Mathematical Programming Computation

, Volume 3, Issue 4, pp 349–390 | Cite as

A recipe for finding good solutions to MINLPs

  • Leo Liberti
  • Nenad Mladenović
  • Giacomo NanniciniEmail author
Full Length Paper


Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard but practically important task, especially when the objective and/or the constraints are nonconvex. With this goal in mind, we present a general-purpose heuristic based on Variable Neighborhood Search, Local Branching, a local Nonlinear Programming algorithm and Branch-and-Bound. We test the proposed approach on MINLPLib, comparing with several existing heuristic and exact methods. An implementation of the proposed heuristic is freely available and can employ all NLP/MINLP solvers with an AMPL interface as the main search tools.

Mathematics Subject Classification (2000)

90C11 90C26 90C59 


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Copyright information

© Springer and Mathematical Optimization Society 2011

Authors and Affiliations

  • Leo Liberti
    • 1
  • Nenad Mladenović
    • 2
    • 3
  • Giacomo Nannicini
    • 4
    • 5
    Email author
  1. 1.LIX, École PolytechniquePalaiseauFrance
  2. 2.Brunel UniversityLondonUK
  3. 3.Institute of Mathematics, Academy of SciencesBelgradeSerbia
  4. 4.Singapore University of Technology and DesignSingaporeSingapore
  5. 5.Sloan School of ManagementMassachusetts Institute of TechnologyCambridgeUSA

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