基于自适应差分进化算法的水稻物候期预测模型参数自动校正

进化算法在作物模型参数校准领域已有广泛应用。由于作物模型的结构包括多组常微分方程，具有非线性、不连续、多峰值特点，因此针对作物模型特点选择合适的进化算法尤为重要。同时，进化算法自身参数对算法性能有较大影响，这些参数选择往往靠经验得出，增加了优化算法在模型参数校准过程中的不确定性。该文针对进化算法应用到作物物候期模型参数校准过程中存在着算法选择和算法参数不确定性问题，以水稻RiceGrow物候期模型为应用对象，分析比较了3类进化算法应用的精度、收敛速度以及稳定鲁棒性。比较的进化算法包括差分进化系列算法（标准差分进化算法和自适应控制参数改进差分进化算法），协同进化遗传算法系列（个体优势遗传算法、M-精英协同进化算法）以及粒子群算法系列（标准粒子群算法、基于自主学习和精英群的多子群粒子群算法）。研究利用武育粳、雪花粘等5个品种在江苏宜兴、兴化和广东高要等不同生态点的多年田间试验资料展开量化分析。结果表明：1）利用自适应控制参数改进差分进化算法校准水稻物候期模型的品种参数准确性较高，算法自身参数易于确定。物候期模型校准以后在拔节期、抽穗期、成熟期的RMSE为1.7～4.6 d、NRMSE为1.8%～5.8%、MAD 为 1.4～3.3 d、R2为 0.977～0.997，比GA系列平均分别小0.634 d、0.608%、0.453 d、0.09%，比PSO系列平均小1.399 d、1.35%、1.039 d、0.23%。 2）自适应控制参数改进差分进化算法在水稻物候期模型参数校准问题上表现出良好的收敛速度及稳定鲁棒性。重复校准试验100次的目标函数标准偏差趋近于0，每次校准得到的品种参数值标准偏差较其他算法最小。在达到同样精准度的情况下，比标准差分算法收敛速度平均快117代，适用于实际应用实践。

Automatic calibration of parameters for crop phenological predicting model based on adaptive differential evolution algorithm

Abstract: Evolutionary algorithms have been widely used in the field of crop model parameter calibration. Since the crop model structure includes multiple sets of ordinary differential equations with nonlinear, discontinuous and multi-peak characteristics, it is especially important to select appropriate evolutionary algorithms based on crop model characteristics. At the same time, the parameters of the evolutionary algorithm have a great influence on the performance of the algorithm. These parameter selections are often based on experience, which increases the uncertainty of the optimization algorithm in the model parameters calibration process . This article was targeted on problem of selection and parameter uncertainty of the evolutionary algorithm applied to the crop phenological model parameter correction quasi-process . In this paper, the rice RiceGrow phenological predicting model was applied to compare the correction accuracy, convergence speed and stability robustness of 3-tyepe evolutionary algorithms in application. Comparison algorithms included differential evolution series algorithms (standard differential evolution algorithm(DE) and adaptive control parameters modified differential evolution algorithm(ACPMDE)), co-evolutionary genetic algorithm series (individual advantage genetic algorithm, M-elite co-evolution algorithm) and particle swarm optimization series (standard particle swarm optimization, multi-subgroup particle swarm optimization based on autonomous learning and elite groups). Using the multi-year field experiment data of 5 species of Wuyujing and Xuehuanian in different ecological points such as Yixing, Xinghua in Jiangsu province and Gaoyao in Guangdong province, the accuracy, convergence rate and stability robustness of the automatic correction of the model parameters was quantitatively analyzed with different evolutionary algorithms. The results showed that: 1) the correction accuracy of the model parameters of the model with adaptive control parameters modified differential evolution algorithm was higher than other algorithms, and the parameters of the algorithm were easier to determine. The cross-probability factor and scaling factor of the algorithm were adaptively adjusted with the individual fitness function during the evolution process, in which the dependence of the standard DE algorithm parameters on the optimization problem was avoided and the robustness of the algorithm was improved. The RMSE(root mean square error) between the predicted and observed values of jointing, heading and maturity stage was 1.7-4.6 days; The normalized root mean spuare error was 1.8%-5.8%; MAD(mean absolute difference) was 1.4-3.3 days, and determination coefficient R2 was 0.977-0.997, which was 0.634 days, 0.608%,0.453 days, 0.09% smaller than co-evolutionary genetic algorithm series, 1.399 days, 1.35%, 1.039 days,0.23% smaller than PSO series. 2) Applying adaptive control parameters to improve the differential evolution algorithm showed good convergence speed and stable robustness on the phenomenological model parameter correction. The standard deviation of the objective function value of 100 times repeated calibration experiment approached 0, and the standard deviation of the variety parameter values obtained by each correction was also smaller than other algorithms. With the same accuracy, the adaptive control parameter modified differential evolution algorithm converges 117 iterations faster than the standard differential evolution algorithm. The research showed that the automatic correction quasi-method of crop phenological model parameters based on adaptive control parameters modified differential evolution algorithm had good accuracy and stability and was suitable for practical application.