Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 419043, 7 pages http://dx.doi.org/10.1155/2013/419043 Research Article Design Optimization of a Speed Reducer Using Deterministic Techniques Ming-Hua Lin, 1 Jung-Fa Tsai, 2 Nian-Ze Hu, 3 and Shu-Chuan Chang 2,4 1 Department of Information Technology and Management, Shih Chien University, No. 70, Dazhi Street, Taipei 10462, Taiwan 2 Department of Business Management, National Taipei University of Technology, No. 1, Section 3, Chung-Hsiao E. Road, Taipei 10608, Taiwan 3 Department of Information Management, No. 64, Wunhua Road, Huwei Township, Yunlin County 632, Taiwan 4 Department of Information Management, St. John’s University, No. 499, Section 4, Tam King Road, Tamsui District, New Taipei City 25135, Taiwan Correspondence should be addressed to Jung-Fa Tsai; jfsai@ntut.edu.tw Received 26 June 2013; Accepted 10 September 2013 Academic Editor: Yi-Chung Hu Copyright © 2013 Ming-Hua Lin et al. Tis 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. Te 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 fnd the global optimum of a generalized geometric programming problem, this paper applies an efcient deterministic approach to globally solve speed reducer design problems. Te original problem is converted by variable transformations and piecewise linearization techniques. Te 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. 1. Introduction Many engineering design problems are formulated as math- ematical programming models. In last few decades, these nonlinear engineering problems have been investigated in much research that solved the formulated problems by diferent methods. Te methods can be generally categorized into metaheuristic and deterministic approaches. To compare the performance of diferent optimization algorithms, several structural engineering applications are ofen solved to vali- date or test the suitability of the optimization algorithms. Te speed reducer problem is one of the benchmark problems in structural optimization. Te problem represents the design of a simple gear box used in a light airplane between the engine and propeller to allow each to rotate at its most efcient speed. A large number of algorithms have been developed to solve diferent engineering optimization problems. In order to overcome the computational drawbacks of existing numer- ical methods, many metaheuristic algorithms that combine rules and randomness to imitate natural phenomena [1] have been developed. Te most general metaheuristic methods include evolutionary computation (EC), tabu search (TS), simulated annealing (SA), ant colony optimization (ACO), and particle swarm (PS) [2]. Te surveys of applications and algorithmic advances for metaheuristic algorithms are provided by Glover and Kochenberger [3], Lee and Geem [1], and Bianchi et al. [4]. Li and Papalambros [5] used the global optimization knowledge that is incorporated in several types of rules concerning constraint activity, redundancy, and dominance to solve the speed reducer problem. Ku et al. [6] solved the speed reducer problem using the Taguchi method that emphasizes the design of a robust product insensitive to disturbances. Akhtar et al. [7] developed an optimization algorithm based on a sociobehavioural concept of society and