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Branch and Bound Based Coordinate Search Filter Algorithm for Nonsmooth Nonconvex Mixed-Integer Nonlinear Programming Problems

  • Florbela P. Fernandes
  • M. Fernanda P. Costa
  • Edite M. G. P. Fernandes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8580)

Abstract

A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex then they are the most difficult to solve above all. We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy. To solve the relaxed subproblems at each node of the branch and bound tree search, an algorithm based on a multistart strategy with a coordinate search filter methodology is implemented. The produced numerical results show the robustness of the proposed methodology.

Keywords

nonconvex MINLP branch and bound multistart coordinate search filter method 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Florbela P. Fernandes
    • 1
    • 3
  • M. Fernanda P. Costa
    • 2
    • 3
  • Edite M. G. P. Fernandes
    • 4
  1. 1.ESTiGPolytechnic Institute of BragançaBragançaPortugal
  2. 2.Department of Mathematics and ApplicationsUniversity of MinhoGuimarãesPortugal
  3. 3.Centre of MathematicsUniversity of MinhoBragaPortugal
  4. 4.Algoritmi Research CentreUniversity of MinhoBragaPortugal

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