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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.9 No.1 pp.10-19

Optimization of Triple Response Systems by Using the Dual Response Approach and the Hooke-Jeeves Search Method

Shu-Kai S. Fan †, Chia-Fen Huang, Ko-Wei Chang, Yu-Chiang Chuang
Department of Industrial Engineering and Management Yuan Ze University
Received, July 25, 2009; Revised, January 11, 2010; Accepted, January 25, 2010


This paper presents an extended computing procedure for the global optimization of the tripleresponse system (TRS) where the response functions are nonconvex (nonconcave) quadratics and the inputfactors satisfy a radial region of interest. The TRS arising from response surface modeling can be approximatedusing a nonlinear mathematical program involving one primary (objective) function and two secondary(constraints) functions. An optimization algorithm named triple response surface algorithm (TRSALG) isproposed to determine the global optimum for the nondegenerate TRS. In TRSALG, the Lagrange multipliers oftarget (secondary) functions are computed by using the Hooke-Jeeves search method, and the Lagrangemultiplier of the radial constraint is located by using the trust region (TR) method at the same time. To ensureglobal optimality that can be attained by TRSALG, included is the means for detecting the degenerate case. Inthe field of numerical optimization, as the family of TR approach always exhibits excellent mathematicalproperties during optimization steps, thus the proposed algorithm can guarantee the global optimal solutionwhere the optimality conditions are satisfied for the nondegenerate TRS. The computing procedure is illustratedin terms of examples found in the quality literature where the comparison results with a gradient-based methodare used to calibrate TRSALG.