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分类和回归模型辅助求解高计算代价优化问题的差分演化算法设计与分析

Classification- and Regression-Assisted Differential Evolution for Computationally Expensive Problems

  • 摘要: 差分演化(Differential Evolution, 简称DE)是一种被广泛使用并且高效的演化算法。然而, DE通常需要大量的适应度评估来定位一个临近最优的解, 而高计算代价问题的每一次适应度评估都是非常耗时的, 这点限制了它在高计算代价问题中的应用。近年来, 越来越多的研究集中在整合代理模型到演化算法中, 从而减轻它在高计算代价问题上的计算负担。不过, 以DE作为基本算法的研究却很少。而且, 尽管不同类型的代理模型, 即回归模型、排序模型以及分类模型都被单独整合到演化算法中过, 没有研究表明哪一种类型的模型表现最优。通过分析DE的特殊的选择机制, 本文提出了一种将回归模型和分类模型结合起来共同辅助DE的方法, 即回归和分类模型辅助的差分演化算法(Classification- and Regression-Assisted DE, 简称CRADE)。对16个经典测试函数的仿真结果表明, 不论是与分类或者回归单独协助的DE相比, 还是与当前最好的三个DE的变体相比, CRADE算法在有限的计算预算情况下都获得质量更高的解。

     

    Abstract: Differential Evolution (DE) has been well accepted as an effective evolutionary optimization technique. However, it usually involves a large number of fltness evaluations to obtain a satisfactory solution. This disadvantage severely restricts its application to computationally expensive problems, for which a single fltness evaluation can be highly time-consuming. In the past decade, a lot of investigations have been conducted to incorporate a surrogate model into an evolutionary algorithm (EA) to alleviate its computational burden in this scenario. However, only limited work was devoted to DE. More importantly, although various types of surrogate models, such as regression, ranking, and classiflcation models, have been investigated separately, none of them consistently outperforms others. In this paper, we propose to construct a surrogate model by combining both regression and classiflcation techniques. It is shown that due to the speciflc selection strategy of DE, a synergy can be established between these two types of models, and leads to a surrogate model that is more appropriate for DE. A novel surrogate model-assisted DE, named Classiflcation-and Regression-Assisted DE (CRADE) is proposed on this basis. Experimental studies are carried out on a set of 16 benchmark functions, and CRADE has shown signiflcant superiority over DE-assisted with only regression or classiflcation models. Further comparison to three state-of-the-art DE variants, i.e., DE with global and local neighborhoods (DEGL), JADE, and composite DE (CoDE), also demonstrates the superiority of CRADE.

     

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