The use of discrete variables in optimal design models offers the opportunity to deal rigorously with an expanded variety of design situations, as opposed to using only continuous variables. However, complexity and solution difficulty increase dramatically and model formulation becomes very important. A particular problem arising from the design of a gear train employing four spur gear pairs is introduced and formulated in several different ways. An interesting aspect of the problem is its exhibition of three different types of discreteness. The problem could serve as a test for a variety of optimization or artificial intelligence techniques. The best known solution is included in this article, while its derivation is given in a sequel article.

Issue Section:
Research Papers
Topics:
Design, Gear trains, Artificial intelligence, Optimization, Spur gears
1.
Bean, J. C., 1982, “A Branch-and-Bound Algorithm for the Multiple Choice Integer Program,” Technical Report No. 82-1, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor.
2.
Bean
J. C.
,
1984
, “
A Lagrangian Algorithm for the Multiple Choice Integer Program
,”
Operations Research
, Vol.
32
, No.
5
, pp.
1185
–
1193
.
3.
Brown, D. C., and Chandrasekaran, B., 1983, “An Approach to Expert Systems for Mechanical Design,” Proceedings of the IEEE Computer Society, Trends and Applications ’83, Gaithersburg, MD, pp. 173–180.
4.
Juvinall, R. C., 1983, Fundamentals of Machine Component Design, John Wiley & Sons, New York.
5.
Papadimitriou, C. H., and Steiglitz, K., 1982, Combinatorial Optimization, Prentice-Hall, New Jersey.
6.
Pomrehn
L. P.
, and
Papalambros
P. Y.
,
1995
, “
Infeasibility and Non-Optimality Tests for Solution Space Reduction in Discrete Optimal Design
,”
ASME JOURNAL OF MECHANICAL DESIGN
, Vol.
117
, No.
3
, Sept., pp.
425
–
432
.
This content is only available via PDF.
Copyright © 1995
 by The American Society of Mechanical Engineers
You do not currently have access to this content.