As a bi-level optimization method, collaborative optimization can solve multidisciplinary design optimization problems in practical engineering effectively. However, if there are high-dimensional couplings in a multidisciplinary design optimization problem, a large number of compatibility constraints will be required in collaborative optimization. In this situation, collaborative optimization will not be suitable to be utilized because of low computational efficiency or divergence issue. To solve this problem, an efficient interaction balance optimization method is proposed in this article. In interaction balance optimization method, the simple coordination strategy of interaction balance principle and the distributed optimization strategy of collaborative optimization can be integrated effectively. Lagrange multipliers are used instead of compatibility constraints to maintain the consistency between any two coupled disciplines. Two examples are given to show the effectiveness of the proposed method.
AgarwalHRenaudJEPrestonEL. (2004) Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering and System Safety85(1): 281–294.
2.
AlexandrovNMLewisRM (2002) Analytical and computational aspects of collaborative optimization for multidisciplinary design. AIAA Journal40(2): 301–309.
3.
AmgaiRAbdelwahedS (2014) Power management of shipboard power systems using Interaction Balance Principle. In: Proceedings of the North American power symposium (NAPS), Pullman, WA, 7–9 September, pp. 1–6. New York: IEEE.
4.
BallingRWilkinsonC (1997) Execution of multidisciplinary design optimization approaches on common test problems. AIAA Journal35(1): 178–186.
5.
BarthelemyJFSobieszczanski-SobieskiJ (1983) Optimum sensitivity derivatives of objective functions in nonlinear programming. AIAA Journal21(6): 910–915.
6.
BraunRD (1996) Collaborative optimization: an architecture for large-scale distributed design. PhD Thesis, Stanford University, Stanford, CA.
ChenSZhangFKhalidM (2002) Evaluation of three decomposition MDO algorithms. In: Proceedings of the 23rd international congress of aerospace sciences, Toronto, ON, Canada, 8–13 September, pp. 113.1–113.10. Bonn, Germany: International Council of the Aeronautical Sciences (ICAS).
9.
ChhabraREmamiMR (2014) A holistic approach to concurrent engineering and its application to robotics. Concurrent Engineering: Research and Applications22(1): 48–61.
10.
CramerEJ (1992) On alternative problem formulations for MDO. In: Proceedings of the 4th symposium on multidisciplinary analysis and optimization, Cleveland, OH, 21–23 September 1992.
11.
CramerEJDennisJJEFrankPD. (1994) Problem formulation for multidisciplinary optimization. SIAM Journal on Optimization4(4): 754–776.
12.
DenerAHickenJE (2014) Revisiting individual discipline feasible using matrix-free Inexact-Newton-Krylov. In: Proceedings of the 10th AIAA multidisciplinary design optimization conference, National Harbor, MD, 13–17 January, pp. 1–13. Reston, VA: AIAA.
13.
DeshmukhMSchausVFischerPM. (2013) Decision support tool for concurrent engineering in space mission design. In: StjepandićJRockGBilC (eds) Concurrent Engineering Approaches for Sustainable Product Development in a Multi-Disciplinary Environment. London: Springer, pp. 497–508.
14.
FindeisenWBaileyFNBrdysM. (1980) Control and Coordination in Hierarchical Systems. London: John Wiley & Sons.
15.
HaftkaRT (1994) Simultaneous analysis and design. AIAA Journal23(7): 1099–1103.
16.
HuangHZZhangXYuanW. (2011) Collaborative reliability analysis under the environment of multidisciplinary design optimization. Concurrent Engineering: Research and Applications19(3): 245–254.
17.
HulmeKFBloebaumCL (2000) A simulation-based comparison of multidisciplinary design optimization solution strategies using CASCADE. Structural and Multidisciplinary Optimization19(1): 17–35.
18.
HwangJTLeeDYCutlerJW. (2014) Large-scale multidisciplinary optimization of a small satellite’s design and operation. Journal of Spacecraft and Rockets51(5): 1648–1663.
19.
JeremyJMPanosYP (2005) An efficient weighting update method to achieve acceptable consistency deviation in analytical target cascading. Journal of Mechanical Design127(2): 206–214.
20.
KimHM (2001) Target cascading in optimal system design. PhD Thesis, University of Michigan, Ann Arbor, MI.
21.
KodiyalamSSobieszczanski-SobieskiJ (2001) Multidisciplinary design optimization-some formal methods, framework requirements, and application to vehicle design. International Journal of Vehicle Design25(1): 3–22.
LambeABMartinsJRRA (2012) Extensions to the design structure matrix for the description of multidisciplinary design, analysis, and optimization processes. Structural and Multidisciplinary Optimization46(2): 273–284.
24.
LiHMaMZhangW (2014) Improving collaborative optimization for MDO problems with multi-objective subsystems. Structural and Multidisciplinary Optimization49(4): 609–620.
25.
LiangHZhuMGuoX. (2012) Conceptual design optimization of high altitude airship in concurrent subspace optimization. In: Proceedings of the 50th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition, Nashville, TN, 9–12 January.
26.
MartinsJRRALambeAB (2013) Multidisciplinary design optimization: a survey of architectures. AIAA Journal51(9): 2049–2075.
27.
MehrotraRAbdelwahedS (2014) Towards autonomic performance management of large scale data centers using interaction balance principle. Cluster Computing17(3): 979–999.
28.
MengDZhangXHuangHZ. (2014) Interaction prediction optimization in multidisciplinary design optimization problems. The Scientific World Journal2014: 698453 (7 pp.).
29.
OstrosiEStjepandićJFukudaS. (2014) Modularity: new trends for product platform strategy support in concurrent engineering. In: Proceedings of the 21st ISPE international conference on concurrent engineering, Beijing, China, 9–11 September, pp. 414–423. Amsterdam, The Netherlands: IOS Press.
30.
PerezRELiuHHTBehdinanK (2004) Evaluation of multidisciplinary optimization approaches for aircraft conceptual design. In: Proceedings of the 10th AIAA/ISSMO multidisciplinary analysis and optimization conference, Albany, NY, 30 August–1 September, pp. 1–11. AIAA.
31.
RenaudJEGabrieleGA (1994) Approximation in nonhierarchic system optimization. AIAA Journal32(1): 198–205.
32.
RoshanianJEbrahimiMTaheriE. (2014) Multidisciplinary design optimization of space transportation control system using genetic algorithm. Journal of Aerospace Engineering228(4): 518–529.
33.
SadatiNMarvastED (2006) Stochastic control of two-level nonlinear large-scale systems; Part II—interaction balance principle. In: Proceedings of international conference on systems, man and cybernetics(IEEE), Taipei, Taiwan, 8–11 October, pp. 3856–3861. New York: IEEE.
34.
Sobieszczanski-SobieskiJAltusDTPhillipsM. (2003) Bi-level system synthesis (BLISS) for concurrent and distributed processing. AIAA Journal41(10): 1996–2003.
35.
Sobieszczanski-SobieskiJHaftkaRT (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Structural and Multidisciplinary Optimization14(1): 1–23.
36.
TappetaRVRenaudJE (1997) Multiobjective collaborative optimization. Journal of Mechanical Design119(3): 403–411.
37.
TosseramsSEtmanLFPRoodaJE (2009) A classification of methods for distributed system optimization based on formulation structure. Structural and Multidisciplinary Optimization39(5): 503–517.
38.
WujekBARenaudJEBatillSM (1996) Concurrent subspace optimization using design variable shared in a distributed computing environment. Concurrent Engineering: Research and Applications4(4): 361–377.
39.
YiSIShinJKParkGJ (2008) Comparison of MDO methods with mathematical examples. Structure and Multidiscipline Optimization35(5): 391–402.
40.
YuBYHondaTZubairS (2014) Multi-disciplinary design optimization for large-scale reverse osmosis systems. In: Proceedings of ASME 2014: international design engineering technical conferences and computers and information in engineering conference, Buffalo, NY, 17–20 August, pp. 1–9. New York: ASME.
41.
ZhangDTangS (2015) Concurrent subspace design optimization and analysis of hypersonic vehicles based on response surface models. Aerospace Science and Technology42: 39–49.
42.
ZhangXHuangHZWangZ. (2011) A new method for achieving flexibility in hierarchical multilevel system design. Concurrent Engineering: Research and Applications19(2): 187–196.
43.
ZhangXHuangHZWangZ. (2013) A Pareto set coordination method for analytical target cascading. Concurrent Engineering: Research and Applications21(4): 286–295.
44.
ZhaoMCuiW (2011) On the development of bi-level integrated system collaborative optimization. Structural and Multidisciplinary Optimization43(1): 73–84.
45.
ZhaoWZXuXHWangCY (2012) Multidiscipline collaborative optimization of differential steering system of electric vehicle with motorized wheels. Science China Technological Sciences55(12): 3462–3468.
46.
ZhouHJiangPShaoX. (2014) An improved bi-level integrated system collaborative optimization method for multidisciplinary design optimization. In: Proceedings of the 6th international conference on modeling, identification & control (ICMIC), Melbourne, VIC, Australia, 3–5 December, pp. 365–370. IEEE.
