Managing approximation models in collaborative optimization

Collaborative optimization (CO), one of the multidisciplinary design optimization techniques, has been credited with guaranteeing disciplinary autonomy while maintaining interdisciplinary compatibility due to its bi-level optimization structure. However, a few difficulties caused by certain features of its architecture have been also reported. The architecture, with discipline-level optimizations nested in a system-level optimization, leads to considerably increased computational time. In addition, numerical difficulties such as the problem of slow convergence or unexpected nonlinearity of the compatibility constraint in the system-level optimization are known weaknesses of CO.This paper proposes the use of an approximation model in place of the disciplinary optimization in the system-level optimization in order to relieve the aforementioned difficulties. The disciplinary optimization result, the optimal discrepancy function value, is modeled as a function of the interdisciplinary target variables, and design variables of the system level. However, since this approach is hindered by the peculiar form of the compatibility constraint, it is hard to exploit well-developed conventional approximation methods. In this paper, neural network classification is employed as a classifier to determine whether a design point is feasible or not. Kriging is also combined with the classification to make up for the weakness that the classification cannot estimate the degree of infeasibility.In addition, for the purpose of enhancing the accuracy of the predicted optimum, this paper also employs two approximation management frameworks for single-objective and multi-objective optimization problem in the system-level optimization. The approximation is continuously updated using the information obtained from the optimization process. This can cut down the required number of disciplinary optimizations considerably and lead to a design (or Pareto set) near to the true optimum (or true Pareto set) of the system-level optimization.

[1]  Natalia Alexandrov,et al.  Comparative properties of collaborative optimization and other approaches to MDO , 1999 .

[2]  Vassili Toropov,et al.  Simulation approach to structural optimization , 1989 .

[3]  N. M. Alexandrov,et al.  Analytical and Computational Properties of Distributed Approaches to MDO , 2000 .

[4]  Ilan Kroo,et al.  Use of the Collaborative Optimization Architecture for Launch Vehicle Design , 1996 .

[5]  V. Markine,et al.  Refinements in the multi-point approximation method to reduce the effects of noisy structural responses , 1996 .

[6]  T. Simpson.  A concept exploration method for product family design , 1998 .

[7]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[8]  Beom-Seon Jang,et al.  Managing approximation models in multiobjective optimization , 2003 .

[9]  Ilan Kroo,et al.  Collaborative Optimization: Status and Directions , 2000 .

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

[11]  Ilan Kroo,et al.  Collaborative optimization using response surface estimation , 1998 .

[12]  Angel-Victor DeMiguel,et al.  An analysis of collaborative optimization methods , 2000 .

[13]  Timothy W. Simpson,et al.  GOAL PROGRAMMING APPLICATIONS IN MULTIDISCIPLINARY DESIGN OPTIMIZATION , 2000 .

[14]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[15]  Farrokh Mistree,et al.  SPATIAL CORRELATION METAMODELS FOR GLOBAL APPROXIMATION IN STRUCTURAL DESIGN OPTIMIZATION , 1998 .

[16]  Virginia Torczon,et al.  Numerical Optimization Using Computer Experiments , 1997 .

[17]  Ian Patrick Sobieski,et al.  Multidisciplinary design using collaborative optimization , 1998 .

[18]  A. J. Booker,et al.  A rigorous framework for optimization of expensive functions by surrogates , 1998 .

[19]  M. E. Johnson,et al.  Minimax and maximin distance designs , 1990 .

[20]  I. Kroo,et al.  Response surface estimation and refinement in collaborative optimization , 1998 .

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

[22]  Kroo Ilan,et al.  Multidisciplinary Optimization Methods for Aircraft Preliminary Design , 1994 .

[23]  N. M. Alexandrov,et al.  A trust-region framework for managing the use of approximation models in optimization , 1997 .

[24]  J. Sobieszczanski-Sobieski,et al.  An algorithm for solving the system-level problem in multilevel optimization , 1994 .

[25]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[26]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .