Multidisciplinary Design Optimization: A Survey of Architectures
Abstract
Multidisciplinary design optimization is a field of research that studies the application of numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Since the inception of multidisciplinary design optimization, various methods (architectures) have been developed and applied to solve multidisciplinary design-optimization problems. This paper provides a survey of all the architectures that have been presented in the literature so far. All architectures are explained in detail using a unified description that includes optimization problem statements, diagrams, and detailed algorithms. The diagrams show both data and process flow through the multidisciplinary system and computational elements, which facilitate the understanding of the various architectures, and how they relate to each other. A classification of the multidisciplinary design-optimization architectures based on their problem formulations and decomposition strategies is also provided, and the benefits and drawbacks of the architectures are discussed from both theoretical and experimental perspectives. For each architecture, several applications to the solution of engineering-design problems are cited. The result is a comprehensive but straightforward introduction to multidisciplinary design optimization for nonspecialists and a reference detailing all current multidisciplinary design-optimization architectures for specialists.
References
[1] , “Structural Design by Systematic Synthesis,” 2nd Conference on Electronic Computation, American Society of Civil Engineers, New York, 1960, pp. 105–132.
[2] , “Synthesis of an Airfoil at Supersonic Mach Number,” NASA CR-144, Jan. 1965.
[3] , “Structural Synthesis: Its Genesis and Development,” AIAA Journal, Vol. 19, No. 10, 1981, pp. 1249–1263. doi:https://doi.org/10.2514/3.7859 AIAJAH 0001-1452
[4] , “Structural Synthesis: Precursor and Catalyst, Recent Experiences in Multidisciplinary Analysis and Optimization,” NASA CP-2337, 1984.
[5] , “Automated Procedure for Design of Wing Structures to Satisfy Strength and Flutter Requirements,” NASA Langley Research Center TN-D-7264, Hampton, VA, 1973.
[6] , “Comparison of Two Types of Optimization Procedures for Flutter Requirements,” AIAA Journal, Vol. 13, No. 10, 1975, pp. 1333–1339. doi:https://doi.org/10.2514/3.60545 AIAJAH 0001-1452
[7] , “Optimization of Flexible Wing Structures Subject to Strength and Induced Drag Constraints,” AIAA Journal, Vol. 14, No. 8, 1977, pp. 1106–1977. doi:https://doi.org/10.2514/3.7400 AIAJAH 0001-1452
[8] , “Approximate Methods for Combined Thermal/Structural Design,” NASA TP-1428, June 1979.
[9] , “On Making Things the Best: Aeronautical Uses of Optimization,” Journal of Aircraft, Vol. 19, No. 1, 1982, pp. 5–28. doi:https://doi.org/10.2514/3.57350 JAIRAM 0021-8669
[10] , “Aeroelastic Tailoring of Aft-Swept High-Aspect-Ratio Composite Wings,” Journal of Aircraft, Vol. 24, No. 11, 1987, pp. 812–819. doi:https://doi.org/10.2514/3.45525 JAIRAM 0021-8669
[11] , “Integrated Aerodynamic/Structural Design of a Sailplane Wing,” Journal of Aircraft, Vol. 25, No. 9, 1988, pp. 855–860. doi:https://doi.org/10.2514/3.45670 JAIRAM 0021-8669
[12] , “Integrated Aerodynamic-Structural Design of a Transport Wing,” Journal of Aircraft, Vol. 27, No. 12, 1990, pp. 1050–1056. doi:https://doi.org/10.2514/3.45980 JAIRAM 0021-8669
[13] , “Towards Integrated Multidisciplinary Synthesis of Actively Controlled Fiber Composite Wings,” Journal of Aircraft, Vol. 27, No. 12, 1990, pp. 979–992. doi:https://doi.org/10.2514/3.45972 JAIRAM 0021-8669
[14] , “Integrated Aeroservoelastic Optimization: Status and Direction,” Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 122–145. doi:https://doi.org/10.2514/2.2419 JAIRAM 0021-8669
[15] , “Aerostructural Optimization of Nonplanar Lifting Surfaces,” Journal of Aircraft, Vol. 47, No. 5, 2010, pp. 1491–1503. doi:https://doi.org/10.2514/1.44727 JAIRAM 0021-8669
[16] , “Multidisciplinary Considerations in the Design of Wings and Wing Tip Devices,” Journal of Aircraft, Vol. 47, No. 2, 2010, pp. 534–543. doi:https://doi.org/10.2514/1.41833 JAIRAM 0021-8669
[17] , “Multidisciplinary Optimization Methods for Aircraft Preliminary Design,” Proceedings of the AIAA 5th Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 1994-4325,
Panama City Beach, FL , 1994.[18] , “Large-Scale Design of Supersonic Aircraft via Collaborative Optimization,” Ph.D. Thesis, Stanford Univ., Stanford, CA, 1999.
[19] , “Framework for Aircraft Conceptual Design and Environmental Performance Studies,” AIAA Journal, Vol. 43, No. 10, 2005, pp. 2100–2109. doi:https://doi.org/10.2514/1.13017 AIAJAH 0001-1452
[20] , “Aircraft Conceptual Design for Optimal Environmental Performance,” The Aeronautical Journal, Vol. 116, No. 1175, Jan. 2012, pp. 1–22.
[21] , “Multidisciplinary Optimization with Applications to Sonic-Boom Minimization,” Annual Review of Fluid Mechanics, Vol. 44, No. 1, 2012, pp. 505–526. doi:https://doi.org/10.1146/annurev-fluid-120710-101133 ARVFA3 0066-4189
[22] , “Collaborative Optimization with Disciplinary Conceptual Design,” Structural and Multidisciplinary Optimization, Vol. 20, No. 3, 2000, pp. 232–241. doi:https://doi.org/10.1007/s001580050151
[23] , “Analytic Target Cascading in Simulation- Based Building Design,” Automation in Construction, Vol. 14, No. 4, 2005, pp. 551–568. doi:https://doi.org/10.1016/j.autcon.2004.11.004 AUCOES 0926-5805
[24] , “Component-Oriented Decomposition for Multidisciplinary Design Optimization in Building Design,” Advanced Engineering Informatics, Vol. 23, No. 1, 2009, pp. 12–31. doi:https://doi.org/10.1016/j.aei.2008.06.008
[25] , “Multidisciplinary Optimization of Multibody Systems with Application to the Design of Rail Vehicles,” Multibody System Dynamics, Vol. 14, No. 2, 2005, pp. 111–135. doi:https://doi.org/10.1007/s11044-005-4310-0
[26] , “Two-Level Numerical Optimization of Ride Comfort in Railway Vehicles,” Journal of Rail and Rapid Transit, Vol. 220, No. 1, 2006, pp. 1–11. doi:https://doi.org/10.1243/095440905X33279
[27] , “A Multidisciplinary Design and Optimization Methodology for the Adaptive Scanning Optical Microscope (ASOM),” Proceedings of the SPIE, Vol. 6289, 2006, pp. 62890L1–62890L12. doi:https://doi.org/10.1117/12.680450
[28] , “Multidisciplinary Robust Design Optimization of an Internal Combustion Engine,” Journal of Mechanical Design, Vol. 125, No. 1, 2003, pp. 124–130. doi:https://doi.org/10.1115/1.1543978
[29] , “Simulation-Based Optimal Design of Heavy Trucks by Model- Based Decomposition: An Extensive Analytical Target Cascading Case Study,” International Journal of Heavy Vehicle Systems, Vol. 11, No. 3/4, 2004, pp. 403–433. doi:https://doi.org/10.1504/IJHVS.2004.005456
[30] , “Multidisciplinary Design Optimization of a Naval Surface Combatant,” Journal of Ship Research, Vol. 47, No. 1, 2003, pp. 1–12. JSRHAR 0022-4502
[31] , “Multidisciplinary Optimization of a Lightweight Torpedo Structure Subjected to an Underwater Explosion,” Finite Elements in Analysis and Design, Vol. 43, No. 2, 2006, pp. 103–111. doi:https://doi.org/10.1016/j.finel.2006.07.005 FEADEU 0168-874X
[32] , “Study on the Design of Propeller Blade Sections Using the Optimization Algorithm,” Journal of Marine Science and Technology, Vol. 10, No. 2, 2005, pp. 70–81. doi:https://doi.org/10.1007/s00773-005-0197-y
[33] , “Reliability-Based Design and Optimization of Adaptive Marine Structures,” Composite Structures, Vol. 92, No. 2, 2010, pp. 244–253. doi:https://doi.org/10.1016/j.compstruct.2009.07.024 COMSE2 0263-8223
[34] , “Survey of Recent Developments in Rotorcraft Design Optimization,” Journal of Aircraft, Vol. 41, No. 3, 2004, pp. 493–510. doi:https://doi.org/10.2514/1.58 JAIRAM 0021-8669
[35] , “Helicopter Vibration Reduction Throughout the Entire Flight Envelope Using Surrogate-Based Optimization,” Journal of the American Helicopter Society, Vol. 54, No. 1, 2009, pp. 12007-1–12007-15. doi:https://doi.org/10.4050/JAHS.54.012007 JHESAK 0002-8711
[36] , “Optimization Method for Wind Turbine Rotors,” Journal of Wind Engineering and Industrial Aerodynamics, Vol. 80, Nos. 1–2, 1999, pp. 191–206. doi:https://doi.org/10.1016/S0167-6105(98)00191-3 JWEAD6 0167-6105
[37] , “Site-Specific Design Optimization of Wind Turbines,” Wind Energy, Vol. 5, No. 4, 2002, pp. 261–279. doi:https://doi.org/10.1002/we.61 WENTEO
[38] , “Aerostructural Shape Optimization of Wind Turbine Blades Considering Site-Specific Winds,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Sept. 2008.doi:https://doi.org/10.2514/6.2008-6025
[39] , “Collaborative Approach to Launch Vehicle Design,” Journal of Spacecraft and Rockets, Vol. 34, No. 4, 1997, pp. 478–486. doi:https://doi.org/10.2514/2.3237 JSCRAG 0022-4650
[40] , “Optimization of System Parameters for Liquid Rocket Engines with Gas-Generator Cycles,” Journal of Propulsion and Power, Vol. 26, No. 1, 2010, pp. 113–119. doi:https://doi.org/10.2514/1.40649 JPPOEL 0748-4658
[41] , “Large-Scale MDO of a Small Satellite Using a Novel Framework for the Solution of Coupled Systems and Their Derivatives,” Proceedings of the 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference,
Boston, MA , April 2013.doi:https://doi.org/10.2514/6.2013-1599[42] , “A Comparative Evaluation of Genetic and Gradient-Based Algorithms Applied to Aerodynamic Optimization,” European Journal of Computational Mechanics, Vol. 17, Nos. 1–2, Jan. 2008, pp. 103–126. doi:https://doi.org/10.2514/1.40649
[43] , Numerical Optimization, 2nd ed., Springer–Verlag, New York, 2006, p. 321.
[44] , “Multiobjective Collaborative Optimization,” Journal of Mechanical Design, Vol. 119, No. 3, 1997, pp. 403–411. doi:https://doi.org/10.1115/1.2826362
[45] , “The Other Side of Multidisciplinary Design Optimization: Accommodating a Multiobjective, Uncertain and Non-Deterministic World,” Engineering Optimization, Vol. 31, No. 2, 1998, pp. 161–189. doi:https://doi.org/10.1080/03052159808941369 EGOPAX 0305-215X
[46] , Nonlinear Multiobjective Optimization, Kluwer Academic, Norwell, MA, 1998.
[47] , “Decomposition Theory for Multidisciplinary Design Optimization Problems with Mixed Integer Quasiseparable Subsystems,” Optimization and Engineering, Vol. 7, No. 2, 2006, pp. 135–149. doi:https://doi.org/10.1007/s11081-006-6836-2 OEPNBR 1389-4420
[48] , “BB-ATC: Analytical Target Cascading Using Branch and Bound for Mixed Integer Nonlinear Programming,” Proceedings of the ASME Design Engineering Technical Conference,
Philadelphia, PA , DET2006/DAC-99040, 2006.[49] , “Metamodel-Based Collaborative Optimization Framework,” Structural and Multidisciplinary Optimization, Vol. 38, No. 2, 2009, pp. 103–115. doi:https://doi.org/10.1007/s00158-008-0286-8
[50] , Introduction to Derivative-Free Optimization, Society for Industrial and Applied Mathematics, Philadelphia, 2009.
[51] , “Game Theory Approach for Multiobjective Structural Optimization,” Computers and Structures, Vol. 25, No. 1, 1987, pp. 119–127. doi:https://doi.org/10.1016/0045-7949(87)90223-9 CMSTCJ 0045-7949
[52] , “Modeling Interactions in Multidisciplinary Design: A Game Theoretic Approach,” AIAA Journal, Vol. 35, No. 8, 1997, pp. 1387–1392. doi:https://doi.org/10.2514/2.248 AIAJAH 0001-1452
[53] , “Achieving Pareto Optimality in a Decentralized Design Environment,” Proceedings of the International Conference on Engineering Design,
Stanford, CA , Aug. 2009.[54] , “Bilevel Integrated System Synthesis for Concurrent and Distributed Processing,” AIAA Journal, Vol. 41, No. 10, 2003, pp. 1996–2003. doi:https://doi.org/10.2514/2.1889 AIAJAH 0001-1452
[55] , “A Nonhierarchical Formulation of Analytical Target Cascading,” Journal of Mechanical Design, Vol. 132, No. 5, 2010, pp. 051002-1–051002-13. doi:https://doi.org/10.1115/1.4001346
[56] , “Enhanced Collaborative Optimization: Application to an Analytic Test Problem and Aircraft Design,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2008-5841, Sept. 2008.
[57] , “MDO: Assessment and Direction for Advancement, An Opinion of One International Group,” Structural and Multidisciplinary Optimization, Vol. 40, Nos. 1–6, 2010, pp. 17–33. doi:https://doi.org/10.1007/s00158-009-0381-5
[58] , “Target Cascading in Optimal System Design,” Journal of Mechanical Design, Vol. 125, No. 3, 2003, pp. 474–480. doi:https://doi.org/10.1115/1.1582501
[59] , “Convergence Properties of Analytical Target Cascading,” AIAA Journal, Vol. 41, No. 5, 2003, pp. 897–905. doi:https://doi.org/10.2514/2.2025 AIAJAH 0001-1452
[60] , “An Efficient Weighting Update Method to Achieve Acceptable Consistency Deviation in Analytical Target Cascading,” Journal of Mechanical Design, Vol. 127, No. 2, 2005, pp. 206–214. doi:https://doi.org/10.1115/1.1830046
[61] , “Problem Formulation for Multidisciplinary Optimization,” SIAM Journal on Optimization, Vol. 4, No. 4, 1994, pp. 754–776. doi:https://doi.org/10.1137/0804044 SJOPE8 1095-7189
[62] , “Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design,” AIAA Journal, Vol. 40, No. 2, 2002, pp. 301–309. doi:https://doi.org/10.2514/2.1646 AIAJAH 0001-1452
[63] , “Reconfigurability in MDO Problem Synthesis, Part 1,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4307, Sept. 2004.
[64] , “Reconfigurability in MDO Problem Synthesis, Part 2,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4308, Sept. 2004.
[65] , “Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment,” Concurrent Engineering: Research and Applications, Vol. 4, No. 4, 1996, pp. 361–377. doi:https://doi.org/10.1177/1063293X9600400405 CRAPEM 1063-293X
[66] , “Multidisciplinary Design Optimization with Quasiseparable Subsystems,” Optimization and Engineering, Vol. 6, No. 1, 2005, pp. 9–20. doi:https://doi.org/10.1023/B:OPTE.0000048534.58121.93 OEPNBR 1389-4420
[67] , “Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments,” Structural Optimization, Vol. 14, No. 1, 1997, pp. 1–23. doi:https://doi.org/10.1007/BF01197554 SOPTEQ 0934-4373
[68] , “Bilevel Integrated System Synthesis with Response Surfaces,” AIAA Journal, Vol. 38, No. 8, 2000, pp. 1479–1485. doi:https://doi.org/10.2514/2.1126 AIAJAH 0001-1452
[69] , “Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary System Design,” 34th AIAA Aerospace Sciences and Meeting Exhibit, AIAA Paper 1996-0714, Jan. 1996.
[70] , “Bilevel Integrated System Synthesis,” AIAA Journal, Vol. 38, No. 1, 2000, pp. 164–172. doi:https://doi.org/10.2514/2.937 AIAJAH 0001-1452
[71] , “Multidisciplinary Design Optimization Based on Independent Subspaces,” International Journal for Numerical Methods in Engineering, Vol. 64, 2005, pp. 599–617. doi:https://doi.org/10.1002/(ISSN)1097-0207 IJNMBH 0029-5981
[72] , “A Local Convergence Analysis of Bilevel Decomposition Algorithms,” Optimization and Engineering, Vol. 7, No. 2, 2006, pp. 99–133. doi:https://doi.org/10.1007/s11081-006-6835-3 OEPNBR 1389-4420
[73] , “Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment,” Multidisciplinary Design Optimization: State-of-the-Art, edited by Alexandrov N. and Hussaini M. Y., Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 98–116.
[74] , “MDO for Large-Scale Design,” Multidisciplinary Design Optimization: State-of-the-Art, edited by Alexandrov N. and Hussaini M. Y., Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 22–44.
[75] , “Collaborative Optimization Using Response Surface Estimation,” AIAA Journal, Vol. 38, No. 10, 2000, pp. 1931–1938. doi:https://doi.org/10.2514/2.847 AIAJAH 0001-1452
[76] , “Aero-Structural Optimization Using Adjoint Coupled Post Optimality Sensitivities,” Structural and Multidisciplinary Optimization, Vol. 36, No. 1, 2008, pp. 59–70. doi:https://doi.org/10.1007/s00158-007-0200-9
[77] , “On Options for Interdisciplinary Analysis and Design Optimization,” Structural Optimization, Vol. 4, No. 2, 1992, pp. 65–74. doi:https://doi.org/10.1007/BF01759919 SOPTEQ 0934-4373
[78] , “Optimization of Coupled Systems: A Critical Overview of Approaches,” AIAA Journal, Vol. 34, No. 1, 1996, pp. 6–17. doi:https://doi.org/10.2514/3.13015 AIAJAH 0001-1452
[79] Alexandrov N. and Hussaini M. Y. (eds.), Multidisciplinary Design Optimization: State-of-the-Art, Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 22–44.
[80] , “Multilevel Methods for MDO,” Multidisciplinary Design Optimization: State-of-the-Art, edited by Alexandrov N. M. and Hussaini M. Y., Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 79–89.
[81] , “Approaches to MDO Which Support Disciplinary Autonomy,” Multidisciplinary Design Optimization: State-of-the-Art, edited by Alexandrov N. M. and Hussaini M. Y., Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 90–97.
[82] , “Simultaneous Optimization of a Multiple-Aircraft Family,” Journal of Aircraft, Vol. 40, No. 4, 2003, pp. 616–622. doi:https://doi.org/10.2514/2.3156 JAIRAM 0021-8669
[83] , “Preliminary Aerostructural Optimization of a Large Business Jet,” Journal of Aircraft, Vol. 44, No. 5, 2007, pp. 1422–1438. doi:https://doi.org/10.2514/1.26989 JAIRAM 0021-8669
[84] , “Multidisciplinary Design Optimization for Complex Engineered Systems Design: Report from an NSF Workshop,” Journal of Mechanical Design, Vol. 133, No. 10, Oct. 2011, pp. 101002-1–101002-10. doi:https://doi.org/10.1115/1.4004465
[85] , “A Classification of Methods for Distributed System Optimization Based on Formulation Structure,” Structural and Multidisciplinary Optimization, Vol. 39, No. 5, 2009, pp. 503–517. doi:https://doi.org/10.1007/s00158-008-0347-z
[86] , “Extensions to the Design Structure Matrix for the Description of Multidisciplinary Design, Analysis, and Optimization Processes,” Structural and Multidisciplinary Optimization, Vol. 46, No. 2, 2012, pp. 273–284. doi:https://doi.org/10.1007/s00158-012-0763-y
[87] , “The Design Structure Matrix: A Method for Managing the Design of Complex Systems,” IEEE Transactions on Engineering Management, Vol. 28, 1981, pp. 71–74. doi:https://doi.org/10.1109/TEM.1981.6448589 IEEMA4 0018-9391
[88] , “Applying the Design Structure Matrix to System Decomposition and Integration Problems: A Review and New Directions,” IEEE Transactions on Engineering Management, Vol. 48, No. 3, 2001, pp. 292–306. doi:https://doi.org/10.1109/17.946528 IEEMA4 0018-9391
[89] , “Simultaneous Analysis and Design,” AIAA Journal, Vol. 23, No. 7, 1985, pp. 1099–1103. doi:https://doi.org/10.2514/3.9043 AIAJAH 0001-1452
[90] , “Multilevel Approach to Minimum Weight Design Including Buckling Constraints,” AIAA Journal, Vol. 16, No. 2, 1978, pp. 97–104. doi:https://doi.org/10.2514/3.60867 AIAJAH 0001-1452
[91] Biegler L. T., Ghattas O., Heinkenschloss M. and van Bloemen Waanders B. (eds.), Large-Scale PDE-Constrained Optimization, Springer–Verlag, New York, 2003.
[92] , “Using Complex Variables to Estimate Derivatives of Real Functions,” SIAM Review, Vol. 40, No. 1, 1998, pp. 110–112. doi:https://doi.org/10.1137/S003614459631241X SIREAD 0036-1445
[93] , “The Complex-Step Derivative Approximation,” ACM Transactions on Mathematical Software, Vol. 29, No. 3, 2003, pp. 245–262. doi:https://doi.org/10.1145/838250 ACMSCU 0098-3500
[94] , “Sensitivity Analysis of Discrete Structural Systems,” AIAA Journal, Vol. 24, No. 5, 1986, pp. 823–832. doi:https://doi.org/10.2514/3.48671 AIAJAH 0001-1452
[95] , “Aerodynamic Design via Control Theory,” Journal of Scientific Computing, Vol. 3, No. 3, 1988, pp. 233–260. doi:https://doi.org/10.1007/BF01061285 JSCOEB 0885-7474
[96] , “Algorithm Developments for Discrete Adjoint Methods,” AIAA Journal, Vol. 41, No. 2, 2003, pp. 198–205. doi:https://doi.org/10.2514/2.1961 AIAJAH 0001-1452
[97] , “Review of Options for Structural Design Sensitivity Analysis. Part 1: Linear Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 194, Nos. 30–33, 2005, pp. 3213–3243. doi:https://doi.org/10.1016/j.cma.2005.02.002 CMMECC 0045-7825
[98] , “ADjoint: An Approach for the Rapid Development of Discrete Adjoint Solvers,” AIAA Journal, Vol. 46, No. 4, 2008, pp. 863–873. doi:https://doi.org/10.2514/1.29123 AIAJAH 0001-1452
[99] , “A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design,” Optimization and Engineering, Vol. 6, No. 1, 2005, pp. 33–62. doi:https://doi.org/10.1023/B:OPTE.0000048536.47956.62 OEPNBR 1389-4420
[100] , “A Schur-Newton-Krylov Solver for Steady-State Aeroelastic Analysis and Design Sensitivity Analysis,” Computer Methods in Applied Mechanics and Engineering, Vol. 195, Nos. 17–18, 2006, pp. 2050–2069. doi:https://doi.org/10.1016/j.cma.2004.09.013 CMMECC 0045-7825
[101] , “Aerodynamic Optimization Algorithm with Integrated Geometry Parameterization and Mesh Movement,” AIAA Journal, Vol. 48, No. 2, Feb. 2009, pp. 400–413. doi:https://doi.org/10.2514/1.44033 AIAJAH 0001-1452
[102] , “Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models,” AIAA Journal, 2013. doi:https://doi.org/10.2514/1.J052184. AIAJAH 0001-1452
[103] , “Coupling Strength-Based System Reduction for Complex Engineering Design,” Structural Optimization, Vol. 10, No. 2, 1995, pp. 113–121. doi:https://doi.org/10.1007/BF01743538 SOPTEQ 0934-4373
[104] , “Parallel Solution Methods for Aerostructural Analysis and Design Optimization,” 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, AIAA Paper 2010-9308, Sept. 2010.
[105] , “An Efficient Feasible Directions Algorithm for Design Synthesis,” AIAA Journal, Vol. 22, No. 11, 1984, pp. 1633–1640. doi:https://doi.org/10.2514/3.8829 AIAJAH 0001-1452
[106] , “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM Review, Vol. 47, No. 1, 2005, pp. 99–131. doi:https://doi.org/10.1137/S0036144504446096 SIREAD 0036-1445
[107] , Primal-Dual Interior Point Methods, Society for Industrial and Applied Mathematics, Philadelphia, 1997.
[108] , “Sensitivity of Complex, Internally Coupled Systems,” AIAA Journal, Vol. 28, No. 1, 1990, pp. 153–160. doi:https://doi.org/10.2514/3.10366 AIAJAH 0001-1452
[109] , “A Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Derivative Computations,” AIAA Journal, 2013 (in press).
[110] , “Multi-Point High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration,” Journal of Aircraft, 2013 (in press).
[111] , “Reconfigurable Semi-Analytic Sensitivity Methods and MDO Architectures Within the Framework,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2008-5956, Sept. 2008.
[112] , “Review and Unification of Discrete Methods for Computing Derivatives of Single- and Multi-Disciplinary Computational Models,” AIAA Journal (in press).
[113] , Optimization Theory for Large Systems, Macmillan, New York, 1970, pp. 104–143, Chap. 2.
[114] , “A Decomposition Procedure Based on Approximate Newton Directions,” Mathematical Programming, Vol. 93, No. 3, 2002, pp. 495–515. doi:https://doi.org/10.1007/s10107-002-0304-3 MHPGA4 1436-4646
[115] , “Decomposition Principle for Linear Programs,” Operations Research, Vol. 8, No. 1, 1960, pp. 101–111. doi:https://doi.org/10.1287/opre.8.1.101 OPREAI 0030-364X
[116] , “Partitioning Procedures for Solving Mixed Variables Programming Problems,” Numerische Mathematik, Vol. 4, No. 1, 1962, pp. 238–252. doi:https://doi.org/10.1007/BF01386316 NUMMA7 0029-599X
[117] , “A Network Reliability Approach to Optimal Decomposition of Design Problems,” Journal of Mechanical Design, Vol. 117, No. 3, 1995, pp. 433–440. doi:https://doi.org/10.1115/1.2826697
[118] , “A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems,” Computational Optimization and Applications, Vol. 8, No. 2, 1997, pp. 173–196. doi:https://doi.org/10.1023/A:1008673321406 CPPPEF 0926-6003
[119] , “A Specification Language for Problem Partitioning in Decomposition-Based Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 42, No. 5, 2010, pp. 707–723. doi:https://doi.org/10.1007/s00158-010-0512-z
[120] , Parallel and Distributed Computation: Numerical Methods, Athena Scientific, Belmont, MA, 1997, pp. 88–104.
[121] , “Multi-Fidelity Multidisciplinary Design Optimization Based on Collaborative Optimization Framework,” 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 2002-5504, Sept. 2002.
[122] , “Multifidelity Optimization for Variable Complexity Design,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-7114, Sept. 2006.
[123] , “An Asymmetric Suboptimization Approach to Aerostructural Optimization,” Optimization and Engineering, Vol. 10, No. 1, 2009, pp. 133–152. doi:https://doi.org/10.1007/s11081-008-9046-2 OEPNBR 1389-4420
[124] , “Comparative Properties of Collaborative Optimization and Other Approaches to MDO,” NASA Technical Rept. CR-1999-209354, Hampton, VA, July 1999.
[125] , “Overview of Methods for Multilevel and/or Multidisciplinary Optimization,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2010-2914, April 2010.
[126] , “A Hybrid MDO Architecture for Launch Vehicle Conceptual Design,” 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2010-2757, April 2010.
[127] , “Optimization by Decomposition: A Step from Hierarchic to Non- Hierarchic Systems,” NASA Langley Research Center TR-CP-3031, Hampton, VA, Sept. 1988.
[128] , “Non-Hierarchic System Decomposition in Structural Optimization,” Engineering Optimization, Vol. 19, No. 3, 1992, pp. 171–186. doi:https://doi.org/10.1080/03052159208941227 EGOPAX 0305-215X
[129] , “Computational Study of a Nonhierarchical Decomposition Algorithm,” Computational Optimization and Applications, Vol. 2, No. 3, 1993, pp. 273–293. doi:https://doi.org/10.1007/BF01299452 CPPPEF 0926-6003
[130] , “Approximation in Non-Hierarchic System Optimization,” AIAA Journal, Vol. 32, No. 1, 1994, pp. 198–205. doi:https://doi.org/10.2514/3.11967 AIAJAH 0001-1452
[131] , “Improved Coordination in Nonhierarchic System Optimization,” AIAA Journal, Vol. 31, No. 12, 1993, pp. 2367–2373. doi:https://doi.org/10.2514/3.11938 AIAJAH 0001-1452
[132] , “Multi-Objective Genetic Algorithm Concurrent Subspace Optimization (MOGACSSO) for Multidisciplinary Design,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-2047, May 2006.
[133] , “Multi-Objective Pareto Concurrent Subspace Optimization for Multidisciplinary Design,” AIAA Journal, Vol. 45, No. 8, 2007, pp. 1894–1906. doi:https://doi.org/10.2514/1.19972 AIAJAH 0001-1452
[134] , “Bilevel Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization,” AIAA Journal, Vol. 46, No. 10, 2008, pp. 2611–2622. doi:https://doi.org/10.2514/1.36853 AIAJAH 0001-1452
[135] , “Robust Multi-Objective Genetic Algorithm Concurrent Subspace Optimization (R-MOGACSSO) for Multidisciplinary Design,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-6907, Sept. 2006.
[136] , “A Multidisciplinary Design Optimization Approach for High Temperature Aircraft Engine Components,” Structural Optimization, Vol. 18, Nos. 2–3, 1999, pp. 134–145. doi:https://doi.org/10.1007/BF01195988 SOPTEQ 0934-4373
[137] , “Evaluation of Multidisciplinary Optimization Approaches for Aircraft Conceptual Design,” 10th AIAA/ISSMO Muldisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4537, Aug. 2004.
[138] , “Comparison of MDO Methods with Mathematical Examples,” Structural and Multidisciplinary Optimization, Vol. 39, No. 5, 2008, pp. 391–402. doi:https://doi.org/10.1007/s00158-007-0150-2
[139] , “Benchmarking Multidisciplinary Design Optimization Algorithms,” Optimization and Engineering, Vol. 11, No. 1, 2010, pp. 159–183. doi:https://doi.org/10.1007/s11081-009-9082-6 OEPNBR 1389-4420
[140] , “Numerical Comparison of Multi-Level Optimization Techniques,” 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2007-1895, April 2007.
[141] , “Collaborative Optimization: An Architecture for Large-Scale Distributed Design,” Ph.D. Thesis, Stanford Univ., Stanford, CA, 1996.
[142] , “Implementation and Performance Issues in Collaborative Optimization,” 6th AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis and Optimization Symposium, AIAA Paper 1996-4017, Sept. 1996.
[143] , “An Analysis of Collaborative Optimization Methods,” 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 2000-4720, 2000.
[144] , “Analysis and Enhancement of Collaborative Optimization for Multidisciplinary Design,” AIAA Journal, Vol. 42, No. 2, 2004, pp. 348–360. doi:https://doi.org/10.2514/1.9098 AIAJAH 0001-1452
[145] , Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Society for Industrial and Applied Mathematics, Philadelphia, 1990, pp. 53–72.
[146] , “Evaluation of Multidisciplinary Optimization Techniques Applied to a Reusable Launch Vehicle,” Journal of Spacecraft and Rockets, Vol. 43, No. 6, 2006, pp. 1289–1300. doi:https://doi.org/10.2514/1.16577 JSCRAG 0022-4650
[147] , “A Multidisciplinary Optimization Framework for Flight Dynamics and Control Integration in Aircraft Design,” Ph.D. Thesis, Univ. of Toronto, Toronto, 2007.
[148] , “Automatic Implementation of Multidisciplinary Design Optimization Architectures Using ,” M.S. Thesis, Univ. of Toronto, Toronto, 2008.
[149] , “Geometric Analysis of Collaborative Optimization,” Structural and Multidisciplinary Optimization, Vol. 35, No. 4, 2008, pp. 301–313. doi:https://doi.org/10.1007/s00158-007-0127-1
[150] , “Design and Deployment of a Satellite Constellation Using Collaborative Optimization,” Journal of Spacecraft and Rockets, Vol. 41, No. 6, 2004, pp. 956–963. doi:https://doi.org/10.2514/1.14254 JSCRAG 0022-4650
[151] , “Optimized Solutions for Kistler K-1 Branching Trajectories Using Multidisciplinary Design Optimization Techniques,” Journal of Spacecraft and Rockets, Vol. 39, No. 3, 2002, pp. 420–429. doi:https://doi.org/10.2514/2.3825 JSCRAG 0022-4650
[152] , “Multidisciplinary Optimization Framework for Control-Configuration Integration in Aircraft Conceptual Design,” Journal of Aircraft, Vol. 43, No. 6, 2006, pp. 1937–1948. doi:https://doi.org/10.2514/1.22263 JAIRAM 0021-8669
[153] , “Aircraft Family Design Using Decomposition-Based Methods,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-6950, Sept. 2006.
[154] , “Integrating Linear Physical Programming Within Collaborative Optimization for Multiobjective Multidisciplinary Design Optimization,” Structural and Multidisciplinary Optimization, Vol. 29, No. 3, 2005, pp. 178–189. doi:https://doi.org/10.1007/s00158-004-0481-1
[155] , “Decision-Based Collaborative Optimization,” Journal of Mechanical Design, Vol. 124, No. 1, 2002, pp. 1–13. doi:https://doi.org/10.1115/1.1432991
[156] , “Implicit Uncertainty Propagation for Robust Col-laborative Optimization,” Journal of Mechanical Design, Vol. 128, No. 4, 2006, pp. 1001–1013. doi:https://doi.org/10.1115/1.2205869
[157] , “Multidisciplinary Collaborative Optimization Using Fuzzy Satisfaction Degree and Fuzzy Sufficiency Degree Model,” Soft Computing, Vol. 12, No. 10, 2008, pp. 995–1005. doi:https://doi.org/10.1007/s00500-007-0268-6
[158] , “Aircraft Family Design Using Enhanced Collaborative Optimization,” Ph.D. Thesis, Stanford Univ., Stanford, CA, 2008.
[159] , “Evaluation of Methods for Multidisciplinary Design Optimization (MDO), Phase I,” NASA CR-1998-208716, Sept. 1998.
[160] , “Evaluation of Methods for Multidisciplinary Design Optimization (MDO), Part 2,” NASA CR-2000-210313, Nov. 2000.
[161] , Trust Region Methods, Society for Industrial and Applied Mathematics, Philadelphia, 2000.
[162] , “Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4545, Aug. 2004.
[163] , “An Efficient Strategy for Reliability-Based Multidisciplinary Design Optimization Using BLISS,” Structural and Multidisciplinary Optimization, Vol. 31, No. 5, 2006, pp. 363–372. doi:https://doi.org/10.1007/s00158-005-0565-6
[164] , “Improving the Performance of Design Decomposition Methods with POD,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4465, Aug. 2004.
[165] , “The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows,” Annual Review of Fluid Mechanics, Vol. 25, 1993, pp. 539–575. doi:https://doi.org/10.1146/annurev.fl.25.010193.002543 ARVFA3 0066-4189
[166] , “Integrated System-of-Systems Synthesis,” AIAA Journal, Vol. 46, No. 5, 2008, pp. 1072–1080. doi:https://doi.org/10.2514/1.27953 AIAJAH 0001-1452
[167] , “Target Cascading in Optimal System Design,” Ph.D. Thesis, Univ. of Michigan, Ann Arbor, MI, 2001.
[168] , “Augmented Lagrangian Coordination for Distributed Optimal Design in MDO,” International Journal for Numerical Methods in Engineering, Vol. 73, 2008, pp. 1885–1910. doi:https://doi.org/10.1002/(ISSN)1097-0207 IJNMBH 0029-5981
[169] , “Lagrangian Coordination for Enhancing the Convergence of Analytical Target Cascading,” AIAA Journal, Vol. 44, No. 10, 2006, pp. 2197–2207. doi:https://doi.org/10.2514/1.15326 AIAJAH 0001-1452
[170] , “An Augmented Lagrangian Relaxation for Analytical Target Cascading Using the Alternating Direction Method of Multipliers,” Structural and Multidisciplinary Optimization, Vol. 31, No. 3, 2006, pp. 176–189. doi:https://doi.org/10.1007/s00158-005-0579-0
[171] , Constrained Optimization and Lagrange Multiplier Methods, Athena Scientific, Belmont, MA, 1996, pp. 104–125.
[172] , “Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading,” Journal of Mechanical Design, Vol. 130, No. 5, 2008, pp. 051402-1–051402-11. doi:https://doi.org/10.1115/1.2838334
[173] , “On Convergence of an Augmented Lagrangian Decomposition Method for Sparse Convex Optimization,” Mathematics of Operations Research, Vol. 20, No. 3, 1995, pp. 634–656. doi:https://doi.org/10.1287/moor.20.3.634 MOREDQ 0364-765X
[174] , “A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading,” Journal of Mechanical Design, Vol. 132, No. 3, 2010, pp. 021003-1–021003-8. doi:https://doi.org/10.1115/1.4000758
[175] , Nonlinear Programming: Theory and Algorithms, Wiley, New York, 2006, pp. 568–576.
[176] , “Calculation of the Move Limits for the Sequential Linear Programming Method,” International Journal for Numerical Methods in Engineering, Vol. 36, No. 15, 1993, pp. 2661–2679. doi:https://doi.org/10.1002/(ISSN)1097-0207 IJNMBH 0029-5981
[177] , “A Note on the Convergence of Analytical Target Cascading with Infinite Norms,” Journal of Mechanical Design, Vol. 132, No. 3, 2010, pp. 034502-1–034502-6. doi:https://doi.org/10.1115/1.4001001
[178] , “Extension of the Target Cascading Formulation to the Design of Product Families,” Structural and Multidisciplinary Optimization, Vol. 24, No. 4, 2002, pp. 293–301. doi:https://doi.org/10.1007/s00158-002-0240-0
[179] , “Target Cascading in Vehicle Redesign: A Class VI Truck Study,” International Journal of Vehicle Design, Vol. 29, No. 3, 2002, pp. 199–225. doi:https://doi.org/10.1504/IJVD.2002.002010 IJVDDW 0143-3369
[180] , “Analytical Target Cascading in Automotive Vehicle Design,” Journal of Mechanical Design, Vol. 125, No. 3, 2003, pp. 481–490. doi:https://doi.org/10.1115/1.1586308
[181] , “Continuously Variable Transmission Design for Optimum Vehicle Performance by Analytical Target Cascading,” International Journal of Heavy Vehicle Systems, Vol. 11, No. 3/4, 2004, pp. 327–348. doi:https://doi.org/10.1504/IJHVS.2004.005454
[182] , “A New Solution for Two-Bag Air Suspension System with Leaf Spring for Heavy-Duty Vehicle,” Vehicle System Dynamics, Vol. 44, No. 2, 2006, pp. 107–138. doi:https://doi.org/10.1080/00423110500385907 VSDYA4 0042-3114
[183] , “The Application of Analytical Target Cascading in Parallel Hybrid Electric Vehicle,” IEEE Vehicle Power and Propulsion Conference, IEEE Publ., Piscataway, NJ, 2009, pp. 1602–1607.
[184] , “Optimal Design of Hybrid Electric Fuel Cell Vehicles Under Uncer-tainty and Enterprise Considerations,” Journal of Fuel Cell Science and Technology, Vol. 7, No. 2, 2010, pp. 021020-1–021020-9. doi:https://doi.org/10.1115/1.3179762
[185] , “Analytical Target Cascading in Aircraft Design,” 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-1325, Jan. 2006.
[186] , “Product and Process Tolerance Allocation in Multistation Compliant Assembly Using Analytical Target Cascading,” Journal of Mechanical Design, Vol. 130, No. 9, 2008, pp. 091701-1–091701-9. doi:https://doi.org/10.1115/1.2943296
[187] , “Extending Analytical Target Cascading for Optimal Configuration of Supply Chains with Alternative Autonomous Suppliers,” International Journal of Production Economics, Vol. 115, No. 1, 2008, pp. 39–54. doi:https://doi.org/10.1016/j.ijpe.2008.04.008
[188] , “Linking Marketing and Engineering Product Design Decisions via Analytical Target Cascading,” Journal of Product Innovation Management, Vol. 22, No. 1, 2005, pp. 42–62. doi:https://doi.org/10.1111/jpim.2005.22.issue-1 JPIMDD 0737-6782
[189] , “Extensible Multi-Agent System for Optimal Design of Complex Systems Using Analytical Target Cascading,” International Journal of Advanced Manufacturing Technology, Vol. 30, Nos. 1–10, 2006, pp. 917–926. doi:https://doi.org/10.1007/s00170-005-0064-3 IJATEA 1433-3051
[190] , “Coordination Specification in Distributed Optimal Design of Multilevel Systems Using the Language,” Structural and Multidisciplinary Optimization, Vol. 29, No. 3, 2005, pp. 198–212. doi:https://doi.org/10.1007/s00158-004-0467-z
[191] , “Design Optimization of Hierarchically Decomposed Multilevel Systems Under Uncertainty,” Journal of Mechanical Design, Vol. 128, No. 2, 2006, pp. 503–508. doi:https://doi.org/10.1115/1.2168470
[192] , “Probabilistic Analytical Target Cascading: A Moment Matching Formulation for Multilevel Optimization Under Uncertainty,” Journal of Mechanical Design, Vol. 128, No. 4, 2006, pp. 991–1000. doi:https://doi.org/10.1115/1.2205870
[193] , “Block-Separable Linking Constraints in Augmented Lagrangian Coordination in MDO,” Structural and Multidisciplinary Optimization, Vol. 37, No. 5, 2009, pp. 521–527. doi:https://doi.org/10.1007/s00158-008-0244-5
[194] , “Two Decomposition Algorithms for Nonconvex Optimization Problems with Global Variables,” Ph.D. Thesis, Stanford Univ., Stanford, CA, 2001.
[195] , “An Augmented Lagrangian Decomposition Method for Quasiseparable Problems in MDO,” Structural and Multidisciplinary Optimization, Vol. 34, No. 3, 2007, pp. 211–227. doi:https://doi.org/10.1007/s00158-006-0077-z
[196] , “Application of the Multidisciplinary Design Optimization Algorithm to the Design of a Belt-Integrated Seat While Considering Crashworthiness,” Journal of Automobile Engineering, Vol. 219, No. 11, 2005, pp. 1281–1292. doi:https://doi.org/10.1243/095440705X34928
[197] , “Global-Local Structural Optimization Using Response Surfaces of Local Optimization Margins,” Structural and Multidisciplinary Optimization, Vol. 27, No. 5, 2004, pp. 352–359. doi:https://doi.org/10.1007/s00158-004-0393-0
[198] , “High-Fidelity Aerostructural Design Optimization of a Supersonic Business Jet,” Journal of Aircraft, Vol. 41, No. 3, 2004, pp. 523–530. doi:https://doi.org/10.2514/1.11478 JAIRAM 0021-8669
[199] , “Aerostructural Optimization of Aircraft Structures Using Asymmetric Subspace Optimization,” 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2008-5847, Sept. 2008.
[200] , “Variable-Complexity Response Surface Approximations for Wing Structural Weight in HSCT Design,” Computational Mechanics, Vol. 18, No. 2, 1996, pp. 112–126. doi:https://doi.org/10.1007/BF00350530 0178-7675
[201] , “Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport,” Optimization and Engineering, Vol. 2, No. 4, 2001, pp. 431–452. doi:https://doi.org/10.1023/A:1016094522761 OEPNBR 1389-4420
[202] , “A Simulation-Based Comparison of Multidisciplinary Design Optimization Solution Strategies Using CASCADE,” Structural and Multidisciplinary Optimization, Vol. 19, No. 1, 2000, pp. 17–35. doi:https://doi.org/10.1007/s001580050083
[203] , “On Selecting Single-Level Formulations for Complex System Design Optimization,” Journal of Mechanical Design, Vol. 129, No. 9, 2007, pp. 898–906. doi:https://doi.org/10.1115/1.2747632
[204] , “pyMDO: An Object-Oriented Framework for Multidisciplinary Design Optimization,” ACM Transactions on Mathematical Software, Vol. 36, No. 4, 2009, pp. 20:1–20:25. doi:https://doi.org/10.1145/1555386 ACMSCU 0098-3500
[205] , “OpenMDAO: An Open Source Framework for Multidisciplinary Analysis and Optimization,” 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference, AIAA Paper 2010-9101, Sept. 2010.
[206] , “Graph Partitioning-Based Coordination Methods for Large-Scale Multidisciplinary Design Optimization Problems,” Proceedings of the 14th AIAA/ISSMO Multidisciplinary Analysis Optimization Conference,
Indianapolis, IN , AIAA Paper 2012-5522, 2012.[207] , “Multidisciplinary Environments: A History of Engineering Framework Development,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-7083, Sept. 2006.
[208] , “Multidisciplinary Design Optimization: Somemal Methods, Framework Requirements, and Application to Vehicle Design,” International Journal of Vehicle Design, Vol. 25, No. 1/2, 2001, pp. 3–22. doi:https://doi.org/10.1504/IJVD.2001.001904 IJVDDW 0143-3369
[209] , “Balanced HPC Infrastructure for CFD and Associated Multi-Discipline Simulations of Engineering Systems,” Journal of Aerospace Sciences and Technologies, Vol. 61, No. 3, 2009, pp. 434–443.
[210] , “A Micro-Accelerometer MDO Benchmark Problem,” Structural and Multidisciplinary Optimization, Vol. 41, No. 2, 2010, pp. 255–275. doi:https://doi.org/10.1007/s00158-009-0422-0
[211] , “Multi-Modality in Augmented Lagrangian Co-ordination for Distributed Optimal Design,” Structural and Multidisciplinary Optimization, Vol. 40, Nos. 1–6, 2010, pp. 329–352. doi:https://doi.org/10.1007/s00158-009-0371-7
[212] , “MDO Test Suite at NASA Langley Research Center,” 6th AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 1996-4028, Sept. 1996.