Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization

2010 ◽  
Author(s):  
Michael J. Alexander ◽  
James T. Allison ◽  
Panos Y. Papalambros ◽  
David J. Gorsich
Keyword(s):  
Design Optimization ◽  
Poor Performance ◽  
Support Vector ◽  
Reduced Representation ◽  
Coordination Strategies ◽  
Model Validity ◽  
Target Cascading ◽  
Coupling Variables ◽  
Domain Description ◽  
Proper Orthogonal

In decomposition-based design optimization strategies, such as Analytical Target Cascading (ATC), it is sometimes necessary to use reduced dimensionality representations to approximate functions of large dimensionality whose values need to be exchanged among subproblems. The reduced representation variables may not be physically meaningful, and it can become challenging to constrain them properly and define the model validity region. For example, in coordination strategies like ATC, representing vector-valued coupling variables with improperly constrained reduced representation variables can lead to poor performance or convergence failure. This paper examines two approaches for constraining effectively the model validity region of reduced representation variables based on proper orthogonal decomposition: a penalty value-based heuristic and a support vector domain description. An ATC application on electric vehicle design helps to illustrate the concepts discussed.

Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Michael J. Alexander ◽  
James T. Allison ◽  
Panos Y. Papalambros ◽  
David J. Gorsich
Keyword(s):  
Design Optimization ◽  
Support Vector ◽  
Management Technique ◽  
Efficient Design ◽  
Reduced Representation ◽  
Constraint Management ◽  
Target Cascading ◽  
Simple Bounds ◽  
Domain Description ◽  
Reduced Representations

In decomposition-based design optimization strategies such as analytical target cascading (ATC), it is sometimes necessary to use reduced representations of highly discretized functional data exchanged among subproblems to enable efficient design optimization. However, the variables used by such reduced representation methods are often abstract, making it difficult to constrain them directly beyond simple bounds. This problem is usually addressed by implementing a penalty value-based heuristic that indirectly constrains the reduced representation variables. Although this approach is effective, it leads to many ATC iterations, which in turn yields an ill-conditioned optimization problem and an extensive runtime. To address these issues, this paper introduces a direct constraint management technique that augments the penalty value-based heuristic with constraints generated by support vector domain description (SVDD). A comparative ATC study between the existing and proposed constraint management methods involving electric vehicle design indicates that the SVDD augmentation is the most appropriate within decomposition-based design optimization.

scholarly journals Machine Learning for Design Optimization of Electromagnetic Devices: Recent Developments and Future Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1627
Author(s):  
Yanbin Li ◽  
Gang Lei ◽  
Gerd Bramerdorfer ◽  
Sheng Peng ◽  
Xiaodong Sun ◽  
...  
Keyword(s):  
Machine Learning ◽  
Design Optimization ◽  
Optimization Methods ◽  
Machine Learning Algorithms ◽  
Cloud Services ◽  
Robust Design Optimization ◽  
Support Vector ◽  
Future Directions ◽  
Electromagnetic Devices ◽  
Recent Developments

This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.

Support Vector Regression-Based Multidisciplinary Design Optimization for Ship Design

2012 ◽  
Author(s):  
Dongqin Li ◽  
Yifeng Guan ◽  
Qingfeng Wang ◽  
Zhitong Chen
Keyword(s):  
Design Optimization ◽  
Support Vector Regression ◽  
Design Process ◽  
Multidisciplinary Design Optimization ◽  
Initial Point ◽  
Ship Design ◽  
Collaborative Optimization ◽  
Multidisciplinary Design ◽  
Support Vector ◽  
Independent Design

The design of ship is related to several disciplines such as hydrostatic, resistance, propulsion and economic. The traditional design process of ship only involves independent design optimization within each discipline. With such an approach, there is no guarantee to achieve the optimum design. And at the same time improving the efficiency of ship optimization is also crucial for modem ship design. In this paper, an introduction of both the traditional ship design process and the fundamentals of Multidisciplinary Design Optimization (MDO) theory are presented and a comparison between the two methods is carried out. As one of the most frequently applied MDO methods, Collaborative Optimization (CO) promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, Design Of Experiment (DOE) and a new support vector regression algorithm are applied to CO to construct statistical approximation model in this paper. The support vector regression algorithm approximates the optimization model and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method. Then this new Collaborative Optimization (CO) method using approximate technology is discussed in detail and applied in ship design which considers hydrostatic, propulsion, weight and volume, performance and cost. It indicates that CO method combined with approximate technology can effectively solve complex engineering design optimization problem. Finally, some suggestions on the future improvements are proposed.

scholarly journals An Enhanced Analytical Target Cascading and Kriging Model Combined Approach for Multidisciplinary Design Optimization

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ping Jiang ◽  
Jianzhuang Wang ◽  
Qi Zhou ◽  
Xiaolin Zhang
Keyword(s):  
Design Optimization ◽  
Multidisciplinary Design Optimization ◽  
Kriging Model ◽  
Multidisciplinary Design ◽  
High Approximation ◽  
Engineering Systems ◽  
Analytical Target Cascading ◽  
Combined Approach ◽  
Coordination Strategy ◽  
Target Cascading

Multidisciplinary design optimization (MDO) has been applied widely in the design of complex engineering systems. To ease MDO problems, analytical target cascading (ATC) organizes MDO process into multilevels according to the components of engineering systems, which provides a promising way to deal with MDO problems. ATC adopts a coordination strategy to coordinate the couplings between two adjacent levels in the design optimization process; however, existing coordination strategies in ATC face the obstacles of complicated coordination process and heavy computation cost. In order to conquer this problem, a quadratic exterior penalty function (QEPF) based ATC (QEPF-ATC) approach is proposed, where QEPF is adopted as the coordination strategy. Moreover, approximate models are adopted widely to replace the expensive simulation models in MDO; a QEPF-ATC and Kriging model combined approach is further proposed to deal with MDO problems, owing to the comprehensive performance, high approximation accuracy, and robustness of Kriging model. Finally, the geometric programming and reducer design cases are given to validate the applicability and efficiency of the proposed approach.

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