A trust region-based approach to optimize triple response systems
A trust region-based approach to optimize triple response systems
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DOI：
10.1080/0305215x.2013.791814
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发表时间：
2014-02
影响因子：
2.7
通讯作者：
Shu-Kai S. Fan;C. Fan;Chia-Fen Huang
中科院分区：
文献类型：
--
作者：
Shu-Kai S. Fan;C. Fan;Chia-Fen Huang
本文提出了一种新的三响应系统(TRS)全局优化的计算方法，其中响应函数为非凸二次曲面，输入因子满足径向约束的感兴趣区域。由响应面建模产生的TRS可以使用考虑一个主目标函数和两个次约束函数的非线性数学程序来近似。提出了一种确定非退化TRS全局最优解的三重响应面算法(TRSALG)。在TRSALG中，二次函数的拉格朗日乘子用Hooke-Jeeves搜索法确定，径向约束的拉格朗日乘子用信赖域方法在全局最优空间中定位。所提出的算法通过出现在质量控制文献中的三个例子来说明。文中还给出了TRSALG方法与基于梯度的方法的比较结果。
This article presents a new computing procedure for the global optimization of the triple response system (TRS) where the response functions are non-convex quadratics and the input factors satisfy a radial constrained region of interest. The TRS arising from response surface modelling can be approximated using a nonlinear mathematical program that considers one primary objective function and two secondary constraint functions. An optimization algorithm named the triple response surface algorithm (TRSALG) is proposed to determine the global optimum for the non-degenerate TRS. In TRSALG, the Lagrange multipliers of the secondary functions are determined using the Hooke–Jeeves search method and the Lagrange multiplier of the radial constraint is located using the trust region method within the global optimality space. The proposed algorithm is illustrated in terms of three examples appearing in the quality-control literature. The results of TRSALG compared to a gradient-based method are also presented.