Abstract
The multiobjective robust collaborative optimization framework consists of optimization both at the system and autonomous subsystem levels. Linear physical programming is used in the system level optimization, which avoids the difficulty in choosing the multidimensional Pareto set. The non-dominated sorting genetic algorithm (NSGA-II) is used in the subsystem optimization with physical objectives. The interdisciplinary incompatibility function and physical objectives have different priority levels. At the first priority level, the best individual should be in the feasible region of the subsystem. At the second priority level, the interdisciplinary incompatibility function of the best individual should be no more than the feasibility threshold. The physical objectives are improved after the achievement of the above levels. A method for producing initial population with feasibility and diversity is proposed to improve the calculation efficiency and accuracy of the subsystem optimization at the first priority level. A method for setting dynamic feasibility threshold is proposed for the non-dominated sorting to help the physical objectives to obtain better solutions at the second priority level. Finally, the results of the speed reducer show that the presented method is efficient.
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References
P. Zadeh, V. Toropov and A. Wood, Metamodel-based collaborative optimization framework, Structural and Multidisciplinary Optimization, 38(2) (2009) 103–115.
J. K. Allen, C. Seepersad, H. J. Choi and F. Mistree, Robust design for multiscale and multidisciplinary Applications, Transactions of the ASME, 128(4) (2006) 832–843.
M. Li and S. Azarm, Multiobjective collaborative robust optimization with interval uncertainty and interdisciplinary uncertainty propagation, Journal of Mechanical Design, 130(8) (2008) 1–11.
X. P. Du and W. Chen, Efficient uncertainty analysis methods for multidisciplinary robust design, AIAA Journal, 40(3) (2002) 545–552.
X. Y. Gu, J. E. Renaud, S. M. Batill, R. M. Brach and A. S. Budhiraja, Worst case propagated uncertainty of multidisciplinary systems in robust design optimization, Structural and Multidisciplinary Optimization, 20(3) (2000) 190–213.
X. Y. Gu, J. E. Renaud and C. L. Penninger, Implicit uncertainty propagation for robust collaborative optimization, Journal of Mechanical Design, 128(4) (2006) 1001–1013.
W. M. Wang, Y. H. Peng, J. Hu and Z. M. Cao, Collaborative robust optimization under uncertainty base on generalized dynamic constraints network, Structural and multidisciplinary optimization, 38(2) (2009) 159–170.
R. V. Tappeta and J. E. Renaud, Multiobjective collaborative optimization, Journal of Mechanical Design, 119(3) (1997) 403–411.
C. D. Mcallister, T. W. Simpson, K. Hacker, K. Lewis and A. Messac, Integrating linear physical programming within collaborative optimization for multiobjective multidisciplinary design, Structural and Multidisciplinary Optimization, 29(3) (2005) 178–189.
C. D. Mcallister and T. W. Simpson, Multidisciplinary robust design optimization of an internal combustion engine, Journal of Mechanical Design, 125(3) (2003) 124–130.
C. D. Mcallister, T. W. Simpson, K. Hacker, K. Lewis and A. Messac, Robust multiobjective optimization through collaborative optimization and linear physical programming, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, NY, USA (2004) 2745–2760.
H. Z. Huang, Y. Tao and Y. Liu, Multidisciplinary collaborative optimization using fuzzy satisfaction degree and fuzzy sufficiency degree model, Soft Computing, 12(10) (2008) 995–1005.
A. Vikrant and A. Shapour, A genetic algorithms based approach for multidisciplinary multiobjective collaborative optimization, 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Portsmouth, VA, USA (2006) 630–646.
S. Rabeau, P. Dépincé and F. Bennis, Collaborative optimization of complex systems: a multidisciplinary approach, International Journal on Interactive Design and Manufacturing, 1(4) (2007) 209–218.
A. Messac, S. M. Gupta and B. Akbulut, Linear physical programming: a new approach to multiple objective optimization, Transactions on operational research, 8(10) (1996) 39–59.
N. M. Alexandrov and R. M. Lewis, Analytical and computational aspects of collaborative optimization, NASA/TM-2000-210104 (2000).
X. Li, W. J. Li and C. A. Liu, Geometric analysis of collaborative optimization, Structural and Multidisciplinary Optimization, 35(4) (2008) 301–313.
K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multi-objective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6(2) (2002) 182–197.
W. Y. Gong, Z. H. Cai and L. Zhu, An efficient multiobjective differential evolution algorithm for engineering design, Structural and Multidisciplinary Optimization, 38(2) (2009) 137–157.
S. Kodiyalam, Evaluation of methods for multidisciplinary design optimization(MDO), NASA/CR-1998-208716 (1998).
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This paper was recommended for publication in revised form by Associate Editor Jeonghoon Yoo
Haiyan Li received her B.S., M.S. and Ph.D. in Control Theory and Control Engineering from Northeastern University, Shenyang, China. Presently, she is working as an assistant professor of Multidisciplinary Optimal Design at Northeastern University. She has some publications in refereed journals and conferences. Her main research interests include multidisciplinary design optimization and approximation algorithms.
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Li, H., Ma, M. & Jing, Y. A new method based on LPP and NSGA-II for multiobjective robust collaborative optimization. J Mech Sci Technol 25, 1071–1079 (2011). https://doi.org/10.1007/s12206-011-0223-4
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DOI: https://doi.org/10.1007/s12206-011-0223-4