Skip to main content
SpringerLink
Log in

Multiparametric optimization for multidisciplinary engineering design

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

The area of Multiparametric Optimization (MPO) solves problems that contain unknown problem data represented by parameters. The solutions map parameter values to optimal design and objective function values. In this paper, for the first time, MPO techniques are applied to improve and advance Multidisciplinary Design Optimization (MDO) to solve engineering problems with parameters. A multiparametric subgradient algorithm is proposed and applied to two MDO methods: Analytical Target Cascading (ATC) and Network Target Coordination (NTC). Numerical results on test problems show the proposed parametric ATC and NTC methods effectively solve parametric MDO problems and provide useful insights to designers. In addition, a novel Two-Stage ATC method is proposed to solve nonparametric MDO problems. In this new approach elements of the subproblems are treated as parameters and optimal design functions are constructed for each one. When the ATC loop is engaged, steps involving the lengthy optimization of subproblems are replaced with simple function evaluations.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

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

  • Bemporad A, Filippi C (2006) An algorithm for approximate multiparametric convex programming. Comput Optim Appl 35(1):87–108

    Article  MathSciNet  MATH  Google Scholar 

  • Bertsekas D (1999) Nonlinear Programming. Athena Scientific

  • Beyer H, Sendhoff B (2007) Robust optimization – a comprehensive survey. Comput Method Appl M 196 (33–34):3190–3218

    Article  MathSciNet  MATH  Google Scholar 

  • Domínguez L, Pistikopoulos E (2013) A quadratic approximation-based algorithm for the solution of multiparametric mixed-integer nonlinear programming problems. AICHE J 59(2):483– 495

    Article  Google Scholar 

  • Domínguez L, Narciso D, Pistikopoulos E (2010) Recent advances in multiparametric nonlinear programming. Comput Chem Eng 34:707–716

    Article  Google Scholar 

  • Ehrgott M (2005) Multicriteria Optimization, 2nd edn. Springer

  • Fiacco A (1983) Introduction to Sensitivity and Stability Analysis in Nonlinear Programming, Mathematics in Science and Engineering, vol 165. Academic Press

  • Gardenghi M, Wiecek M, Wang W (2013) Biobjective optimization for analytical target cascading: optiMality vs. achievability. Struct Multidiscip O 47:111–133

    Article  MathSciNet  MATH  Google Scholar 

  • Geoffrion A (1968) Proper efficiency and the theory of vector maximization. J Math Anal Appl 22:618–630

    Article  MathSciNet  MATH  Google Scholar 

  • Gobbi M, Mastinu G (2001) Analytical description and optimization of the dynamic behaviour of passively suspended road vehicles. J Sound Vib 245(3):457–481

    Article  Google Scholar 

  • Guarneri M, Gobbi M, Papalambros P (2009) Multi-objective, multi-level design optimization of ground vehicle suspension design. In: 8th WCSMO Conference, Lisbon, Portugal

  • Guarneri M, Gobbi M, Papalambros P (2011) Efficient multi-level design optimization using analytical target cascading and sequential quadratic programming. Struct Multidiscip O 44(3):351– 362

    Article  MathSciNet  MATH  Google Scholar 

  • Guarneri P, Leverenz J, Wiecek M, Fadel G (2013) Optimization of nonhierarchically decomposed problems. J Comput Appl Math 246:312–319

    Article  MathSciNet  MATH  Google Scholar 

  • Haftka R, Gürdal Z (1992) Elements of Structural Optimization, 3rd edn. Kluwer Publishers

  • Hegranæs Ø, Gravdahl J, Tøndel P (2005) Spacecraft altitude control using explicit model predictive control. Automatica 41(12):2107–2114

    Article  MathSciNet  MATH  Google Scholar 

  • Herceg M, Kvasnica M, Jones C, Morari M (2013) Multi-Parametric Toolbox 3.0. In: Proceedings of the European Control Conference. http://control.ee.ethz.ch/mpt, Zürich, Switzerland, pp 502–510

  • Johansen T (2002) On multi-parametric nonlinear programming and explicit nonlinear model predictive control. In: Proceedings 41st IEEE Conf Decis Control, Las Vegas, NV

  • Kim HM, Michelena NF, Papalambros PY, Jiang T (2003a) Target cascading in optimal system design. J Mech Des 125(3):474– 480

  • Kim HM, Rideout DG, Papalambros PY, Stein JL (2003b) Analytical target cascading in automotive vehicle design. J Mech Des 125:481–489

  • Kosmidis V, Panga A, Sakizlis V, Charles G, Kenchington S, Bozinis N, Pistikopoulos E (2006) Output feedback parametric controllers for an active valve train actuation system. In: Proceedings 45th IEEE Conf Decis Control, San Diego, CA

  • Leverenz J (2015) Network Target Coordination for Multiparametric Programming. PhD thesis Clemson University, Clemson, SC

    Google Scholar 

  • Li L, Zabinsky Z (2011) Incorporating uncertainty into a supplier selection problem. Int J Prod Econ 134:344–356

    Article  Google Scholar 

  • Li Y, Lu Z, Michalek J (2008) Diagonal quadratic approximation for parallelization of analytical target cascading. J Mech Des 051(5):402

    Google Scholar 

  • Löfberg J (2004) Yalmip: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD Conference, Taipei, Taiwan, http://users.isy.liu.se/johanl/yalmip

  • Pistikopoulos E, Dua V, Bozinis N, Bemporad A, Morari M (2002) On-line optimization via off-line parametric optimization tools. Comput Chem Eng 26:175–184

    Article  Google Scholar 

  • Simpson T, Martins J (2011) Multidisciplinary design optimization for complex engineered systems design: Report from an NSF workshop. J Mech Des 133(101):002

    Google Scholar 

  • Sobieszczanski-Sobieski J, Altus T, Phillips MRS (2003) Bi-level integrated system synthesis for concurrent and distributed processing. AIAA J 41(10):1996–2003

    Article  Google Scholar 

  • Tosserams S (2008) Distributed optimization for systems design: an augmented lagrangian coordination method. Wohrmann Print Service, Netherlands

    MATH  Google Scholar 

  • Tosserams S, Etman L, Rooda J (2009) A micro-accelerometer mdo benchmark problem. Struct Multidiscip O 41(2):255–275

    Article  Google Scholar 

  • Tosserams S, Kokkolaras M, Etman L, Rooda J (2010) A nonhierarchical formulation of analytical target cascading. J Mech Des 051(5):002

    Google Scholar 

  • Wang W, Xu M, Guarneri P, Fadel G, Blouin V (2012) A consensus optimization via alternating direction method of multipliers for network target coordination

  • Wang W, Blouin V, Gardenghi M, Wiecek M, Fadel G, Sloop B (2013) A cutting plane method for analytical target cascading with augmented Lagrangian coordination. J Mech Des 135(10)

  • Xu M, Wang W, Guarneri P, Fadel G (2013) CADMM Applied to hybrid network decomposition, Orlando, FL

  • Xu M, Wang W, Guarneri P, Fadel G (2014) Solving structure for network-decomposed problems optimized with augmented Lagrangian coordination. In: ASME 2014 IDETC/CIE Conference

  • Xu M, Fadel G, Wiecek MM (2015) Dual residual for centralized augmented Lagrangian coordination based on optiMality conditions. J Mech Des 137(6)

Download references

Acknowledgments

This research was supported by the National Science Foundation, grant number CMMI-1129969. The authors would like to thank Dr. Paolo Guarneri for his assistance with the Matlab code for the car suspension problem and his advice of a suitable choice of parameter for the problem.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Clemson University, Clemson, USA

    Jonathon Leverenz & Margaret M. Wiecek

  2. Department of Mechanical Engineering, Clemson University, Clemson, USA

    Meng Xu

Authors
  1. Jonathon Leverenz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Margaret M. Wiecek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jonathon Leverenz.

Additional information

This research was supported by the National Science Foundation, grant number CMMI-1129969

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Leverenz, J., Xu, M. & Wiecek, M.M. Multiparametric optimization for multidisciplinary engineering design. Struct Multidisc Optim 54, 795–810 (2016). https://doi.org/10.1007/s00158-016-1437-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-016-1437-y

Keywords

Search

Navigation