[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Springer Nature Link
Log in

Use of a biobjective direct search algorithm in the process design of material science applications

  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

This work describes the application of a direct search method to the optimization of problems of real industrial interest, namely three new material science applications designed with the FactSage software. The search method is BiMADS, the biobjective version of the mesh adaptive direct search (MADS) algorithm, designed for blackbox optimization. We give a general description of the algorithm, and, for each of the three test cases, we describe the optimization problem, discuss the algorithmic choices, and give numerical results to demonstrate the efficiency of BiMADS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Abramson MA, Audet C, Couture G, Dennis Jr JE, Le Digabel S, Tribes C (2015) The NOMAD project. https://www.gerad.ca/nomad

  • Abramson MA, Audet C, Dennis JE Jr, Le Digabel S (2009) OrthoMADS: a deterministic MADS instance with orthogonal directions. SIAM J Optim 20(2):948–966

    Article  MathSciNet  MATH  Google Scholar 

  • Audet C, Dennis JE Jr (2006) Mesh adaptive direct search algorithms for constrained optimization. SIAM J Optim 17(1):188–217

    Article  MathSciNet  MATH  Google Scholar 

  • Audet C, Dennis JE Jr (2009) A progressive barrier for derivative-free nonlinear programming. SIAM J Optim 20(1):445–472

    Article  MathSciNet  MATH  Google Scholar 

  • Audet C, Béchard V, Le Digabel S (2008a) Nonsmooth optimization through mesh adaptive direct search and variable neighborhood search. J Glob Optim 41(2):299–318

    Article  MATH  Google Scholar 

  • Audet C, Savard G, Zghal W (2008b) Multiobjective optimization through a series of single-objective formulations. SIAM J Optim 19(1):188–210

    Article  MathSciNet  MATH  Google Scholar 

  • Audet C, Dennis JE Jr, Le Digabel S (2010a) Globalization strategies for mesh adaptive direct search. Comput Optim Appl 46(2):193–215

    Article  MathSciNet  MATH  Google Scholar 

  • Audet C, Savard G, Zghal W (2010b) A mesh adaptive direct search algorithm for multiobjective optimization. Eur J Oper Res 204(3):545–556

    Article  MathSciNet  MATH  Google Scholar 

  • Bale CW, Bélisle E, Chartrand P, Decterov SA, Eriksson G, Hack K, Jung I-H, Kang Y-B, Melançon J, Pelton AD, Robelin C, Petersen S (2009) FactSage thermochemical software and databases—recent developments. CALPHAD Comput Coupling Phase Diagr Thermochem 33(2):295–311

    Article  Google Scholar 

  • Chartrand P, Pelton AD (2002) A predictive thermodynamic model for the Al–NaF–AlF3 system. In: Schneider WA (ed) Light metals 2002. Minerals, Metals and Materials Society, Warrendale, pp 245–252

    Google Scholar 

  • Chrenkova M, Danek V, Silny A, Utigard TA (1996) Density, electrical conductivity and viscosity of low melting baths for aluminium electrolysis. In: Hale W (ed) Light metals 1996. Minerals, Metals and Materials Society, Warrendale, pp 227–232

    Google Scholar 

  • Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York. Reissued in 1990 by SIAM Publications, Philadelphia, as vol 5 in the series classics in applied mathematics

  • Conn AR, Le Digabel S (2013) Use of quadratic models with mesh-adaptive direct search for constrained black box optimization. Optim Methods Softw 28(1):139–158

    Article  MathSciNet  MATH  Google Scholar 

  • Conn AR, Scheinberg K, Vicente LN (2009) Introduction to derivative-free optimization. MOS-SIAM series on optimization. SIAM, Philadelphia

    Book  Google Scholar 

  • Custódio AL, Madeira JFA, Vaz AIF, Vicente LN (2011) Direct multisearch for multiobjective optimization. SIAM J Optim 21(3):1109–1140

    Article  MathSciNet  MATH  Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197

    Article  Google Scholar 

  • Degarmo EP, Black JT, Kohser RA (2003) Materials and processes in manufacturing, 9th edn. Wiley, New York

    Google Scholar 

  • Dmitrieva O, Ponge D, Inden G, Millán J, Choi P, Sietsma J, Raabe D (2011) Chemical gradients across phase boundaries between martensite and austenite in steel studied by atom probe tomography and simulation. Acta Mater 59(1):364–374

    Article  Google Scholar 

  • Fermi E, Metropolis (1952) Numerical solution of a minimum problem. Los Alamos unclassified report LA-1492. Los Alamos National Laboratory, Los Alamos

  • Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Program A 91:239–269

    Article  MathSciNet  MATH  Google Scholar 

  • Gheribi AE, Robelin C, Le Digabel S, Audet C, Pelton AD (2011) Calculating all local minima on liquidus surfaces using the FactSage software and databases and the Mesh Adaptive Direct Search algorithm. J Chem Thermodyn 43(9):1323–1330

    Article  Google Scholar 

  • Gheribi AE, Audet C, Le Digabel S, Bélisle E, Bale CW, Pelton AD (2012) Calculating optimal conditions for alloy and process design using thermodynamic and properties databases, the FactSage software and the Mesh Adaptive Direct Search algorithm. CALPHAD Comput Coupling Phase Diagr Thermochem 36:135–143

    Article  Google Scholar 

  • Gheribi AE, Le Digabel S, Audet C, Chartrand P (2013) Identifying optimal conditions for magnesium based alloy design using the Mesh Adaptive Direct Search algorithm. Thermochim Acta 559:107–110

    Article  Google Scholar 

  • Haupin W (1991) The influence of additives on Hall–Héroult bath properties. JOM 43(11):28–34

    Article  Google Scholar 

  • Kaufman L, Bernstein H (1970) Computer calculation of phase diagrams. Academic, New York

    Google Scholar 

  • Le Digabel S (2011) Algorithm 909: NOMAD: nonlinear optimization with the MADS algorithm. ACM Trans Math Softw 37(4):44:1–44:15

    Article  Google Scholar 

  • Pelton AD, Chartrand P, Eriksson G (2001) The modified quasi-chemical model: Part IV. Two-sublattice quadruplet approximation. Metall Mater Trans A 32(6):1409–1416

    Article  Google Scholar 

  • Renaud E, Robelin C, Gheribi AE, Chartrand P (2011) Thermodynamic evaluation and optimization of the Li, Na, K, Mg, Ca, Sr//F, Cl reciprocal system. J Chem Thermodyn 43(8):1286–1298

    Article  Google Scholar 

  • Robelin C, Chartrand P (2007a) A density model based on the modified quasichemical model and applied to the NaF–AlF\(_3\)–CaF\(_2\)–Al\(_2\)O\(_3\) electrolyte. Metall Mater Trans B 38(6):881–892

    Article  Google Scholar 

  • Robelin C, Chartrand P (2007b) Predictive models for the density and viscosity of the NaF–AlF3–CaF2–Al2O3 electrolyte. In: Sorlie M (ed) Light metals 2007. Minerals, Metals and Materials Society, Warrendale, pp 565–570

    Google Scholar 

  • Robelin C, Chartrand P, Eriksson G (2007) A density model for multicomponent liquids based on the modified quasichemical model: application to the NaCl–KCl–MgCl\(_2\)–CaCl\(_2\) system. Metall Mater Trans B 38(6):869–879

    Article  Google Scholar 

  • Saunders N, Miodownik AP (eds) (1998) Chapter 6: phase stabilities. In: Pergamon materials series, vol 1. Pergamon. doi:10.1016/S1470-1804(98)80026-6

  • Sha W (2013) Ultra high-strength maraging steel. In: Steels. Springer, London, pp 141–161

  • Sourmail T, Garcia-Mateo C (2005a) A model for predicting the Ms temperatures of steels. Comput Mater Sci 34(2):213–218

    Article  Google Scholar 

  • Sourmail T, Garcia-Mateo C (2005b) Critical assessment of models for predicting the Ms temperature of steels. Comput Mater Sci 34(4):323–334

    Article  Google Scholar 

  • Tiwaria S, Fadelb G, Deb K (2011) AMGA2: improving the performance of the archive-based micro-genetic algorithm for multi-objective optimization. Eng Optim 43(4):377–401

    Article  Google Scholar 

  • Torczon V (1997) On the convergence of pattern search algorithms. SIAM J Optim 7(1):1–25

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank Christopher Hutchinson and Chad Sinclair for their approach to the steel-design problem, which allowed us to test BiMADS on this complex application. The work of the first, fifth, and sixth authors was supported by a Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) via the Magnesium Strategic Research Network. The last author was supported by NSERC Grant 418250 and by AFOSR FA9550-12-1-0198.

Author information

Authors and Affiliations

  1. CRCT, Centre de Recherche en Calcul Thermochimique, Département de Génie Chimique, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montreal, QC, H3C 3A7, Canada

    Aïmen E. Gheribi, Eve Bélisle, Christian Robelin, Patrice Chartrand, Arthur D. Pelton & Christopher W. Bale

  2. Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, QC, H3A 2B2, Canada

    Jean-Philippe Harvey

  3. GERAD and Département de Mathématiques et Génie Industriel, École Polytechnique de Montréal, C.P. 6079, Succ. Centre-ville, Montreal, QC, H3C 3A7, Canada

    Sébastien Le Digabel

Authors
  1. Aïmen E. Gheribi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Philippe Harvey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eve Bélisle
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Christian Robelin
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Patrice Chartrand
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Arthur D. Pelton
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Christopher W. Bale
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Sébastien Le Digabel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sébastien Le Digabel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gheribi, A.E., Harvey, JP., Bélisle, E. et al. Use of a biobjective direct search algorithm in the process design of material science applications. Optim Eng 17, 27–45 (2016). https://doi.org/10.1007/s11081-015-9301-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-015-9301-2

Keywords

Mathematics Subject Classification

Search

Navigation