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Improving Efficiency of a Multistart with Interrupted Hooke-and-Jeeves Filter Search for Solving MINLP Problems

  • Florbela P. FernandesEmail author
  • M. Fernanda P. Costa
  • Ana Maria A. C. Rocha
  • Edite M. G. P. Fernandes
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9786)

Abstract

This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are sufficiently close to other points already used to invoke the local search is analyzed. A variant of the Hooke-and-Jeeves filter algorithm for MINLP is proposed with the goal of interrupting the iterative process if the accepted iterate falls inside an \(\epsilon \)-neighborhood of an already computed minimizer. Preliminary numerical results are included.

Keywords

nonconvex MINLP Multistart Hooke-and-Jeeves Filter method 
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Notes

Acknowledgments

The authors wish to thank two anonymous referees for their comments and suggestions. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e Tecnologia, within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Florbela P. Fernandes
    • 1
    Email author
  • M. Fernanda P. Costa
    • 2
    • 3
  • Ana Maria A. C. Rocha
    • 4
    • 5
  • Edite M. G. P. Fernandes
    • 5
  1. 1.ESTiG, Polytechnic Institute of BragançaBragançaPortugal
  2. 2.Department of Mathematics and ApplicationsUniversity of MinhoGuimarãesPortugal
  3. 3.Centre of MathematicsBragaPortugal
  4. 4.Department of Production and SystemsUniversity of MinhoBragaPortugal
  5. 5.Algoritmi Research CentreUniversity of MinhoBragaPortugal

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