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MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys

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  • Peter A. Graf

    (National Renewable Energy Laboratory)

  • Stephen Billups

    (University of Colorado Denver)

Abstract

Computational materials design has suffered from a lack of algorithms formulated in terms of experimentally accessible variables. Here we formulate the problem of (ternary) alloy optimization at the level of choice of atoms and their composition that is normal for synthesists. Mathematically, this is a mixed integer problem where a candidate solution consists of a choice of three elements, and how much of each of them to use. This space has the natural structure of a set of equilateral triangles. We solve this problem by introducing a novel version of the DIRECT algorithm that (1) operates on equilateral triangles instead of rectangles and (2) works across multiple triangles. We demonstrate on a test case that the algorithm is both robust and efficient. Finally, we offer an explanation of the efficacy of DIRECT—specifically, its balance of global and local search—by showing that “potentially optimal rectangles” of the original algorithm are akin to the Pareto front of the “multi-component optimization” of global and local search.

Suggested Citation

  • Peter A. Graf & Stephen Billups, 2017. "MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys," Computational Optimization and Applications, Springer, vol. 68(3), pages 671-687, December.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:3:d:10.1007_s10589-017-9922-9
    DOI: 10.1007/s10589-017-9922-9
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    References listed on IDEAS

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    1. Alberto Franceschetti & Alex Zunger, 1999. "The inverse band-structure problem of finding an atomic configuration with given electronic properties," Nature, Nature, vol. 402(6757), pages 60-63, November.
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    Cited by:

    1. Jeffrey Larson & Sven Leyffer & Prashant Palkar & Stefan M. Wild, 2021. "A method for convex black-box integer global optimization," Journal of Global Optimization, Springer, vol. 80(2), pages 439-477, June.
    2. Brian Irwin & Eldad Haber, 2023. "Secant penalized BFGS: a noise robust quasi-Newton method via penalizing the secant condition," Computational Optimization and Applications, Springer, vol. 84(3), pages 651-702, April.

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