Abstract
We revisit a simple, yet capable to provide good solutions, procedure for solving the Distance Geometry Problem (DGP). This procedure combines two main components: the first one identifying an initial approximated solution via semidefinite programming, which is thereafter projected to the target dimension via PCA; and another component where this initial solution is refined by locally minimizing the Smooth STRESS function. In this work, we propose the use of the projected Levenberg-Marquart algorithm for this second step. In spite of the simplicity, as well as of its heuristic character, our experiments show that this procedure is able to exhibit good performances in terms of quality of the solutions for most of the instances we have selected for our experiments. Moreover, it seems to be promising not only for the DGP application arising in structural biology, which we considered in our computational experiments, but also in other ongoing studies related to the DGP and its applications: we finally provide a general discussion on how extending the presented ideas to other applications.
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Acknowledgments
The authors are very grateful to CAPES/Brazil for the CAPES-PRINT project, process number 88887.578009/2020-00, allowing AM to visit DG at UFSC, Florianópolis (SC, Brazil) for a 2-week time in December 2021. Most of the presented work was performed during such a visit. AM is also thankful to the ANR for the support on the international France-Taiwan project multiBioStruct (ANR-19-CE45-0019). DG thanks the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grant 305213/2021-0.
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Gonçalves, D.S., Mucherino, A. (2022). A Distance Geometry Procedure Using the Levenberg-Marquardt Algorithm and with Applications in Biology but Not only. In: Rojas, I., Valenzuela, O., Rojas, F., Herrera, L.J., Ortuño, F. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2022. Lecture Notes in Computer Science(), vol 13347. Springer, Cham. https://doi.org/10.1007/978-3-031-07802-6_13
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