MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECTinspired optimization algorithm for experimentally accessible computational material design
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. Lastly, 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 'multicomponent optimization' of global and local search.
 Authors:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Univ. of Colorado Denver, Denver, CO (United States)
 Publication Date:
 Research Org.:
 National Renewable Energy Lab. (NREL), Golden, CO (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1395085
 Report Number(s):
 NREL/JA2C0060589
Journal ID: ISSN 09266003
 Grant/Contract Number:
 AC3608GO28308
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Computational Optimization and applications
 Additional Journal Information:
 Journal Volume: 68; Journal Issue: 3; Journal ID: ISSN 09266003
 Publisher:
 Springer
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; mixed integer optimization; DIRECT optimization; Pareto front; Sierpinski triangle; computational material design
Citation Formats
Graf, Peter A., and Billups, Stephen. MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECTinspired optimization algorithm for experimentally accessible computational material design. United States: N. p., 2017.
Web. doi:10.1007/s1058901799229.
Graf, Peter A., & Billups, Stephen. MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECTinspired optimization algorithm for experimentally accessible computational material design. United States. doi:10.1007/s1058901799229.
Graf, Peter A., and Billups, Stephen. 2017.
"MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECTinspired optimization algorithm for experimentally accessible computational material design". United States.
doi:10.1007/s1058901799229.
@article{osti_1395085,
title = {MDTri: robust and efficient global mixed integer search of spaces of multiple ternary alloys: A DIRECTinspired optimization algorithm for experimentally accessible computational material design},
author = {Graf, Peter A. and Billups, Stephen},
abstractNote = {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. Lastly, 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 'multicomponent optimization' of global and local search.},
doi = {10.1007/s1058901799229},
journal = {Computational Optimization and applications},
number = 3,
volume = 68,
place = {United States},
year = 2017,
month = 7
}

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