

Mathematics Subject Classification

90C30 90C56 65K05 



We are thankful to three anonymous reviewers whose stimulating comments and suggestions greatly helped us improving the paper. Also, we would like to thank Prof. Ana Luísa Custódio, José F. Aguilar Madeira, A. Ismael F. Vaz, and Luís Nunes Vicente for providing us the matlab code of their direct multisearch algorithm (DMS). Work partially supported by INDAM-GNCS.


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria dell’InformazioneUniversità di FirenzeFlorenceItaly
  2. 2.Istituto di Analisi dei Sistemi ed InformaticaConsiglio Nazionale delle RicercheRomeItaly
  3. 3.Dipartimento di Ingegneria IndustrialeUniversità di FirenzeFlorenceItaly

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