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首页> 外文期刊>Journal of Hydroinformatics >Pareto-optimality and a search for robustness: choosing solutions with desired properties in objective space and parameter space
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Pareto-optimality and a search for robustness: choosing solutions with desired properties in objective space and parameter space

机译：帕累托最优性和鲁棒性搜索：在目标空间和参数空间中选择具有所需属性的解决方案

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摘要

Multi-objective genetic algorithms are increasingly being applied to calibrate hydrological models by generating several competitive solutions usually referred to as a Pareto-optimal set. The Pareto-optimal set comprises non-dominated solutions at the calibration phase but it is usually unknown whether all or only a subset of non-dominated solutions at the calibration phase remains non-dominated at the validation phase, in practice, users would like to know solutions (and their associated properties) which remain non-dominated at both the calibration and validation phases. This study investigates robustness of the Pareto-optimal set by developing a model characterization framework (MCF). The MCF uses cluster analysis to examine the distribution of solutions in parameter space and objective space, and conditional probability to combine linkages between the distributions of solutions in both spaces. The MCF has been illustrated for calibration output generated from application of the Non-dominated Sorting Genetic Algorithm-ll to calibrate the Soil and Water Assessment Tool for streamflow in the Fairchild Creek watershed in southern Ontario. Our results show that not all non-dominated solutions found at the calibration phase perform the same for different validation periods. The MCF illustrates that robust solutions - non-dominated solutions which cluster in similar locations in parameter space and objective space - performed consistently well for several validation periods.
机译：通过生成通常称为帕累托最优集的几种竞争解决方案，多目标遗传算法正越来越多地用于校准水文模型。帕累托最优集包括在校准阶段的非支配溶液，但是通常不知道在校准阶段是全部还是仅一部分非支配溶液在验证阶段仍处于非支配状态，实际上，用户希望知道在校准和验证阶段仍不占主导地位的解决方案（及其相关属性）。本研究通过开发模型表征框架（MCF），研究了帕累托最优集的鲁棒性。 MCF使用聚类分析来检查参数空间和目标空间中解的分布，并使用条件概率来组合两个空间中解的分布之间的联系。已经说明了MCF的校准输出，该校准输出是通过应用非支配排序遗传算法-ll来校准安大略省南部Fairchild Creek流域中用于水流的土壤和水评估工具的。我们的结果表明，并非在校准阶段发现的所有非支配解决方案在不同的验证期间都具有相同的性能。 MCF说明了健壮的解决方案（非主导解决方案，它们聚集在参数空间和目标空间的相似位置）在多个验证期内均表现良好。

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