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Mathematical Problems in Engineering
Volume 2013, Article ID 419043, 7 pages
Research Article

Design Optimization of a Speed Reducer Using Deterministic Techniques

1Department of Information Technology and Management, Shih Chien University, No. 70, Dazhi Street, Taipei 10462, Taiwan
2Department of Business Management, National Taipei University of Technology, No. 1, Section 3, Chung-Hsiao E. Road, Taipei 10608, Taiwan
3Department of Information Management, No. 64, Wunhua Road, Huwei Township, Yunlin County 632, Taiwan
4Department of Information Management, St. John’s University, No. 499, Section 4, Tam King Road, Tamsui District, New Taipei City 25135, Taiwan

Received 26 June 2013; Accepted 10 September 2013

Academic Editor: Yi-Chung Hu

Copyright © 2013 Ming-Hua Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The optimal design problem of minimizing the total weight of a speed reducer under constraints is a generalized geometric programming problem. Since the metaheuristic approaches cannot guarantee to find the global optimum of a generalized geometric programming problem, this paper applies an efficient deterministic approach to globally solve speed reducer design problems. The original problem is converted by variable transformations and piecewise linearization techniques. The reformulated problem is a convex mixed-integer nonlinear programming problem solvable to reach an approximate global solution within an acceptable error. Experiment results from solving a practical speed reducer design problem indicate that this study obtains a better solution comparing with the other existing methods.