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Maximum feasible subsystems of distance geometry constraints

Author

Listed:
  • Maurizio Bruglieri

    (Politecnico di Milano)

  • Roberto Cordone

    (Università degli Studi di Milano)

  • Leo Liberti

    (LIX CNRS Ecole Polytechnique, Institut Polytechnique de Paris)

Abstract

We study the problem of satisfying the maximum number of distance geometry constraints with minimum experimental error. This models the determination of the shape of proteins from atomic distance data which are obtained from nuclear magnetic resonance experiments and exhibit experimental and systematic errors. Experimental errors are represented by interval constraints on Euclidean distances. Systematic errors occur from a misassignment of distances to wrong atomic pairs: we represent such errors by maximizing the number of satisfiable distance constraints. We present many mathematical programming formulations, as well as a “matheuristic” algorithm based on reformulations, relaxations, restrictions and refinement. We show that this algorithm works on protein graphs with hundreds of atoms and thousands of distances.

Suggested Citation

  • Maurizio Bruglieri & Roberto Cordone & Leo Liberti, 2022. "Maximum feasible subsystems of distance geometry constraints," Journal of Global Optimization, Springer, vol. 83(1), pages 29-47, May.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:1:d:10.1007_s10898-021-01003-4
    DOI: 10.1007/s10898-021-01003-4
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    References listed on IDEAS

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    1. Dimitris Achlioptas & Assaf Naor & Yuval Peres, 2005. "Rigorous location of phase transitions in hard optimization problems," Nature, Nature, vol. 435(7043), pages 759-764, June.
    2. Leo Liberti, 2020. "Rejoinder on: Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 350-357, July.
    3. Douglas S. Gonçalves & Antonio Mucherino & Carlile Lavor & Leo Liberti, 2017. "Recent advances on the interval distance geometry problem," Journal of Global Optimization, Springer, vol. 69(3), pages 525-545, November.
    4. Leo Liberti & Fabrizio Marinelli, 2014. "Mathematical programming: Turing completeness and applications to software analysis," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 82-104, July.
    5. Carlile Lavor & Leo Liberti & Antonio Mucherino, 2013. "The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances," Journal of Global Optimization, Springer, vol. 56(3), pages 855-871, July.
    6. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.
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