Advertisement

Research in Engineering Design

, Volume 23, Issue 1, pp 71–83 | Cite as

An information-passing strategy for achieving Pareto optimality in the design of complex systems

  • Francesco Ciucci
  • Tomonori Honda
  • Maria C. Yang
Original Paper

Abstract

As engineering systems grow in complexity, it becomes more challenging to achieve system-level designs that effectively balance the trade-offs among subsystems. Lewis and others have developed a well-known, traditional game-theoretic approach for formally modeling complex systems that can locate a Nash equilibrium design with a minimum of information sharing in the form of a point design. This paper builds on Lewis’ work by proposing algorithms that are capable of converging to Pareto-optimal system-level designs by increasing cooperation among subsystems through additional passed information. This paper investigates several forms for this additional passed information, including both quadratic and eigen-based formulations. Such forms offer guidance to designers on how they should change parameter values to better suit the overall system by providing information on directionality and curvature. Strategies for representing passed information are examined in three case studies of 2- and 3-player scenarios that cover a range of system complexity. Depending on the scenario, findings suggest that passing more information generally leads to convergence to a Pareto-optimal set. However, more iterations may be required to reach the Pareto set than if using a traditional game-theoretic approach.

Keywords

Complex system design Distributed design Design optimization Pareto optimality 

Notes

Acknowledgments

The work described in this paper was supported in part by the National Science Foundation under Award CMMI-0830134. The opinions, findings, conclusions, and recommendations expressed are those of the authors and do not necessarily reflect the views of the sponsors.

References

  1. Agte J, de Weck O, Sobieski J, Arendson P, Morris A, Spieck M (2010) MDO: assessment and direction for advancement—an opinion of one international group. Struct Multidiscip Optim 40(1–6):17–33CrossRefGoogle Scholar
  2. Allen TJ (1984) Managing the flow of technology: technology transfer and the dissemination of technological information. MIT, CambridgeGoogle Scholar
  3. Allision JT, Kokkolara M, Papalambros PY (2009) Optimal partitioning and coordination decisions in decomposition-based design optimization. J Mech Des 1(8):081008–1–081008–8Google Scholar
  4. Avnet MS (2009) Socio-cognitive analysis of engineering systems design: shared knowledge, process, and product. PhD thesis, Massachusetts Institute of TechnologyGoogle Scholar
  5. Azarm S, Tits A, Fan MKH (1999) Tradeoff driven optimization-based design of mechanical systems. In: 4-th AIAA/USAF/NASA/OAI symposium on multidisciplinary analysis and optimization, Cleveland, Ohio, USA, AIAA. AIAA-92-4758-CPGoogle Scholar
  6. Chanron V, Lewis K (2004) Convergence and stability in distributed design of large systems. In: ASME design automation conference, Salt Lake City, UtahGoogle Scholar
  7. Chanron V, Lewis K (2005) A study of convergence in decentralized design processes. Res Eng Design 16(3):133–145CrossRefGoogle Scholar
  8. Chanron V, Lewis K, Murase Y, Izui K, Nishiwaki S, Yoshimura M (2005) Handling multiple objectives in decentralized design. In: ASME design automation conference, Long Beach, CAGoogle Scholar
  9. Chanron V, Singh T, Lewis K (2005) Equilibrium stability in decentralized design systems. Int J Syst Sci 36(10):651–662CrossRefzbMATHMathSciNetGoogle Scholar
  10. Chinchuluun A, Pardalos P (2007) A survey of recent developments in multiobjective optimization. Ann Oper Res 154(1):29–50CrossRefzbMATHMathSciNetGoogle Scholar
  11. Cramer EJ, Dennis JE, Frank PD, Lewis RM, Shubin GR (1993) Problem formulation for multidisciplinary optimization. Technical report, Center for Research on Parallel Computation, Rice UniversityGoogle Scholar
  12. Cross N (2000) Engineering design methods: strategies for product design. Wiley, New YorkGoogle Scholar
  13. Das I, Dennis JE (1997) A closer look at drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems. Struct Multidiscip Optim 14(1):63–69Google Scholar
  14. Dauer JP, Stadler W (1986) A survey of vector optimization in infinite-dimensional spaces, part 2. J Optim Theory Appl 51(2):205–241CrossRefzbMATHMathSciNetGoogle Scholar
  15. Ding XP, Park JY, Jung IH (2000) Existence of pareto equilibria for constrained multiobjective games in h-space. Comput Math Appl 39(9–10):125–134zbMATHGoogle Scholar
  16. Ding XP, Park JY, Jung IH (2003) Pareto equilibria for constrained multiobjective games in locally l-convex spaces. Comput Math Appl 46(10–11):1589–1599CrossRefzbMATHMathSciNetGoogle Scholar
  17. Eckart C, Young G (1936) The approximation of one matrix by another of lower rank. Psychometrika 1:211–218CrossRefzbMATHGoogle Scholar
  18. Fernandez MG, Panchal JH, Allen JK, Mistree F (2005) An interactions protocol for collaborative decision making—concise interactions and effective management of shared design spaces. In: ASME design engineering technical conferences, Long Beach, CAGoogle Scholar
  19. Fliege J, Svaiter BF (2000) Steepest descent methods for multicriteria optimization. Math Methods Oper Res 51(3):479–494CrossRefzbMATHMathSciNetGoogle Scholar
  20. Franssen M, Bucciarelli LL (2004) On rationality in engineering design. J Mech Des 126(6):945–949CrossRefGoogle Scholar
  21. GarcÌa-Palomares UM, Burguillo-Rial JC, Gonzalez-Castano FJ (2008) Explicit gradient information in multiobjective optimization. Oper Res Lett 36(6):722–725CrossRefzbMATHMathSciNetGoogle Scholar
  22. Golinski J (1970) Optimal synthesis problems solved by means of nonlinear programming and random methods. J Mech 5Google Scholar
  23. Haimes Y (1973) Integrated system identification and optimization. Control Dyn Syst Adv Theory Appl 10:435–518MathSciNetGoogle Scholar
  24. Hazelrigg GA (1998) A framework for decision-based engineering design. J Mech Des 120:653–658CrossRefGoogle Scholar
  25. Homma T, Saltelli A (1996) Importance measures in global sensitivity analysis of nonlinear models. Reliab Eng Syst Saf 52:1–17CrossRefGoogle Scholar
  26. Honda T, Ciucci F, Yang MC (August 2007) Achieving pareto optimality in a decentralized design environment. In: 17th international conference on engineering design (ICED). The Design SocietyGoogle Scholar
  27. Huang CH, Galuski J, Bloebaum CL (2007) Multi-objective pareto concurrent subspace optimization for multidisciplinary design. AIAA J 45(8):1894–1906CrossRefGoogle Scholar
  28. Jet Propulsion Laboratory (2010) Team X. ([http://jplteamx.jpl.nasa.gov/])
  29. Jian JB, Ju QJ, Tang CM, Zheng HY (2007) A sequential quadratically constrained quadratic programming method of feasible directions. Appl Math Optim 56(56):343–363CrossRefzbMATHMathSciNetGoogle Scholar
  30. Keeney RL (2009) The foundations of collaborative group decisions. Int J Collab Eng 1(1–2):4–18CrossRefGoogle Scholar
  31. Kurpati A, Azarm S, Wu J (2002) Constraint handling improvements for multiobjective genetic algorithms. Struct Multidiscip Optim 23(3):204–213CrossRefGoogle Scholar
  32. Laumanns M, Thiele L, Zitzler E (2006) An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method. Eur J Oper Res 169(3):932–942CrossRefzbMATHMathSciNetGoogle Scholar
  33. Lewis K (1996) An algorithm for integrated subsystem embodiment and system synthesis. PhD thesis, Georgia Institute of TechnologyGoogle Scholar
  34. Lewis K, Mistree F (1997) Modeling the interactions in multidisciplinary design: a game theoretic approach. AIAA J Aircraft 35:1387–1397zbMATHGoogle Scholar
  35. Lewis K, Mistree F (1999) Collaborative, sequential, and isolated decisions in design. ASME J Mech Des 120:643–652CrossRefGoogle Scholar
  36. Lewis K, Mistree F (2001) Modeling subsystem interactions: a game theoretic approach. J Des Manuf Autom 1:17–36CrossRefGoogle Scholar
  37. Lewis, KE, Chen, W, Schmidt, LC (eds) (2006) Decision making in engineering design. American Society of Mechanical Engineers, New YorkGoogle Scholar
  38. Li M, Azarm S (2007) Multiobjective collaborative robust optimization (mcro) with interval uncertainty and interdisciplinary uncertainty propagation. In: Proceedings of the ASME 2007 international design engineering technical conferences & computers and information in engineering conference IDETC/CIE 2007, Las Vegas, Nevada, USA, ASME. DETC2007-34818Google Scholar
  39. Lin JI (1976) Multiple-objective problems: pareto-optimal solutions by method of proper equality constrains. IEEE Trans Autom Control 21(5):641–650CrossRefzbMATHGoogle Scholar
  40. Lu S, Kim HM (2010) Optimized sequencing of analysis components in multidisciplinary systems. J Mech Des 132(4):041005-1–041005-12CrossRefGoogle Scholar
  41. Marglin S (1967) Public investment criteria. MIT, CambridgeGoogle Scholar
  42. Mark G (2002) Extreme collaboration. Commun ACM 45(6):89–93CrossRefGoogle Scholar
  43. Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395CrossRefMathSciNetGoogle Scholar
  44. Mistree F, Marinopoulos S, Jackson DM, Shupe JA (1988) The design of aircraft using the decision support problem technique. Technical report NAS 1.26:4134, NASA-CR-4134, NASAGoogle Scholar
  45. Olesen K, Myers MD (1999) Trying to improve communication and collaboration with information technology. an action research project which failed. Inf Technol People 12(4):317–332CrossRefGoogle Scholar
  46. Park GJ (2007) Analytic methods in design practice. Springer, BerlinGoogle Scholar
  47. Rao JRJ, Badhrinath K, Pakala R, Mistree F (1997) A study of optimal design under conflict using models of multi-player games. Eng Optim 28:63–94CrossRefGoogle Scholar
  48. RV Tappeta, JE Renaud (1997) Multiobjective collaborative optimization. J Mech Des 119:403–411CrossRefGoogle Scholar
  49. Scott MJ (1999) Formalizing negotiation in engineering design. PhD thesis, California Institute of Technology, Pasadena, CAGoogle Scholar
  50. Scott MJ, Antonsson EK (2000) Arrow’s theorem and engineering design decision making. Res Eng Design 11(4):218–228CrossRefGoogle Scholar
  51. Senge PM (1990) The fifth discipline: The art & practice of the learning organization. Crown Business, New YorkGoogle Scholar
  52. Shaja AS, Sudhakar K (2010) Optimized sequencing of analysis components in multidisciplinary systems. Res Eng Design 21(3):173–187CrossRefGoogle Scholar
  53. Shin MK, Park GJ (2005) Multidisciplinary design optimization based on independent subspaces. Int J Numer Methods Eng 64:599–617CrossRefzbMATHGoogle Scholar
  54. Simaan M, Cruz JB (1973) On the stackelberg strategy in nonzero-sum games. J Optim Theory Appl 11(5):533–555CrossRefzbMATHMathSciNetGoogle Scholar
  55. Smith J, Koenig L, Wall SD (1999) Team efficiencies within a model-driven design process. In: INCOSE symposium, Brighton, EnglandGoogle Scholar
  56. Sobieszczanski-Sobieski J (1988) Optimization by decomposition: A step from hierarchic to non-hierarchic systems. Technical report, NASAGoogle Scholar
  57. Sobieszczanski-Sobieski J, Agte JS, Sandusky RR (1998) Bi-level integrated system synthesis (bliss). In: AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, volume AIAA-98-4916. AIAA, pp 1543–1557Google Scholar
  58. Stewart GW (1993) On the early history of the singular value decomposition. SIAM Rev 35:551–566CrossRefzbMATHMathSciNetGoogle Scholar
  59. Tao YR, Han X, Jiang C, Guan FJ (2010) A method to improve computational efficiency for csso and bliss. Struct Multidiscip Optim. Nov.(online):1–6Google Scholar
  60. Tosserams S, Etman LFP, Rooda JE (2010) A micro-accelerometer mdo benchmark problem. Struct Multidiscip Optim 41(2):255–275CrossRefMathSciNetGoogle Scholar
  61. Verbeeck K, Nowe A, Lenaerts T, Parent J (2002) Learning to reach the pareto optimal nash equilibrium as a team. Adv Artif Intell 2557:407–418MathSciNetGoogle Scholar
  62. Vincent TL (1983) Game theory as a design tool. J Mech Transm Autom Des 105:165–170CrossRefGoogle Scholar
  63. Wang F, Zhang K (2008) A hybrid algorithm for nonlinear minimax problems. Ann Oper Res 164(1):167–191CrossRefzbMATHMathSciNetGoogle Scholar
  64. Ward AC (1989) A theory of quantitative inference for artifact sets, applied to a mechanical design compiler. PhD thesis, MITGoogle Scholar
  65. Ward AC, Lozano-Pérez T, Seering WP (1990) Extending the constraint propagation of intervals. Artif Intell Eng Des Manuf 4(1):47–54CrossRefGoogle Scholar
  66. de Weck O (2004) Multiobjective optimization: History and promise. In: The third China-Japan-Korea joint symposium on optimization of structural and mechanical systems, Kanazawa, Japan, 2004. Invited Keynote Paper, GL2-2Google Scholar
  67. Whitfield RI, Duffy AHB, Coates G, Hills B (2002) Distributed design coordination. Res Eng Design 13:243–252Google Scholar
  68. Xiao A, Zheng S, Allen JK, Rosen DW, Mistree F (2005) Collaborative multidisciplinary decision making using game theory and design capability indices. Res Eng Design 16(1–2):57–72CrossRefGoogle Scholar
  69. Yi SI, Shin JK, Park GJ (2008) Comparison of mdo methods with mathematical examples. Struct Multidiscip Optim 35:391–402CrossRefGoogle Scholar
  70. Yu H (2003) Weak pareto equilibria for multiobjective constrained games. Appl Math Lett 16(5):773–776CrossRefzbMATHMathSciNetGoogle Scholar
  71. Zhao M, Cui W (2011) On the development of bi-level integrated system collaborative optimization. Struct Multidiscip Optim 43(1):73–84CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Francesco Ciucci
    • 1
  • Tomonori Honda
    • 2
  • Maria C. Yang
    • 3
  1. 1.Heidelberg Graduate School of Mathematical and Computational Methods for the SciencesUniversität HeidelbergHeidelbergGermany
  2. 2.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Department of Mechanical Engineering and Engineering System DivisionMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations