MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys A DIRECT-inspired optimization algorithm for experimentally accessible computational material design

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 i...

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Vydané v:Computational optimization and applications Ročník 68; číslo 3; s. 671 - 687
Hlavní autori: Graf, Peter A., Billups, Stephen
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.12.2017
Springer
Predmet:
computational material design
Convex and Discrete Geometry
DIRECT optimization
Management Science
Mathematics
MATHEMATICS AND COMPUTING
Mathematics and Statistics
mixed integer optimization
Operations Research
Operations Research/Decision Theory
Optimization
Pareto front
Sierpinski triangle
Statistics
Computational material design
Pareto front
DIRECT optimization
Mixed integer optimization
Sierpinski triangle
ISSN:0926-6003, 1573-2894
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Shrnutí: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.
Bibliografia:AC36-08GO28308
USDOE Office of Science (SC)
NREL/JA-2C00-60589
ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-017-9922-9