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

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.