Meta-Modeling in Multiobjective Optimization
Meta-Modeling in Multiobjective Optimization
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DOI：
10.1007/978-3-540-88908-3_10
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发表时间：
2008-10
期刊：
影响因子：
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通讯作者：
Joshua D. Knowles;H. Nakayama
中科院分区：
文献类型：
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作者：
Joshua D. Knowles;H. Nakayama
在许多实际工程设计和其他科学优化问题中，目标函数不是以设计变量的封闭形式给出的。给定设计变量的值，目标函数的值可以通过一些数值分析来获得，例如结构分析、流体力学分析、热力学分析等，甚至可以通过进行真实的（物理）实验和直接测量来获得。通常，这些评估比封闭形式函数的评估要耗时得多。为了使评估的次数尽可能少，我们可以将联合收割机迭代搜索与元建模相结合。在优化过程中，通过将函数拟合到评估点来对目标函数进行建模。然后，该模型用于帮助预测未来搜索点的值，以便更快地识别设计空间的高性能区域。在这一章中，元建模方法及其适用于特定的问题上下文的调查。评价的维度、噪声、昂贵性等方面与方法的选择有关。对于元建模问题的多目标版本，必须考虑进一步的方面，例如如何定义帕累托近似集的改进，以及如何对每个目标函数进行建模。还讨论了元建模与决策相结合的交互式方法的可能性。包括两个示例应用程序。一个是多目标生物化学问题，涉及仪器优化;另一个涉及斜拉桥加固中的抗震设计。
In many practical engineering design and other scientific optimization problems, the objective function is not given in closed form in terms of the design variables. Given the value of the design variables, the value of the objective function is obtained by some numerical analysis, such as structural analysis, fluidmechanic analysis, thermodynamic analysis, and so on. It may even be obtained by conducting a real (physical) experiment and taking direct measurements. Usually, these evaluations are considerably more time-consuming than evaluations of closed-form functions. In order to make the number of evaluations as few as possible, we may combine iterative search withmeta-modeling. The objective function is modeled during optimization by fitting a function through the evaluated points. This model is then used to help predict the value of future search points, so that high performance regions of design space can be identified more rapidly. In this chapter, a survey of meta-modeling approaches and their suitability to specific problem contexts is given. The aspects of dimensionality, noise, expensiveness of evaluations and others, are related to choice of methods. For the multiobjective version of the meta-modeling problem, further aspects must be considered, such as how to define improvement in a Pareto approximation set, and how to model each objective function. The possibility of interactive methods combining meta-modeling with decision-making is also covered. Two example applications are included. One is a multiobjective biochemistry problem, involving instrument optimization; the other relates to seismic design in the reinforcement of cable-stayed bridges.