Mathematical Foundations and Convergence Characteristics for Reliability-Based Optimization Problems with Complex Structures

Large-scale design problems are high dimensional and deeply-coupled in nature. The complexity of such large-scale systems prevents designers from solving them as a whole. Analytical target cascading (ATC) provides a systematic approach in solving decomposed large-scale systems that has solvable subsystems. By coordinating between subsystems, ATC can obtain the same optima as they were undecomposed. However, series of ATC iterations are still needed to reach a convergent coordination that may hinder the efficiency of ATC. In this research, a sequential linear programming algorithm is proposed to improve the efficiency of ATC. The proposed linearization techniques are applied to each ATC iteration, therefore each iteration has all linear subsystems that can be solved with high efficiency. The linearization techniques are integrated within a trust-region algorithm resulting in a more efficient ATC solution approach. The global convergence of this sequential linear programming algorithm is ensured by a filter to determine the acceptance of the optima at each iteration and the corresponding trust region. A geometric programming example demonstrates the efficiency of the proposed method over standard ATC solution process without loss of accuracy.

[1]  Panos Y. Papalambros,et al.  Simulation-based optimal design of heavy trucks by model-based decomposition: an extensive analytical target cascading case study , 2004 .

[2]  Panos Y. Papalambros,et al.  Analytical Target Setting: An Enterprise Context in Optimal Product Design , 2003, DAC 2003.

[3]  Panos Y. Papalambros,et al.  An Adaptive Sequential Linear Programming Algorithm for Optimal Design Problems With Probabilistic Constraints , 2007 .

[4]  Panos Y. Papalambros,et al.  PRODUCT TOLERANCE ALLOCATION IN COMPLIANT MULTISTATION ASSEMBLY THROUGH VARIATION PROPAGATION AND ANALYTICAL TARGET CASCADING , 2004 .

[5]  Jeremy J. Michalek,et al.  AN EFFICIENT WEIGHTING UPDATE METHOD TO ACHIEVE ACCEPTABLE CONSISTENCY DEVIATION IN ANALYTICAL TARGET CASCADING , 2005 .

[6]  Jeremy J. Michalek,et al.  Linking Marketing and Engineering Product Design Decisions via Analytical Target Cascading , 2005 .

[7]  Philippe L. Toint,et al.  Non-monotone trust-region algorithms for nonlinear optimization subject to convex constraints , 1997, Math. Program..

[8]  Panos Y. Papalambros,et al.  A Hypergraph Framework for Optimal Model-Based Decomposition of Design Problems , 1997, Comput. Optim. Appl..

[9]  Panos Y. Papalambros,et al.  Convergence properties of analytical target cascading , 2002 .

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

[11]  Devadatta M. Kulkarni,et al.  Hierarchical overlapping coordination for large-scale optimization by decomposition , 1999 .

[12]  Panos Y. Papalambros,et al.  Analytic target cascading in simulation-based building design , 2005 .

[13]  Ting-Yu Chen.  Calculation of the move limits for the sequential linear programming method , 1993 .