A neural network based interactive physical programming approach is proposed in this paper. The approximate model of Pareto surface at a given Pareto design is developed based on neural networks, and a map from Pareto designs to their corresponding evaluation values is built. Genetic algorithms is used to find the Pareto design that best satisfies the designer

Hong-Zhong Huang received the B.S. degree from Wuhan University, Wuhan, China, in 1983, the M.S. degree from Chongqing University, Chongqing, China, in 1988, and the Ph.D. degree from Shanghai Jiao Tong University, Shanghai, China, in 1999. He is Professor in the School of Mechanical Engineering at Dalian University of Technology, Dalian, China. He is currently a Visiting Professor of Department of Mechanical Engineering, University of Alberta, Edmonton, Canada. He has published 120 journal articles and 5 books in fields of reliability engineering, optimization design, and fuzzy sets theory. He is a (senior) member of several professional societies, and has served on the boards of several professional societies. His research interests include reliability engineering, robust design, and optimization design.

The contents and meanings of mapping relationships between physical domain and function domain in different design stages, such as conceptual design, detail design and enhancement design, were analyzed. According to the analysis results, the fuzzy mapping between physical domain and function domain in different design stages was established by integrating objective information and subjective information in the design process, such as expert's knowledge, designer's preferences and customer's requirements, where the fuzzy sets, fuzzy mapping and fuzzy transition were used. The property table of structure behavior parameters was established based on the fuzzy mapping relationships. The fuzzy mapping is very important to optimize product structure, perfect product function, meet the diversified and individual requirements of customers. Finally, an example was used to illustrate the fuzzy mapping relationships between physical domain and function domain in different design stages.

The preliminary design optimization of multi-stage spur gear reduction units has been a subject of considerable interest, since many high-performance power transmission applieations (e.g., automotive in the optimal design of multi-stage spur gear reduction unit, such as minimizing the volume and maximizing the surface fatigue life. It is reasonable to formulate the design of spur gear reductio unit as a multi-objective optimization problem, and find an design of spur gear reduction unit as a multi-objective optimization problem. and find an appropriate approach to solve it. In this paper an interactive physical programming approach is developed to place physical programming into an interactive framework in a natural way. Class functions, which are used to represent the designer's preferences on design objectives, are fixed during the interactive physical programming procedure. After a Pareto solution is generated, a preference offset is added into the class function of each objective based on whether the designer would like to improve this objective or sacrifice the objective so as to improve other objectives. The preference offsets are adjusted during the interactive physical programming procedure, and an optimal solution that satisfies the designer's preferences is supposed to be obtained by the end of the procedure. An optimization problem of three-stage spur gear reduction unit is given to illustrate the effectiveness of the proposed approach.