Sequential approximate multi-objective optimization using radial basis function network
Sequential approximate multi-objective optimization using radial basis function network
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DOI：
10.1007/s00158-013-0911-z
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发表时间：
2013-09-01
影响因子：
3.9
通讯作者：
Yamazaki, Koetsu
中科院分区：
文献类型：
--
作者：
Kitayama, Satoshi;Srirat, Jirasak;Yamazaki, Koetsu
在工业设计优化中，目标和约束通常以设计变量的隐式形式给出，并通过计算密集型数值模拟进行评估。在这种情况下，响应面法是设计优化的有用方法之一。其中一种方法称为顺序近似优化 (SAO)，近年来越来越受欢迎。在 SAO 中，获得高精度全局最小值的采样策略仍然是一个关键问题。在本文中，我们提出了一种在径向基函数（RBF）网络中使用顺序近似多目标优化（SAMOO）的新采样策略。为了通过少量函数评估来识别部分帕累托最优解，我们提出的采样策略包括三个阶段：（1）将响应面的帕累托最优解作为新的采样点； (2)在未探索区域及其周围添加新点； (3) 使用称为帕累托适应度函数的新函数来识别帕累托最优解的其他部分。然后将该帕累托适应度函数的最优解作为新的采样点。这种方法的结果是阶段（2）和（3）添加了采样点，但没有解决多目标优化问题。描述了用 RBF 网络构造帕累托适应度函数的详细过程。通过数值例子，讨论了所提出的采样策略的有效性。
In industrial design optimization, objectives and constraints are generally given as implicit form of the design variables, and are evaluated through computationally intensive numerical simulation. Under this situation, response surface methodology is one of helpful approaches to design optimization. One of these approaches, known as sequential approximate optimization (SAO), has gained its popularity in recent years. In SAO, the sampling strategy for obtaining a highly accurate global minimum remains a critical issue. In this paper, we propose a new sampling strategy using sequential approximate multi-objective optimization (SAMOO) in radial basis function (RBF) network. To identify a part of the pareto-optimal solutions with a small number of function evaluations, our proposed sampling strategy consists of three phases: (1) a pareto-optimal solution of the response surfaces is taken as a new sampling point; (2) new points are added in and around the unexplored region; and (3) other parts of the pareto-optimal solutions are identified using a new function called the pareto-fitness function. The optimal solution of this pareto-fitness function is then taken as a new sampling point. The upshot of this approach is that phases (2) and (3) add sampling points without solving the multi-objective optimization problem. The detailed procedure to construct the pareto-fitness function with the RBF network is described. Through numerical examples, the validity of the proposed sampling strategy is discussed.