多作物种植结构和灌溉水量优化模型及算法研究

Optimized model and algorithm for multi-crop planting structures and irrigation amount

  • 摘要: 在综合考虑作物灌溉水量、种植面积、水分生产函数、产量反应系数、水分敏感指数等因素基础上, 以实现灌区作物总产量最大为目标函数, 建立了多作物种植结构和灌溉水量优化分解协调模型, 设计了改进实码遗传算法与分解协调迭代算法相结合的模型求解算法, 并利用中国科学院盐亭紫色土农业生态试验站多年试验数据, 运用上述模型和算法对玉米、小麦联合种植的种植结构、灌溉水量以及玉米、小麦灌溉制度进行了优化计算。结果表明: 产量反应系数大的作物分配的灌溉水量和种植面积大, 且随灌溉水量增加其增产速度越快; 当作物某些生育阶段灌水前的潜在腾发量与可供利用水量的差值相差不大时, 水分敏感指数大的作物生育阶段获得灌溉水量较多, 反之, 即使水分敏感指数大的作物生育阶段也有可能分配不到更多的灌溉水量。这一结果与作物产量反应系数的几何意识、边际效益递减规律等理论以及节水增收初衷相符合, 充分说明模型在实现灌区有限水资源在多作物间和各作物生育阶段优化分配的同时, 实现了灌区多作物种植结构优化, 具有较强推广价值。改进实码遗传算法克服了传统实码遗传算法计算精度低、易早熟、求解结果不能严格满足等式约束等缺陷, 能够搜索到严格满足约束条件的模型最优解, 表明该改进实码遗传算法在解决这类包含等式和不等式约束的最优化问题上具有一定应用价值。分解协调迭代算法能使模型在允许迭代误差范围内收敛, 能够获得使模型整体效果较为理想的最优解, 表明分解协调迭代算法在求解复杂大系统优化问题上具有很好的应用前景。

     

    Abstract: Accompanying the increasing consumption of industrial and city water, irrigation water has been reduced due to fast growing national economy and urbanization. This has led to a strong conflict between supply and demand of irrigation water. The fraction of irrigation water in society's total water consumption has reduced from 80% in the 1970s to 60% at the present state. Discussing the distribution of limited water resources among different crops and crop growth stages in an optimal way that maximizes yields or profits has been particularly critical for alleviating irrigation water resources shortage. In this paper, a decomposition and coordination model was set up based on maximum total yield of crops in irrigation areas. The aim of the model was to simultaneously attain optimal allocation of planting structures and irrigation amount in multi-crops system at different crop growth stages. The key related factors considered during the model setting up included irrigation amoung, planting area, water production function, productivity reactivity coefficient and water sensitivity index. The model was driven by an algorithm that combined improved real coding genetic algorithm with decomposing and coordinating iterative algorithm. The model algorithm was used to optimize the planting structures and irrigation amount of mixed planting of corn and wheat. This in turn optimized irrigation schemes for corn and wheat using multi-year experimental data from the Yanting Purple Soil Agro-Ecological Experimental Station of Chinese Academy of Sciences. The results showed that higher productivity reactivity coefficient meant faster yield increment with increased irrigation amount. The crops with higher high productivity reactivity coefficient shared greater irrigation amount and planting area. Higher water sensitivity index implied more irrigation amount of crops at different growth stages when potential evapotranspiration was close to available usable water. On the contrary, it was possible that crops with high water sensitivity index had insufficient irrigation amount. The results were consistent with the theories of geometric meaning of crop productivity reactivity coefficient, the law of diminishing marginal utility, and the notion of increased income from water saving. The results further illustrated that the model was strongly practical not only in optimation of multi-crop planting structures, but also in optimal distribution of limited water resources among different crops and at different growth stages. The improved real coding genetic algorithm overcame the shortfalls of the traditional real coding genetic algorithm such as low accuracy, easy early maturing, inconsistent equality constraint requirements, and it could find optimal solution within a short time. This proved that the improved real coding genetic algorithm had practical application value for solving problems of equality and inequality constraints due to its high optimum solution capability that fully satisfied equality constraint requirements. The decomposing and coordinating iterative algorithm attained model convergence within the allowable range of iterative error under different irrigation amounts. It attained optimal solution with a satisfactory overall effect of the model. The study showed that the decomposing and coordinating iterative algorithm had comparative advantage in solving complex large-scale optimization problems.

     

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