Eurofuse 2011 pp 293-301 | Cite as

Penalty Fuzzy Function for Derivative-Free Optimization

  • J. Matias
  • P. Mestre
  • A. Correia
  • P. Couto
  • C. Serodio
  • P. Melo-Pinto
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 107)


Penalty and Barrier methods are normally used to solve Nonlinear Optimization Constrained Problems. The problems appear in areas such as engineering and are often characterized by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot be used. A Java based API was implemented, including only derivative-free optimization methods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalization when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the proposed penalty function besides being very robust also exhibits a very good performance.


Penalty Function Unconstrained Optimization Problem Barrier Method Direct Search Method Mesh Adaptive Direct Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • J. Matias
    • 1
  • P. Mestre
    • 1
  • A. Correia
    • 2
  • P. Couto
    • 1
  • C. Serodio
    • 1
  • P. Melo-Pinto
    • 1
  1. 1.CM-UTADVila RealPortugal
  2. 2.CM-UTAD and CIICESI/ESTGF/IPPFelgueirasPortugal

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