Optimize the Irrigation and Fertilizer Schedules by Combining DSSAT and GA

As one of the main food crops in the world, the yield of maize directly affects the food security of the world. The optimization of irrigation and fertilizer schedules is also one of the hot issues in the world. In this paper, the genetic algorithm (GA) and DSSAT crop model were combined to provide theoretical basis for the optimization of irrigation and fertilizer schedules of maize in China. On the basis of eld experimental data in previous references, the model was calibrated and veried, and get a well simulation result with RMSE ranged from 0.262 to 0.580 Mg/ha. After that, GA and DSSAT were run to obtain the optimized irrigation and fertilizer schedules. Compared with the results of previous references, the new optimization schedules can improve the yield (1.9~2.6%) and economic benets (7.3~8.9%). It is proved that this method has a good optimization effect, and the method also has a wide range of research prospects.


Introduction
As one of the main food crops in the world, the yield of maize directly affects the food security of the world (Gao et al. 2019). As one of the main producing countries, China has a large area of maize planting, but the average yield of maize is far less than that of the United States (Zheng et al. 2020). The main reason is that there are many de ciencies in the cultivation mode and management system of maize (Hu et al. 2020). Among them, poor irrigation and fertilizer schedules can't fully play the potential of maize production, while the traditional excessive irrigation and fertilization schedules will cause waste of water quality and environmental pollution (Zhao et  . But the limited number of experimental groups will make the solution fall into local optimal. This can not only save water and save fertilizer, but also the yield of crops can't be guaranteed (Chen et al. 2019;Zou et al. 2019). Therefore, an optimal solution of irrigation and fertilizer schedules is needed to solve this kind of nonlinear problems. As an excellent global optimization algorithm, genetic algorithm (GA) can nd the optimal solution of water and fertilizer system only with a given range of water and fertilizer amount, which is very suitable for solving this kind of problem (Ferreiro et al. 2016;Huo et al. 2020). In this paper, the DSSAT model is veri ed by the data of previous references. Under the condition of high simulation accuracy, the irrigation and fertilizer schedules are optimized by combining GA and DSSAT, and analysis the bene ts of simulation results to determine the effect of the optimized model. This optimized model can provide theoretical reference for optimizing water and fertilizer system in maize production.

Data sources
The data for DSSAT model calibration and validation are taken from Zou et al.  The calibration and veri cation data are shown in the table 2 and 3. The naming method of processing group is the same as that in the previous references. Because both literatures have optimized water and fertilizer schedules, which can be used for us to compare the optimized results. In table 2and 3, CI presents conventional irrigation and RI presents half-reduced conventional irrigation, CRN presents Controlled-release urea, N presents conventional urea. I presents irrigation amount and I60 presents 60% of the ETc, F presents N amount.  I90F60  245  60  30  30  I100F60  290  60  30  30   I90F120  306  120  60  60  I100F120  370  120  60  60   I90F180  368  180  90  90  I100F180  450  180  90  90   I90F240  430  240  120  120  I100F240  530  240  120  120   I105F60  245  60  30  30  I120F60  290  60  30  30   I105F120  306  120  60  60  I120F120  370  120  60  60   I105F180  368  180  90  90  I120F180  450  180  90  90   I105F240  430  240  120  120  I120F240  530  240  120  120   Table 3 The calibration and validation data from Li  Among them, irrigation is carried out when the soil moisture is suitable for the lower limit of soil moisture (70% of eld capacity), irrigation amount design percentage of evapotranspiration. Phosphorus and potassium fertilizer are applied to the soil in the form of base fertilizer at one time before planting, and CRN was applied once as basal fertilizer before planting maize, and conventional urea was applied twice: once before planting the maize seeds (50% of the total) and again at V12 (50% of the total) in Li's paper. Four fertilization levels of N-P 2 O 5 -K 2 O (kg/ha) were applied as low, medium, medium high and normal high fertilization rates, 20 % of fertilizers at the seeding stage, 30 % at the six leaf collar stage, 30 % at the tasseling stage and 20 % at the grain lling stage in Zou's paper.

GA
GA is a global optimization algorithm based on the survival of the ttest. GA encodes the solution of the problem as chromosome, and then selects the individuals with high tness value according to the probability distribution of tness function value by creating tness function, and then exchanges chromosome information in the population through selection, crossover and mutation, and nally produces the chromosome (optimal solution) that meets the optimization goal. The main steps of GA include: (1) Generating initial population In this study, the population number is 10. To identify the water and fertilizer regimes, the string length of fertilization and irrigation factor encoded by binary code is 6. The range of fertilizer and irrigation amount is shown in Table 4. Table 4 Range of irrigation and fertilizer amount Irrigation (mm/ha) N fertilizer (kg/ha) P fertilizer (kg/ha) K fertilizer (kg/ha) Range 0-1000 0-500 0-500 0-500 (2) Calculating each tness The tness function of GA used in this paper is mainly to maximize the bene t, and the formula is as follow: where Y r denotes the pro t from the yield; F r is the cost of the amount of fertilizer; W r is the cost of the amount of water, C r is the other cost like seed, land use and machines.
(3) Selection This paper uses roulette selection, which is a playback random sampling method.
(4) Crossover; In this paper, single-point crossover is used, and the crossover probability is 0.9 in this paper.

(5) Mutation;
In this paper, we use gene mutation, and the mutation coe cient is 0.1 in this paper. (2) Soil data: Soil texture, bulk density, soil N, soil organic carbon and water capacity for each soil layer (soil data from table 1); (3) Management data: Irrigation schedule, planting method, fertilizer schedule, planting and harvest date (section 2.1).

The combination of GA and DSSAT
The advantage of GA is that the initial irrigation and fertilization schedules can be generated randomly, and then it can be substituted into DSSAT to solve the yield. After DSSAT obtains the accurate yield, it can be substituted into equation (1) to calculate the tness, repeatedly calculate the tness, selection, crossover and mutation until the genetic algebra is reached, then output result is obtained. The owchart of GA and DSSAT is shown in Fig.2.

Data analysis
To verify whether the model results perform well, the root mean square error (RMSE), mean absolute error (MAE), average root mean square error (nRMSE), and Nash-Sutcliffe e ciency coe cient (NSE) are adopted. Error analysis is conducted to determine the differences between the assessed and measured data. The RMSE, MAE, nMSRE and NSE are calculated as follows: where N denotes the number of lateral measuring points and X and Y represent the calculated and measured values, respectively.

Calibration and validation of the model
The climatic conditions, soil conditions and management conditions for DSSAT are the same as those described in section 2.1 and 2.2. Firstly, we need to solve the six parameters of maize in DSSAT model according to the calibration data. The solution method is solved by applying GLUE, and the results are shown in the table 5 (Liu et al. 2013). The GLUE Coe cient Estimator combining with trial-and-error method was used to estimate the genetic parameters.

Optimal model application
On the basis of proving the accuracy of the model, we use our combined model to solve the optimal water and fertilizer regime. In order to make a better comparison with the previous literatures, the frequency, time and proportion of irrigation and fertilization remain unchanged, we only change the total amount. The other conditions are the same as those described in the literatures. The initial set of total population number is 10, population code length is 6, genetic algebra is 200, selection method roulette, crossover method is single-point with 0.9 of crossover probability, mutation method is gene mutation with 0.1 of mutation coe cient. The initial range of irrigation and fertilization is shown in the table 4. The results of optimization are shown in the gures 3 and 4. The simulation results are completed in the 76th and 74th generations respectively, and the results are the best and keep stable. The optimal economic bene ts are 19533 and 11794 CNY respectively. The corresponding optimization results are shown in the table 7. It can be found that our optimization results are higher than the original optimization results in previous literatures. . We get higher maize yield by adjusting different water and fertilizer systems. In Zou's paper, the experimental data are used to t the three-dimensional surface between irrigation amount, fertilizer amount and economic bene t. Then the formula of the surface is obtained by the three-dimensional surface, and nally the optimal yield is obtained through solution of equation. However, we know that the coupling problem of irrigation and fertilizer schedules is usually not a linear optimization problem, and the surface of irrigation amount, fertilizer amount and economic bene ts is usually not smooth, but there are many peaks and valleys (Gheysari et al. 2009;Li et al. 2010). Therefore, if the smooth surface is used to solve this kind of problem, it is not accurate enough to solve this kind of problem by combining the optimization algorithm and crop model (Islam et al. 2012;Biau et al. 2012). So the global solution method in this paper can obtain better results. At the same time, Zou uses xed proportion compound fertilizer, so the ratio of N, P and K is not changed. In order to compare with the previous results, the ratio of N, P, K used by Zou is also unchanged. However, the total amount of P and K also has interaction with water and fertilizer, and the change of the ratio of N, N and potassium (K) may increase the yield of maize (Xin et al. 2017;Martineauet al. 2017).
Li's paper showed that under the condition of su cient irrigation, the appropriate amount of N fertilizer was 210 kg/ha, and K and N fertilizer were applied to the eld at one time. The optimal conditions given by us are that the irrigation water is less than the su cient irrigation water, and the fertilizer amount of N, P and K is also lower than that of Li as sometimes full irrigation doesn't make the most use rate of the fertilizer ( The results of optimization are mainly re ected in the yield and bene t. Compared with Zou's scheme, our output increased by 1.9%, and the bene t increased by 8.9%. Compared with Li's scheme, our output increased by 2.6% and the bene t increased by 7.3%. According to the proportion of bene t increase, our optimization method has high application value. The optimization method in this paper is not only suitable for conventional irrigation, but also suitable for

Conclusions
In this paper, on the basis of previous experimental data validation, optimal irrigation and fertilizer schedules are obtained by combining GA and DSSAT. The main research results are as follows: (1) The combination of the GA and crop model can obtain the optimal irrigation and fertilizer schedules of maize both in traditional irrigation and drip irrigation, and the yield and economic bene ts are improved 1.9~2.6%, 7.3~8.9% respectively compared with the original optimization scheme.
(2) The optimization method in this paper is not only suitable for conventional irrigation, but also suitable for drip irrigation. At the same time, this method is easier to popularize, which can provide theoretical reference for the decision of water and fertilizer optimization strategy of maize in the world. Figure 1 The study area of this paper Figure 2 The owchart of DSSAT and the GA Figure 3 The optimized results of Zou