On Selecting Single-Level Formulations for Complex System Design Optimization

Design of complex products with several interacting subsystems or disciplinary analyses poses substantive challenges to both analysis and optimization, necessitating specialized solution techniques. A product or system may qualify as complex due to large scale or due to strong interactions. Single-level strategies for complex system optimization centralize decision-making authority, while multilevel strategies distribute the decision-making process. This article studies important differences between two popular single-level formulations: multidisciplinary feasible (MDF) and individual disciplinary feasible (IDF). Results presented aim at aiding practitioners in selecting between formulations. Specifically, while IDF incurs some computational overhead, it may find optima hidden to MDF and is more efficient computationally for strongly coupled problems; further, MDF is sensitive to variations in coupling strength, while IDF is not. Conditions that lead to failure of MDF are described. Two new reproducible design examples are introduced to illustrate these findings and to provide test problems for other investigations.

[1]  Thomas Schuster.  Convergence and stability , 2007 .

[2]  Jaroslaw Sobieszczanski-Sobieski,et al.  OPTIMIZATION OF COUPLED SYSTEMS: A CRITICAL OVERVIEW OF APPROACHES , 1994 .

[3]  T Haftka Raphael,et al.  Multidisciplinary aerospace design optimization: survey of recent developments , 1996 .

[4]  N. M. Alexandrov,et al.  Algorithmic Perspectives on Problem Formulations in MDO , 2000 .

[5]  Y. Jaluria,et al.  An Introduction to Heat Transfer , 1950 .

[6]  R. Haftka,et al.  On options for interdisciplinary analysis and design optimization , 1992 .

[7]  Panos Y. Papalambros,et al.  Principles of Optimal Design: Modeling and Computation , 1988 .

[8]  Terrance Carl Wagner,et al.  A general decomposition methodology for optimal system design. , 1993 .

[9]  Steven D. Eppinger,et al.  The Misalignment of Product Architecture and Organizational Structure in Complex Product Development , 2004, Manag. Sci..

[10]  Robert D. Braun,et al.  Collaborative optimization: an architecture for large-scale distributed design , 1996 .

[11]  Arnold Neumaier,et al.  Introduction to Numerical Analysis , 2001 .

[12]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

[13]  Anneli Folkesson,et al.  Numerical methods for engineers , 2007 .

[14]  Panos Y. Papalambros,et al.  On the Use of Analytical Target Cascading and Collaborative Optimization for Complex System Design , 2005 .

[15]  Begnaud Francis Hildebrand,et al.  Introduction to numerical analysis: 2nd edition , 1987 .

[16]  A. Galip Ulsoy,et al.  Quantification and Use of System Coupling in Decomposed Design Optimization Problems , 2005 .

[17]  Christina Bloebaum,et al.  Ordering design tasks based on coupling strengths , 1994 .

[18]  P. Lettieri,et al.  An introduction to heat transfer , 2007 .

[19]  Raphael T. Haftka,et al.  Numerical difficulties associated with using equality constraints to achieve multi-level decomposition in structural optimization , 1986 .

[20]  John E. Dennis,et al.  Problem Formulation for Multidisciplinary Optimization , 1994, SIAM J. Optim..

[21]  Christina Bloebaum,et al.  A simulation-based comparison of multidisciplinary design optimization solution strategies using CASCADE , 2000 .

[22]  Steven D. Eppinger,et al.  Identifying Modular and Integrative Systems and Their Impact on Design Team Interactions , 2003 .

[23]  Kemper Lewis,et al.  Convergence and Stability in Distributed Design of Large Systems , 2004, DAC 2004.

[24]  Richard J. Balling,et al.  Execution of multidisciplinary design optimization approaches on common test problems , 1996 .

[25]  Tao Jiang,et al.  Target Cascading in Optimal System Design , 2003, DAC 2000.