Global optimization algorithms for generalized polynomial design models using a global feasible search approach was discussed in a previous article. A new convex cutting plane algorithm (CONCUT) based on global feasible search and with improved performance is presented in this sequel article. Computational results of the CONCUT algorithm compared to one using linear cuts (LINCUT) are given for various test problems. A speed reducer design example illustrates the application of the algorithms.

Issue Section:
Research Papers
Topics:
Algorithms, Cutting, Design, Polynomials, Optimization algorithms
1.
Azarm, S., 1984, “Local Monotonicity in Optimal Design,” Doctoral dissertation. Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor.
2.
Bracken, J., and McCormick, G. P., 1968, Selected Applications of Nonlinear Programming, John Wiley & Sons, New York.
3.
Beightler, C., and Phillips, D. T., 1976, Applied Geometric Programming, John Wiley & Sons, New York.
4.
Duffin, R. J., Peterson, E. L., and Zener, C., 1967, Geometric Programming, Wiley, New York.
5.
Floudas, C. A., and Pardalos, P. M., 1990, A Collection of Test Problems for Constrained Global Optimization Algorithms, Springer-Verlag, Berlin.
6.
Golinski
J.
,
1970
, “
Optimal Synthesis Problems Solved by Means of Nonlinear Programming and Random Methods
,”
Journal of Mechanisms
, Vol.
5
, pp.
287
–
309
.
7.
Hock, W., and Schittkowski, K., 1981, Test Examples for Nonlinear Programming Codes, Springer-Verlag, Berlin.
8.
Horst, R., and Tuy, H., 1990, Global Optimization, Springer-Verlag, Berlin.
9.
Lasdon, L. S., Waren, A. D., and Ratner, M. W., 1980, GRG2 User’s Guide.
10.
Lo, C., 1991, “Global Optimization of Nonconvex Generalized Polynomial Design Models,” Doctoral dissertation. Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor.
11.
Lo, C., and Papalambros, P. Y., 1990, “A Deterministic Global Design Optimization Method for Nonconvex Generalized Polynomial Problems,” ASME JOURNAL OF MECHANICAL DESIGN, in press. Also, Advances in Design Automation, Ravani, B., ed., ASME, DE-Vol. 23-2, pp. 41–49.
12.
Mangasarian, O. L., 1969, Nonlinear Programming, McGraw-Hill Book Co., New York.
13.
McCormick, G. P., 1983, Nonlinear Programming: Theory, Algorithms and Applications, John Wiley & Sons, New York.
14.
Papalambros, P. Y., and Wilde, D. J., 1988, Principles of Optimal Design: Modeling and Computation, Cambridge University Press, New York.
15.
Rockafellar, R. T., 1970, Convex Analysis, Princeton University Press, Princeton, NJ.
This content is only available via PDF.
Copyright © 1996
 by The American Society of Mechanical Engineers
You do not currently have access to this content.