Structural and Multidisciplinary Optimization

, Volume 47, Issue 1, pp 19–35 | Cite as

New Approximation Assisted Multi-objective collaborative Robust Optimization (new AA-McRO) under interval uncertainty

  • Weiwei Hu
  • Shapour AzarmEmail author
  • Ali Almansoori
Research Paper


Existing collaborative optimization techniques with multiple coupled subsystems are predominantly focused on single-objective deterministic optimization. However, many engineering optimization problems have system and subsystems that can each be multi-objective, constrained and with uncertainty. The literature reports on a few deterministic Multi-objective Multi-Disciplinary Optimization (MMDO) techniques. However, these techniques in general require a large number of function calls and their computational cost can be exacerbated when uncertainty is present. In this paper, a new Approximation-Assisted Multi-objective collaborative Robust Optimization (New AA-McRO) under interval uncertainty is presented. This new AA-McRO approach uses a single-objective optimization problem to coordinate all system and subsystem multi-objective optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the system and subsystem objective functions. The new AA-McRO is able to explore the design space better and obtain optimum design solutions more efficiently. Also, the new AA-McRO obtains an estimate of Pareto optimum solutions for MMDO problems whose system-level objective and constraint functions are relatively insensitive (or robust) to input uncertainties. Another characteristic of the new AA-McRO is the use of online approximation for objective and constraint functions to perform system robustness evaluation and subsystem-level optimization. Based on the results obtained from a numerical and an engineering example, it is concluded that the new AA-McRO performs better than previously reported MMDO methods.


Multi-objective multidisciplinary optimization Collaborative optimization Robust optimization Approximation 



The work presented in this paper was supported in part by The Petroleum Institute (PI), Abu Dhabi, United Arab Emirates, as part of the Education and Energy Research Collaboration (EERC) agreement between the PI and University of Maryland, College Park. The work was also supported in part by an ONR grant. Such support does not constitute an endorsement by the funding agency of the opinions expressed in the paper. A previous version of this paper was presented at the 13th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Fort Worth, TX (Hu et al. 2010).


  1. Ahn J, Kwon JH (2006) An efficient strategy for reliability-based multidisciplinary design optimization using BLISS. Struct Multidisc Optim 31(7):363–372CrossRefGoogle Scholar
  2. Allison JT, Kokkolaras M, Papalambros PY (2009) Optimal partitioning and coordination decisions in decomposition-based design optimization. J Mech Des 131(10):081008-1–081008-8Google Scholar
  3. Aute V, Azarm S (2006) A genetic algorithms based approach for multidisciplinary multiobjective collaborative optimization. In: Proceedings of the 11th AIAA/ISSMO multidisciplinary analysis and optimization conference. Portsmouth, VAGoogle Scholar
  4. Azarm S, Li WC (1988) A two level decomposition method for design optimization. Eng Optim 13:211–224CrossRefGoogle Scholar
  5. Balling RJ, Sobieszczanski-Sobieski J (1996) Optimization of coupled systems: a critical overview of approaches. AIAA J 34(1):6–17zbMATHCrossRefGoogle Scholar
  6. Braun R, Kroo I (1996) Development and application of the collaborative optimization architecture in a multidisciplinary design environment. In: Alexandrov N, Hussaini M (eds) Multidisciplinary design optimization: state-of-the-Art, SIAMGoogle Scholar
  7. Cramer E, Dennis J, Frank P, Lewis R, Shubin G (1994) Problem formulation for multidisciplinary optimization. SIAM J Optim 4:754–776MathSciNetzbMATHCrossRefGoogle Scholar
  8. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, Ltd, New YorkzbMATHGoogle Scholar
  9. DeMiguel A, Murray W (2006) A local convergence analysis of bilevel decomposition algorithms. Optim Eng 7(2):99–133MathSciNetzbMATHCrossRefGoogle Scholar
  10. Elishakoff I, Haftka RT, Fang J (1994) Structural design under bounded uncertainty—optimization with anti-optimization. Comput Struct 53(8):1401–1405zbMATHCrossRefGoogle Scholar
  11. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-WesleyGoogle Scholar
  12. Gu X, Renaud JE, Penninger CL (2006) Implicit uncertainty propagation for robust collaborative optimization. J Mech Des 128(4):1001–1013CrossRefGoogle Scholar
  13. Gunawan S, Azarm S, Wu J, Boyars A (2003) Quality-assisted multi-objective multidisciplinary genetic algorithms. AIAA J 41(11):1752–1762CrossRefGoogle Scholar
  14. Hu W, Azarm S, Almansoori A (2010) Approximation assisted multi-objective collaborative robust optimization (AA-McRO) under interval uncertainty. 13th AIAA/ISSMO multidisciplinary analysis and optimization conference. Forth worth, TXGoogle Scholar
  15. Hu W, Li M, Azarm S, Almansoori A (2011) Improving multi-objective robust optimization under interval uncertainty using online approximation and constraint cuts. J Mech Des 133(8):061002-1–061002-9Google Scholar
  16. Jang BS, Yang YS, Jung HS, Yeun YS (2005) Managing approximation models in collaborative optimization. Struct Multidisc Optim 30(1):11–26CrossRefGoogle Scholar
  17. Kim HM, Michelena NF, Papalambros PY, Jiang T (2003) Target cascading in optimal system design. J Mech Des 125(3):474–480CrossRefGoogle Scholar
  18. Koehler JR, Owen AB (1996) Computer experiments. Handbook of statistics. Elsevier Science, New York, pp 261–308Google Scholar
  19. Kokkolaras M, Mourelatos ZP, Papalambros PY (2006) Design optimization of hierarchically decomposed multilevel systems under uncertainty. J Mech Des 128(2):503–508CrossRefGoogle Scholar
  20. Kroo I, Manning V (2000) Collaborative optimization: status and directions. In: Proceedings of the 8th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization. Long Beach, CAGoogle Scholar
  21. Li M, Azarm S (2008) Multiobjective collaborative robust optimization with interval uncertainty and interdisciplinary uncertainty propagation. J Mech Des 130(10):081402-1–081402-11Google Scholar
  22. Li M, Hamel J, Azarm S (2010) Optimal uncertainty reduction for multi-disciplinary multi-output systems using sensitivity analysis. Struct Multidisc Optim 40:77–96zbMATHCrossRefGoogle Scholar
  23. MATLAB (2011) MATLAB and simulink for technical computing. Mathworks, Version 2011aGoogle Scholar
  24. McAllister CD, Simpson TW, Hacker K, Lewis K, Messac A (2005) Integrating linear physical programming within collaborative optimization for multiobjective multidisciplinary design optimization. Struct Multidisc Optim 29(3):178–189CrossRefGoogle Scholar
  25. Renaud JE, Gabriele GA (1993) Improved coordination in nonhierarchic system optimization. AIAA J 31(14):2367–2373zbMATHCrossRefGoogle Scholar
  26. Roth BD, Kroo IM (2008) Enhanced collaborative optimization: a decomposition-based method for multidisciplinary design. In: Proceedings of the ASME design engineering technical conferences. Brooklyn, NYGoogle Scholar
  27. Simpson TW, Korte JJ, Mauery TM, Mistree F (2001) Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA J 39(14):2233–2241CrossRefGoogle Scholar
  28. Sobieszczanski-Sobieski J (1982) A linear decomposition method for large optimization problem - blueprint for development. NASA TM 83248Google Scholar
  29. Sobieszczanski-Sobieski J (1998) Optimization by decomposition: a step from hierarchic to non-hierarchic systems. In: Proceedings of the 2nd NASA/Air force symposium on recent advances in multidisciplinary analysis and optimization. Hampton, VAGoogle Scholar
  30. Sobieszczanski-Sobieski J, Agte J, Sandusky JR (2000) Bi-level integrated system synthesis (BLISS). AIAA J 38(1):164–172CrossRefGoogle Scholar
  31. Sobieski IP, Manning VM, Kroo IM (1998) Response surface estimation and refinement in collaborative optimization. In: Proceedings of the 7th AIAA/USAF/NASA/ISSMO symposium multidisciplinary analysis and optimization. St. Louis, MOGoogle Scholar
  32. Tappeta RV, Renaud JE (1997) Multiobjective collaborative optimization. J Mech Des 119(3):403–411CrossRefGoogle Scholar
  33. Tosserams S, Etman LFP, Rooda JE (2009) A classification of methods for distributed system optimization based on formulation structure. Struct Multidisc Optim 39(7):503–517MathSciNetCrossRefGoogle Scholar
  34. Wu J, Azarm S (2001) Metrics for quality assessment of a multiobjective design optimization solution set. J Mech Des 123(1):18–25CrossRefGoogle Scholar
  35. Zadeh P, Toropov V, Wood A (2009) Metamodel-based collaborative optimization framework. Struct Multidisc Optim 38(2):103–115CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA
  2. 2.Department of Chemical EngineeringThe Petroleum InstituteAbu DhabiUAE

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