Journal of Global Optimization

, Volume 69, Issue 3, pp 525–545 | Cite as

Recent advances on the interval distance geometry problem

  • Douglas S. Gonçalves
  • Antonio Mucherino
  • Carlile Lavor
  • Leo LibertiEmail author


We discuss a discretization-based solution approach for a classic problem in global optimization, namely the distance geometry problem (DGP). We focus our attention on a particular class of the DGP which is concerned with the identification of the conformation of biological molecules. Among the many relevant ideas for the discretization of the DGP in the literature, we identify the most promising ones and address their inherent limitations to application to this class of problems. The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some distance restraints between pairs of atoms. We present computational results showcasing the usefulness of the new proposed approach. Proteins act on living cells according to their geometric and chemical properties: finding protein conformations can be very useful within the pharmaceutical industry in order to synthesize new drugs.


Distance geometry Discretization Molecular conformation 



DG and CL are thankful to the Brazilian research agencies FAPESP and CNPq for partial financial support. LL was partially supported by the “Bip:Bip” project within the ANR “Investissement d’Avenir” program. AM thanks University of Rennes 1 for financial support. AM and DG also acknowledge Brittany Region (France) for partial financial support.


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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.CFMUniversidade Federal de Santa CatarinaFlorianópolisBrazil
  2. 2.IRISAUniversité de Rennes 1RennesFrance
  3. 3.University of Campinas (IMECC-UNICAMP)Campinas - SPBrazil
  4. 4.CNRS LIX, École PolytechniquePalaiseauFrance

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