Water and fertilizer integrated control strategy recommendation method and system based on multi-objective optimization

Abstract

This invention relates to a method and system for recommending integrated water and fertilizer control strategies based on multi-objective optimization. Multiple water and fertilizer experimental treatments are set up, and irrigation amount, nitrogen, phosphorus, and potassium application rates, yield, and auxiliary parameters are collected to form water and fertilizer samples. Water and fertilizer vectors are constructed and their relative yields are calculated. After outlier cleanup and unit standardization, a sample set is established and water and fertilizer limits are retained. An effective water-nitrogen coupling enhancement feature in the root zone is constructed, and an improved Maternal kernel function Gaussian process surrogate model with fractal dimension scaling and threshold penalty is introduced. A multi-objective function is built based on its posterior prediction. Using this surrogate model as a fast evaluator, multi-objective continuous ant colony optimization is employed. Through population initialization, elite profile maintenance, covariance matrix sampling, and pheromone updates with no stress maintenance days constraint, a Pareto front strategy set is iteratively obtained. Finally, the model and optimization algorithm are deployed to the field system, outputting executable water and fertilizer prescriptions cycle by cycle. This invention can accurately adapt to field water and fertilizer needs, improving quality, efficiency, and saving water and fertilizer.

Description

Technical Field

[0001] This invention relates to the field of integrated water and fertilizer management technology, and in particular to a method and system for recommending integrated water and fertilizer control strategies based on multi-objective optimization. Background Technology

[0002] In modern intensive agriculture, the core challenge of integrated water and fertilizer management lies in how to achieve synergistic optimization of yield and efficiency under resource constraints. Traditional decision-making methods often rely on empirical formulas or single-objective yield maximization models, which struggle to accurately characterize the complex nonlinear interactions between irrigation, nitrogen, phosphorus, and potassium application rates, and generally neglect the difference between "theoretical input" and "actual available input in the root zone."

[0003] Existing technologies objectively suffer from the following shortcomings: Traditional surrogate models directly use the original water and fertilizer inputs as inputs, failing to distinguish between the actual water retention capacity in the root zone and the nitrogen uptake saturation level. This easily leads to the erroneous fitting of ineffective irrigation exceeding soil water storage capacity or excessive nitrogen application exceeding crop uptake capacity as yield-increasing factors, resulting in model prediction bias. Furthermore, commonly used kernel functions employ a uniform length scale for all input dimensions, failing to reflect the response differences between gradual changes in irrigation volume and critical abrupt changes in phosphorus and potassium. This results in insufficient local fitting accuracy when facing nonlinear interactions of different nutrient factors, making it difficult to characterize the true yield response. The sampling distribution lacks directional guidance during continuous optimization, relying mostly on isotropic random perturbations. This results in a large amount of computation being consumed in flat areas with low yield potential. Furthermore, it fails to consider the continuous differences in the number of days that water and fertilizer schemes can maintain without stress in the root zone, making it easy to retain schemes that appear excellent in the short term but quickly fall into the risk of water shortage. Water and fertilizer decisions are generally based on maximizing yield as a single objective, without considering water and fertilizer utilization efficiency as an independent objective for multi-objective trade-offs. This leads to output schemes that cannot reflect the objective contradiction between high yield and high efficiency, making it difficult for managers to obtain differentiated decision support based on actual resource constraints and operational preferences.

[0004] Therefore, this invention proposes a method and system for recommending integrated water and fertilizer control strategies based on multi-objective optimization to solve the above problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method and system for recommending integrated water and fertilizer control strategies based on multi-objective optimization. This invention can accurately adapt to field water and fertilizer needs, improve quality and efficiency, save water and fertilizer, and enhance the real-time nature and applicability of decision-making.

[0006] On the one hand, the technical solution of this invention to solve the technical problem is a method for recommending integrated water and fertilizer control strategies based on multi-objective optimization, including the following steps: S1. Arrange multiple water and fertilizer treatments, record irrigation amount, nitrogen, phosphorus and potassium application amount, yield and auxiliary parameters to obtain water and fertilizer samples, organize the data of each sample into water and fertilizer vectors, convert the relative yield, clean up outliers and unify units to construct water and fertilizer sample set, and save water and fertilizer limits at the same time. S2. Construct effective water-nitrogen coupling enhancement features in the root zone based on water-fertilizer vectors, use them as input, and then establish an improved Matern kernel function Gaussian process surrogate model with fractal scale and threshold penalty. Construct a multi-objective function from the posterior prediction of the Gaussian process surrogate model. S3. Using the Gaussian process surrogate model as a fast evaluator, multi-objective continuous ant colony optimization is performed. First, the ant population is initialized and an elite profile set is established. Then, the direction-guided sampling covariance matrix is ​​constructed and new candidate solutions are generated. Then, pheromone evaporation and incremental updates based on the number of days of maintenance without stress are executed. After iterative updates, the final Pareto front strategy set is output. S4. The trained Gaussian process agent model and the constructed multi-objective continuous ant colony optimization method are deployed in the field water and fertilizer integrated decision system, and an executable water and fertilizer prescription is output in each irrigation decision cycle.

[0007] S1 is as follows: Multiple water and fertilizer treatment combinations were set up in the field test plots corresponding to the target crop, and the amount of irrigation per treatment combination was recorded. Nitrogen application rate Phosphorus application rate Potassium application rate And record the corresponding yield after harvest; For each experimental sample, the auxiliary state parameters at the time of sample formation were recorded. These auxiliary state parameters included field capacity. Soil volumetric moisture content at the time of decision-making Depth of the main active layer of the root system Effective rainfall during the decision-making cycle , reference crop evapotranspiration Crop coefficient at the current growth stage The maximum number of days of stress-free maintenance allowed during the current reproductive stage. Recommended nitrogen application rate for the current growth stage ; The single irrigation amount for each sample Nitrogen application rate Phosphorus application rate Potassium application rate Organize the data into the original water and fertilizer combination vector, and convert the measured yield of each sample into a relative yield; Outlier cleanup and unit standardization were performed on all samples. Samples with obvious missing irrigation, fertilizer, or yield data were deleted. Time alignment was performed on soil moisture content and meteorological data collected by sensors. Abnormal records outside the agronomic allowable range were manually reviewed to obtain the water and fertilizer sample set. At the same time, feasible upper and lower limits for irrigation, nitrogen, phosphorus and potassium application rates should be maintained.

[0008] S2 is as follows: S2.1 Based on the water-fertilizer combination vector and auxiliary state parameters of each sample, calculate the average effective water coefficient and nitrogen availability factor of the root zone to obtain the effective water-nitrogen coupling index of the root zone. Then, concatenate the effective water-nitrogen coupling index of the root zone to the water-fertilizer combination vector to form an enhanced feature vector. S2.2 Calculate the difference between irrigation amount, nitrogen application amount, phosphorus application amount, potassium application amount and effective water-nitrogen coupling index in the root zone for any two enhanced feature vectors. When the difference exceeds the preset threshold, add local distance penalty to establish an improved Matrn kernel function and train a Gaussian process surrogate model on it. S2.3 Extract the posterior predicted mean from the Gaussian process surrogate model, and construct the relative yield objective function and the water and fertilizer efficiency objective function accordingly.

[0009] The specific calculation process of the enhanced eigenvector in S2 is as follows: Read the water and fertilizer combination vector of a single sample and the auxiliary state parameters corresponding to that sample. Based on the current water storage capacity of the soil and the external water supply, calculate the effective water volume in the root zone. First, subtract the current soil volumetric water content from the field water holding capacity, and then multiply by the depth of the main active layer of the root system to calculate the maximum water replenishment depth in the root zone. Then calculate the total water supply within the decision period. Take the smaller value between the maximum water replenishment depth in the root zone and the total water supply to obtain the effective water volume in the root zone. Finally, add it to the single irrigation amount to obtain the total water supply within the decision period. The effective root zone water volume is then divided by the potential transpiration intensity at the current stage to obtain the theoretical number of days without stress. The potential transpiration intensity is represented by the product of the reference crop evapotranspiration and the crop coefficient at the current growth stage. The theoretical number of days without stress is then divided by the maximum allowable number of days without stress at the current growth stage, limiting the result to... arrive Between these values, the root zone average effective water coefficient is obtained; Next, the ratio of the applied nitrogen amount to the recommended nitrogen amount is substituted into the saturated mapping function to obtain the nitrogen availability factor; the average effective water coefficient of the root zone is multiplied by the nitrogen availability factor to obtain the effective water-nitrogen coupling index of the root zone; finally, the original water-fertilizer combination vector is concatenated with the effective water-nitrogen coupling index of the root zone to form an enhanced feature vector.

[0010] The objective function in S2 is constructed as follows: The differences in each dimension of any two enhanced feature vectors are normalized using independent length scales. Then, the base anisotropy distance is calculated, and a threshold is set. If the base anisotropy distances for irrigation, phosphorus, and potassium application exceed the threshold, a threshold penalty is added. Then, the Matrn algorithm is applied. The kernel function calculates the covariance between samples, obtaining the value at the corresponding position in the kernel function matrix; then, a covariance matrix is ​​constructed based on the kernel function values ​​between all samples, and observation noise variance and small jitter terms are added to the diagonal of the covariance matrix; finally, all hyperparameters of the improved Matern kernel function are trained. For any candidate water and fertilizer combination vector, combined with the soil moisture and meteorological conditions of the current decision-making plot, the corresponding enhanced feature vector is obtained through the S2.1 operation. The kernel function value between the candidate enhanced feature vector and the enhanced feature vector of all samples is calculated to form a covariance vector. Then, combined with the covariance matrix obtained in the training phase, the posterior prediction mean and posterior prediction variance of the candidate scheme are obtained according to the Gaussian process regression posterior prediction formula. The posterior prediction mean is used as the first objective function, namely the relative yield objective function. The posterior prediction mean is then combined with the normalized resource input penalty term to obtain the second objective function, namely the water and fertilizer comprehensive efficiency objective function. The relative yield objective function and the water and fertilizer comprehensive efficiency objective function are used as evaluation indicators for subsequent optimization.

[0011] The initialization of the ant colony and the establishment of the elite profile set in S3 are as follows: Within the feasible range of irrigation, nitrogen, phosphorus, and potassium application rates, an initial ant population was generated using Latin hypercube sampling. For each individual ant, the evaluation process in step S2 was called to obtain the relative yield objective function value and the water and fertilizer integrated efficiency objective function value. Then, a fast non-dominated sort was performed on all individual ants to obtain the non-dominated hierarchy. Next, the effective water and nitrogen coupling index of the root zone under the current plot conditions was recalculated for each individual ant, and a root zone water and nitrogen stress perception factor was constructed based on this. The non-dominated hierarchy was then combined with the root zone water and nitrogen stress perception factor to obtain the initial heuristic weights. Finally, a set of high-quality individuals with controlled size was retained based on the non-dominated hierarchy and crowding to form the current elite archive set.

[0012] The calculation process for new candidate solutions, pheromone evaporation, and incremental updates in S3 is as follows: A guide individual is randomly selected from the elite archive set according to the current heuristic weights. The gradient direction of the relative output objective function is estimated at the guide individual. The basic sampling scale is then determined based on the overall dispersion of the elite archive set. The gradient direction is then superimposed on the basic diagonal covariance matrix to construct the directional guided sampling covariance matrix. Finally, new candidate solutions are obtained by sampling from the four-dimensional multivariate Gaussian distribution with the guide individual as the mean and the directional guided sampling covariance matrix as the covariance. For each individual in the elite archive set, the effective water volume in the root zone and the theoretical number of days of no-stress maintenance are calculated under the current plot conditions. Then, the pheromone volatilization coefficient is calculated based on the theoretical number of days of no-stress maintenance. Pheromones are then volatilized for all individuals in the elite archive set. Next, pheromone increments are allocated to newly generated candidate solutions. Specifically, the new candidate solutions are merged with the individuals in the current elite archive set, re-evaluated, and sorted. If a new candidate solution enters a new non-dominated frontier, a fixed increment is directly allocated. If a new candidate solution, although not entering a non-dominated frontier, improves at least one of the relative yield objective function or water and fertilizer efficiency objective function relative to its guiding individual by more than a threshold, a small increment is allocated. Finally, the intermediate weights after volatilization are merged with the reward increments of the new candidate solutions and re-normalized. The elite archive set is then updated according to the principle of non-dominated level priority and crowding degree second priority.

[0013] The calculation process of the final Pareto frontier policy set in S3 is as follows: Using the updated elite archive set as the basis for guiding individual selection in the next round, the calculation process of new candidate solutions, pheromone evaporation and incremental updates is repeated. In each iteration, new candidate solutions are generated, the objective function is evaluated, pheromone evaporation and rewards are executed, and the elite archive set is updated. When the maximum number of iterations or the maximum number of proxy model calls is reached, the iteration stops. All non-dominated candidate solutions are extracted from the elite archive set at the termination time to form the final Pareto front strategy set.

[0014] S4 is as follows: Real-time field status data is collected at the current irrigation decision point. Using the current field status data as input and combined with the auxiliary status parameters of the plot, an enhanced feature vector for the current decision point is constructed. Steps S2 and S3 are called to generate the final Pareto front strategy set corresponding to the current plot. Then, the final Pareto front strategy set is screened a second time according to the business objectives or management constraints to output the recommended water and fertilizer prescription. When entering the next irrigation decision cycle, the latest field status data is read again and the aforementioned steps are repeated to achieve dynamically updated water and fertilizer prescription output.

[0015] On the other hand, the present invention also provides a water and fertilizer integration control strategy recommendation system based on multi-objective optimization, including a module for executing processing instructions for each step in a water and fertilizer integration control strategy recommendation method based on multi-objective optimization, comprising: Sample collection and processing module: used to arrange multiple sets of water and fertilizer treatments, record relevant parameters, organize water and fertilizer vectors, convert relative yields, clean up outliers and unify units to build a sample set, and save water and fertilizer limits; Feature construction and model training module: used to construct effective water-nitrogen coupling enhancement features in the root region, establish an improved Matern kernel function Gaussian process surrogate model and construct a multi-objective function; Multi-objective optimization module: used to initialize ant population, establish elite profile set, construct sampling covariance matrix to generate candidate solutions, update pheromones and iteratively output Pareto front policy set; Decision Deployment Module: Used to deploy models and optimization methods, collect real-time data in each irrigation decision cycle, output executable water and fertilizer prescriptions and update them dynamically.

[0016] The effects described in the invention are merely those of the embodiments, and not all the effects of the invention. The above technical solutions have the following advantages or beneficial effects: This invention discloses a method and system for recommending integrated water and fertilizer control strategies based on multi-objective optimization. It concatenates the effective water-nitrogen coupling index in the root zone into the original water and fertilizer input vector to form an enhanced feature vector. This allows the Gaussian process surrogate model to simultaneously learn the theoretical input amount and the actual absorption state of the crop root zone, thereby avoiding misjudging ineffective irrigation or excessive fertilization as effective yield-increasing signals. This significantly improves the rationality of yield prediction under limited sample conditions. The Gaussian process kernel function is designed with fractal dimensions, and cross-domain threshold penalties are introduced for irrigation, phosphorus, and potassium application rates. This allows the model to retain the overall smooth response of irrigation and nitrogen while also sensitively capturing local abrupt changes when phosphorus and potassium cross critical values, thus enabling the model to adapt to limited experimental samples. This approach can also fit a local response surface that better conforms to agronomic laws. In multi-objective continuous ant colony optimization, the local gradient estimation based on the Gaussian process surrogate model constructs a directional sampling covariance matrix, allowing new solutions to expand directionally along the high-yield gradient direction. At the same time, the number of days without stress is introduced into the pheromone volatilization mechanism, causing the weight of water and fertilizer schemes with poor sustainability to decay rapidly, thereby improving the search efficiency for high-yield and sustainable schemes. A dual objective function of relative yield target and water and fertilizer comprehensive efficiency is constructed, and a set of non-dominated water and fertilizer schemes are output in the form of Pareto front, allowing managers to flexibly choose according to different management objectives such as high yield priority, water conservation priority, or fertilizer reduction priority, overcoming the problem that traditional single optimal prescriptions cannot take into account the conflict of multiple objectives. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0018] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0019] Figure 2 This is a saturation response curve for nitrogen availability.

[0020] Figure 3 This is a surface plot of the posterior predicted mean.

[0021] Figure 4 This is a posterior prediction variance surface plot.

[0022] Figure 5 Optimize the Pareto front plot for multiple objectives.

[0023] Figure 6 Figure (a) shows the evolution of the elite archive set, where Figure (b) shows the result of the 5th iteration, and Figure (c) shows the result of the 10th iteration. Detailed Implementation

[0024] To clearly illustrate the technical features of this solution, the invention will be described in detail below through specific implementation methods and in conjunction with the accompanying drawings.

[0025] Example 1 A method for recommending integrated water and fertilizer management strategies based on multi-objective optimization includes the following steps: S1. Arrange multiple water and fertilizer treatments, record irrigation amount, nitrogen, phosphorus and potassium application amount, yield and auxiliary parameters to obtain water and fertilizer samples, organize the data of each sample into water and fertilizer vectors, convert the relative yield, clean up outliers and unify units to construct water and fertilizer sample set, and save water and fertilizer limits at the same time. S2. Construct effective water-nitrogen coupling enhancement features in the root zone based on water-fertilizer vectors, use them as input, and then establish an improved Matern kernel function Gaussian process surrogate model with fractal scale and threshold penalty. Construct a multi-objective function from the posterior prediction of the Gaussian process surrogate model. S3. Using the Gaussian process surrogate model as a fast evaluator, multi-objective continuous ant colony optimization is performed. First, the ant population is initialized and an elite profile set is established. Then, the direction-guided sampling covariance matrix is ​​constructed and new candidate solutions are generated. Then, pheromone evaporation and incremental updates based on the number of days of maintenance without stress are executed. After iterative updates, the final Pareto front strategy set is output. S4. The trained Gaussian process agent model and the constructed multi-objective continuous ant colony optimization method are deployed in the field water and fertilizer integrated decision system, and an executable water and fertilizer prescription is output in each irrigation decision cycle.

[0026] In a specific implementation, S1 is as follows: This invention first constructs a historical water and fertilizer test sample set for subsequent establishment of a Gaussian process surrogate model. The specific steps are as follows: 1) Set up multiple water and fertilizer treatment combinations in the field test plots corresponding to the target crop, and record the amount of irrigation per treatment combination. Nitrogen application rate Phosphorus application rate Potassium application rate And record the corresponding yield after harvest.

[0027] In practice, to ensure sample comparability, each treatment combination is preferably implemented under the same variety, the same growing season, and comparable soil conditions. When samples come from multiple years or multiple plots, the plot number, year number, and growing stage number are saved simultaneously to facilitate subsequent grouping and correction.

[0028] 2) For each experimental sample, record the auxiliary state parameters at the time of sample formation. The auxiliary state parameters include field capacity. The unit is cubic meters per cubic meter; soil volumetric moisture content at the time of decision-making. The unit is cubic meters per cubic meter; depth of the main active layer of the root system. The unit is millimeters; effective rainfall during the decision-making cycle. Units are in millimeters; reference crop evapotranspiration. The unit is millimeters per day; the crop coefficient at the current growth stage. Dimensionless; the maximum number of days of stress-free maintenance allowed during the current reproductive stage. The unit is per day; recommended nitrogen application rate for the current growth stage. The unit is kilograms per hectare.

[0029] 3) Organize the control variables for each sample into an original water-fertilizer combination vector. ,in, Indicates the first The original water-fertilizer combination vector of each sample has a dimension of . ; Indicates the first The amount of irrigation per sample in a single irrigation, in millimeters; Indicates the first Nitrogen application rate for each sample, in kilograms per hectare; Indicates the first The phosphorus application rate for each sample is expressed in kilograms per hectare. Indicates the first Potassium application rate for each sample, in kilograms per hectare; This indicates a transpose calculation.

[0030] 4) Convert the measured yield of each sample into a relative yield.

[0031] In practice, the yield of the benchmark high-yield treatment in the same test batch is used as the standard yield, and then the measured yield of each sample is divided by the standard yield to obtain the relative yield. ,in, Indicates the first The relative output corresponding to each sample typically ranges from 0 to 1.2.

[0032] In one embodiment, as an example, in a certain experimental batch, the measured yield of the baseline high-yield treatment was: The measured yield of a certain sample is Then the relative yield of this sample .

[0033] It should be noted that using relative yield instead of directly using absolute yield can reduce the scale shift caused by differences in basic soil fertility in different years and plots. This can lead to a systematic overall overestimation or underestimation of absolute yield under the same treatment combination.

[0034] 5) Perform outlier cleanup and unit standardization on all samples.

[0035] In practical implementation, samples with obvious deficiencies in irrigation, fertilization, or yield are deleted; soil moisture content and meteorological data collected by sensors are time-aligned; abnormal records outside the agronomically permissible range are manually reviewed; based on this, a historical water and fertilizer test sample set is obtained. ,in, This represents the historical water and fertilizer experiment sample set, with dimensions of , This indicates the number of historical samples.

[0036] 6) Maintain feasible upper and lower limits for irrigation, nitrogen, phosphorus, and potassium application rates; among which, the feasible upper limit for irrigation is... The lower limit of feasibility is The feasible upper limit for nitrogen application is: The lower limit of feasibility is The feasible upper limit for phosphorus application is: The lower limit of feasibility is The feasible upper limit for potassium application is: The lower limit of feasibility is ; Subscript Indicates the lower limit, subscript Indicates the upper limit.

[0037] In a specific implementation, S2 is as follows: Historical water and fertilizer experiment samples are usually limited in number, and there is a continuous nonlinear interaction relationship between irrigation amount, nitrogen application amount, phosphorus application amount and potassium application amount. If the original water and fertilizer combination vector is directly modeled, it is easy to confuse the "theoretical input amount" and the "actual available amount in the root zone".

[0038] This step first constructs the effective water-nitrogen coupling enhancement features in the root region, then establishes an improved Matern kernel function Gaussian process surrogate model, and finally outputs the objective function value required for subsequent multi-objective optimization from the Gaussian process surrogate model. The specific steps are as follows: S2.1 Constructing the enhanced eigenvector of the effective absorption state in the fusion root region Directly inputting the original water and fertilizer combination vector into the Gaussian process surrogate model makes it difficult to express whether "the current irrigation has truly been converted into effective water supply to the root zone" and "whether the current nitrogen application can be effectively absorbed under the existing water conditions".

[0039] This step first calculates the average available water coefficient in the root zone, then calculates the nitrogen availability factor, and finally obtains the effective water-nitrogen coupling index in the root zone. The effective water-nitrogen coupling index is then concatenated to the original water-fertilizer combination vector to form an enhanced feature vector. The specific steps are as follows: 1) Read the original water-fertilizer combination vector of a single sample And read the auxiliary state parameters corresponding to the sample. Indicates the amount of water irrigated in a single instance; Indicates the amount of nitrogen applied; Indicates the amount of phosphorus applied; This indicates the amount of potassium applied.

[0040] 2) Calculate the effective water volume in the root zone based on the current water storage capacity of the soil and the external water supply.

[0041] In practice, the maximum water replenishment depth of the root zone is first calculated, which is the maximum amount of water that the root zone can hold when replenished from the current water content to the field capacity. This can be obtained by subtracting the current soil volumetric water content from the field capacity and then multiplying it by the depth of the main active layer of the root system. Then, the total water supply within the decision-making cycle is calculated, which is the sum of a single irrigation and effective rainfall. The effective water volume in the root zone is obtained by taking the smaller value between the maximum rechargeable depth in the root zone and the total water supply. ,in, This represents the effective amount of water that can actually be retained in the root zone and utilized by crops, expressed in millimeters.

[0042] In one embodiment, for example, field holding capacity Current soil volumetric moisture content Depth of the main active layer of the root system The maximum rechargeable depth of the root zone. Single irrigation volume Effective rainfall The total water supply is Take the smaller of the two values ​​to get .

[0043] 3) Calculate the theoretical number of days to maintain stability without stress based on the effective water volume in the root zone.

[0044] In practice, the effective water volume in the root zone is first divided by the potential evapotranspiration intensity at the current stage to obtain the theoretical number of days to sustain life without stress. Potential transpiration intensity is represented by the product of the reference crop evapotranspiration and the crop coefficient at the current growth stage. To avoid the denominator being too small, a very small constant can be added to the denominator. , represents a numerically stable term to prevent division by zero (which can be taken as...). For example, effective water volume in the root zone. millimeters, reference crop evapotranspiration Millimeters per day, crop coefficient Numerical stability term Theoretically, the number of days without coercion should be maintained. sky; Then, divide the theoretical number of days of stress-free maintenance by the maximum number of days of stress-free maintenance allowed at the current reproductive stage, and limit the result to... arrive Between these, the root zone average effective water coefficient is obtained. ,in, This indicates the degree to which root zone moisture is close to a stress-free state under current water supply conditions, with a value range of [value missing]. arrive The larger the value, the more sufficient the current water supply.

[0045] In one embodiment, for example, if , , If the depth is millimeters, then the maximum rechargeable depth in the root zone is... millimeters; if millimeters Millimeters, then the effective water volume in the root zone Pick millimeters; if millimeters per day Theoretically, the number of days without coercion should be maintained. Approximately Heaven; if Then the root zone average effective water coefficient It is approximately 0.95. Therefore, although the irrigation amount is 40 mm, the actual extent to which it enhances the stress-free state of the root zone should be determined by both soil carrying capacity and transpiration consumption, rather than just by looking at the irrigation amount itself.

[0046] 4) Calculate the nitrogen availability factor based on the relationship between the nitrogen application rate and the recommended nitrogen application rate.

[0047] In practical implementation, the ratio of the applied nitrogen amount to the recommended nitrogen amount is used, and then substituted into the saturated mapping function to obtain the nitrogen availability factor, which is calculated as follows: ; in, This represents the nitrogen availability factor, with a value ranging from 0 to 1; This represents the curvature coefficient of nitrogen absorption response, with a value ranging from 1.0 to 2.0. It is used to control the rate at which the nitrogen availability factor tends to saturate as the nitrogen application rate increases. This indicates a numerical stability term to prevent the recommended nitrogen application rate from being too small; it can be taken as... ; This represents a natural exponential function; when the nitrogen application rate is low, the nitrogen availability factor increases rapidly, while when the nitrogen application rate approaches or exceeds the recommended application rate, the increase in the nitrogen availability factor gradually slows down.

[0048] It should be noted that a saturated mapping function is a nonlinear function in which the output growth gradually slows down and tends to an upper bound as the input increases.

[0049] In one embodiment, for example, if kilograms per hectare, kilograms per hectare, Nitrogen effectiveness factor Therefore, the current nitrogen application rate is sufficient to provide a certain level of effective nitrogen supply, but it has not yet reached the point of near saturation.

[0050] In one embodiment, such as Figure 2 As shown, the nitrogen availability saturation response curve is analyzed, displaying the theoretical response curve of the nitrogen availability factor with nitrogen application rate and the scatter plot of historical samples. The horizontal axis represents the nitrogen application rate (unit: kg / ha), and the vertical axis represents the nitrogen availability factor (dimensionless). The red scatter plots represent the actual values ​​of historical samples, and the blue curve is the saturation function curve calculated based on typical recommended nitrogen application rate parameters. The experimental results show that the nitrogen availability factor rises rapidly at low nitrogen application rates and tends to saturate after approaching or exceeding the recommended nitrogen application rate, which is consistent with the crop nitrogen absorption law. This demonstrates that the method of converting nitrogen application rate into effective nitrogen supply using the saturation exponential function can reasonably reflect the agronomic reality that "more application does not equal more absorption."

[0051] 5) Multiply the root zone average available water coefficient by the nitrogen availability factor to obtain the root zone available water-nitrogen coupling index, which represents the degree to which water and nitrogen can be utilized synergistically within the root zone. The calculation method is expressed as follows: ; in, This represents the effective water-nitrogen coupling index in the root zone, with a value ranging from 0 to 1.

[0052] It should be noted that sufficient water but insufficient nitrogen, or high nitrogen input but water shortage in the root zone, cannot form an efficient absorption state. Only when both are in a relatively optimal range will the effective water-nitrogen coupling index in the root zone be high.

[0053] In one embodiment, following the example above, if the root zone average effective water coefficient Nitrogen effectiveness factor The effective water-nitrogen coupling index in the root zone is... Therefore, although the current water supply conditions are good, the overall availability will not reach a high value close to 1 because the nitrogen application rate is still lower than the recommended range.

[0054] 6) Concatenate the original water-fertilizer combination vector with the effective water-nitrogen coupling index in the root zone to form an enhanced feature vector. .in, This represents the enhanced feature vector, with dimension . This approach retains the original input information while introducing the actual absorption state information of the root region.

[0055] It should be noted that this step constructs the root zone average available water coefficient and nitrogen availability factor, and couples them into a root zone available water-nitrogen coupling index. This compresses "root zone water retention capacity" and "nitrogen absorption saturation" into a single root zone available water-nitrogen coupling index that can be directly incorporated into a machine learning model. Based on this, the crop absorption mechanism is embedded into the data-driven model, enabling the model to prioritize learning the water and nitrogen changes that are truly effective for yield even with limited samples. This reduces the risk of the model misinterpreting "ineffective irrigation" or "excessive nitrogen application" as effective yield-increasing signals.

[0056] S2.2, Construct an improved Matrn kernel function with fractal dimension scaling and threshold penalty. The smoothness of yield response caused by different water and fertilizer factors is not consistent. Irrigation amount usually shows a gradual change on a large scale, while phosphorus and potassium application amount are prone to abrupt yield response caused by soil nutrient threshold in local ranges. If the same scale is used for all dimensions, this difference will be weakened.

[0057] This step sets length scales for different dimensions and adds a local distance penalty when the differences in irrigation amount, phosphorus application amount, and potassium application amount exceed a threshold, thereby establishing an improved Matrn kernel function. The specific steps are as follows: 1) For any two enhanced feature vectors and The differences in irrigation amount, nitrogen application rate, phosphorus application rate, potassium application rate, and the effective water-nitrogen coupling index in the root zone were calculated separately, and the differences in each dimension were normalized according to an independent length scale. , , , and , representing the length scales of irrigation amount, nitrogen application amount, phosphorus application amount, potassium application amount, and effective water-nitrogen coupling index in the root zone, respectively. All are positive hyperparameters. The smaller the length scale, the more sensitive the Gaussian process surrogate model is to changes in this dimension.

[0058] It should be noted that the Gaussian process surrogate model is a nonparametric surrogate model based on a Bayesian framework. It refers to the kernel function structure that is explicitly defined in subsequent steps and the specific model obtained after completing hyperparameter training.

[0059] In one embodiment, for example, if the difference in irrigation amount Length scale By normalizing the differences in each dimension according to independent length scales, the normalized distance for that dimension is: .

[0060] 2) Calculate the basic anisotropic distance based on the normalized differences in each dimension.

[0061] In practice, the squared normalized differences of each dimension are summed, and then the square root is taken to obtain the basic anisotropic distance. This distance reflects the degree of fundamental difference between the two samples in the five-dimensional enhanced feature space.

[0062] In one embodiment, for example, the normalized five-dimensional differences are respectively Then the basic anisotropic distance .

[0063] 3) Add threshold penalties for irrigation amount, phosphorus application amount and potassium application amount.

[0064] In the specific implementation, irrigation volume thresholds are set separately. Phosphorus application threshold Potassium application threshold When the difference in a certain dimension does not exceed the threshold of that dimension, no additional penalty is added; when the difference in a certain dimension exceeds the threshold of that dimension, the "part exceeding the threshold" is normalized according to the feasible range of that dimension and then added to an additional distance term; the calculation method for the threshold exceeding penalty term for irrigation amount, phosphorus application amount, and potassium application amount is expressed as follows: ; ; ; in, This indicates that the threshold for irrigation volume exceeds the penalty item; This indicates that the threshold for phosphorus application exceeds the penalty. This indicates that the threshold for potassium application exceeds the penalty. This represents a function that takes the maximum value, retaining only the portion exceeding the threshold.

[0065] In one embodiment, for example, if the difference in phosphorus application rate between two samples is 2 kg / ha, and the phosphorus application rate threshold is... kilograms per hectare, then This indicates that the two samples can still be considered locally similar in terms of phosphorus application rate; if the difference in phosphorus application rate is... If the weight is 1 kg per hectare, then the excess is 3 kg per hectare. It is a positive value.

[0066] In one implementation, the basic anisotropic distance is combined with the threshold exceedance penalty term to obtain the improved distance. ; This represents the combined improved distance between two samples in the enhanced feature space after incorporating fractal length scaling and cross-threshold penalty terms. This distance is used for subsequent calculation of the improved Matrn kernel function. The difference between two samples in irrigation amount, phosphorus application amount, or potassium application amount exceeds their respective thresholds. It will be significantly larger than the basic anisotropic distance. This causes the kernel function value to drop rapidly, thereby reducing the correlation between the two samples; the improved distance calculation method is expressed as: ; in, This represents the threshold penalty reinforcement coefficient, with a value ranging from 3.0 to 10.0. This represents the sum of squares of the penalty terms in each dimension.

[0067] In one embodiment, for example, the basic anisotropic distance If the difference in phosphorus application exceeds the threshold, it will produce... The penalty terms for the remaining dimensions are 0, and the threshold penalty enhancement coefficient is... ,but Improve distance .

[0068] 4) Using Matern The kernel function calculates the covariance between samples, yielding the value at the corresponding position in the kernel function matrix. The calculation method is expressed as follows: ; in, Indicating improvements to Matern The kernel function value represents the similarity between any two samples in the surrogate model. The kernel function values ​​of all sample pairs together constitute the covariance matrix, which is the core basis for Gaussian process prediction and inference. Represents the signal variance, used to control the overall magnitude of the covariance output. It is a hyperparameter of the kernel function, which is automatically learned during the model training phase by maximizing the marginal log-likelihood.

[0069] It should be noted that the Matrn 3 / 2 kernel function is a standard covariance function for Gaussian processes. Its characteristic is that the generated random process has first-order mean-square differentiability, and its smoothness is between that of the exponential kernel and the square exponential kernel. It is suitable for describing physical processes with a certain degree of roughness.

[0070] It should also be noted that this step uses a modified Matrn method. The kernel function, an improvement on the distance metric based on the standard Matrn 3 / 2 kernel function structure, involves two aspects: firstly, the distance input to the kernel function... Each dimension has an independent length scale, rather than a uniform scale; secondly, An additional cross-threshold penalty term is embedded for irrigation amount, phosphorus application amount, and potassium application amount.

[0071] 5) Construct the covariance matrix based on the kernel function values ​​between all pairs of historical samples.

[0072] Specifically, the covariance matrix is ​​composed of the kernel function values ​​between all pairwise historical samples. 2D symmetric positive definite matrix Symmetric positive definite matrix No. OK The elements of the column are .

[0073] Furthermore, to improve numerical stability, observation noise variance is added to the diagonal of the covariance matrix. and tiny jitter items ;in, Indicates the variance of observation noise; This represents a numerically stable term, which can be taken as... arrive .

[0074] In one embodiment, as an example, assuming there are 3 historical samples, the diagonal elements of the calculated original covariance matrix (3×3) are all signal variances. The variance of the observation noise is set to Numerical stability term Pick Then the diagonal elements of the enhanced covariance matrix become Off-diagonal elements retain their original covariance values.

[0075] 6) Train all hyperparameters of the improved Matrn kernel function. Specifically, the parameters to be trained include signal variance, length scales of each dimension, threshold penalty enhancement coefficient, thresholds, and observation noise variance.

[0076] In practical implementation, hyperparameters are learned by maximizing the marginal log-likelihood. The optimization method can employ the L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) continuous optimization method. For example, when using the L-BFGS method, the maximum number of iterations can be set to 200. This is achieved when the gradient norm of the objective function (negative log-marginal likelihood) is less than... Or the change in function value between two adjacent iterations is less than Optimization is terminated early; to avoid non-physical parameters, positive constraints are set for length scale, threshold and variance parameters. The initial value of each length scale can be 10 to 30 of the feasible range of the corresponding variable, and the initial value of each threshold can be 5 to 15 of the feasible range of the corresponding variable.

[0077] It should be noted that maximizing the marginal log-likelihood is a method that automatically determines the optimal hyperparameters of a model by finding the combination of hyperparameters that maximizes the probability of the current observed data. This method can achieve a balance between model complexity and data fit, avoiding overfitting. The L-BFGS continuous optimization method is a quasi-Newton optimization algorithm that finds the optimal solution of the objective function by approximating the inverse of the Hessian matrix (second derivative matrix).

[0078] It should also be noted that this step introduces both fractal dimension scaling and cross-threshold penalty mechanisms. The model can retain the overall smooth response of irrigation amount and nitrogen application amount, and can quickly reduce sample correlation when phosphorus or potassium application amount crosses the critical interval. Based on this, under the condition of limited experimental samples, it can still fit a local response surface that is more in line with agronomic experience.

[0079] S2.3 Constructing a multi-objective function based on posterior prediction using a Gaussian process surrogate model After training the Gaussian process surrogate model, the predicted yield distribution can be quickly obtained for any water and fertilizer strategy to be evaluated. This step extracts the posterior predicted mean from the Gaussian process surrogate model and constructs the relative yield objective function and the water and fertilizer efficiency objective function accordingly, providing an evaluation basis for subsequent multi-objective continuous optimization. The specific steps are as follows: 1) For any candidate original water-fertilizer combination vector Based on the soil moisture and meteorological conditions of the current site to be decided, the calculation process in S2.1 is repeated to obtain the corresponding enhanced feature vector. The effective water-nitrogen coupling index in the root region reflects the actual absorption potential of the candidate scheme at the "current decision-making moment".

[0080] 2) Calculate the kernel function value between the candidate enhanced feature vector and the enhanced feature vectors of all historical samples to form a covariance vector. Then, combine this with the covariance matrix obtained during the training phase, and use the Gaussian process regression posterior prediction formula to obtain the posterior prediction mean and posterior prediction variance of the candidate scheme. The calculation method is expressed as follows: ; ; in, The corresponding scheme to be evaluated 3D Enhanced Feature Vector; Let be the covariance vector, representing the difference between the scheme to be evaluated and . Between historical samples Dimensional covariance vector; For historical samples Dimension covariance matrix; To observe the noise variance; for 3D identity matrix; Composed of relative yield observations from all historical samples dimensional vector; The kernel function value of the candidate solution and itself is equal to... ; This represents the posterior mean of the Gaussian process surrogate model's predictions of the relative output of the candidate solution, and is dimensionless. This represents the dimensionless posterior prediction variance of the Gaussian process surrogate model for the relative output of the candidate solution.

[0081] It should be noted that the covariance vector Enhanced feature vectors from candidate schemes Enhanced feature vectors for each historical sample in the training set The improved Matrn kernel function value is calculated sequentially between these steps. Arrange these values ​​into a Composed of column vectors of dimension, covariance vector The element .

[0082] In one embodiment, for example, for a candidate solution, the model predicts a relative output mean of 0.9 and a posterior prediction variance of 0.01, indicating that the predicted output of the solution fluctuates roughly between 0.8 and 1.0. The larger the variance, the higher the uncertainty of the prediction.

[0083] 3) Using the posterior predicted mean as the first objective function, i.e., the relative yield objective function, it is expressed as: ;in, This represents the relative output objective function value of the candidate solution; a larger value indicates a higher predicted relative output.

[0084] In one embodiment, such as Figure 3 and Figure 4 As shown, the posterior predicted mean surface plot and the posterior predicted variance surface plot (irrigation amount - nitrogen application amount) are analyzed. Figure 3 and Figure 4 The X-axis of the two 3D surface plots represents the irrigation amount (unit: mm), and the Y-axis represents the nitrogen application rate (unit: kg / ha). Figure 3 The Z-axis represents the predicted relative output (dimensionless). Figure 4 The Z-axis represents the prediction variance (dimensionless). Figure 3 The overall response trend of the model to the yield of water-nitrogen combination was analyzed. The experimental results showed that the peak region appeared at the combination of medium irrigation and high nitrogen application, which is consistent with the agronomic law of synergistic yield increase of water and nitrogen. Figure 4 The variance was significantly higher in the marginal regions of irrigation and nitrogen application, indicating that the Gaussian process can not only provide predictions but also quantify uncertainty.

[0085] 4) Combining the posterior predicted mean with the normalized resource input penalty term yields the second objective function, namely the water and fertilizer efficiency objective function. This is used to avoid inconsistencies caused by directly adding different units of measurement. The calculation method is expressed as follows: ; in, This represents the objective function value of the water and fertilizer efficiency of the candidate scheme; The penalty weight representing the amount of irrigation is between 0.1 and 1.0. The penalty weight representing the amount of nitrogen applied ranges from 0.1 to 1.0. The penalty weight representing the amount of phosphorus applied ranges from 0.1 to 1.0; The penalty weight for potassium application ranges from 0.1 to 1.0.

[0086] 5) Both the relative yield objective function and the water and fertilizer efficiency objective function are used as evaluation indicators for subsequent optimization. Specifically, the relative yield objective function tends to find high-yield solutions, while the water and fertilizer efficiency objective function tends to find low-input, high-return solutions. Since these two functions conflict, the subsequent optimization outputs a set of non-dominated solutions, rather than a single, unique solution.

[0087] It should be noted that this step simultaneously constructs two objective functions: "high yield" and "high efficiency." This more realistically reflects the conflict between yield demands and resource constraints in agricultural decision-making scenarios, ensuring that the final output is not a single answer, but rather a set of Pareto frontier strategies that managers can choose according to their operational objectives. The Pareto front is a set of non-dominated solutions in multi-objective optimization where it is impossible to improve the performance of any other objective without compromising the performance of at least one objective; it represents the optimal trade-off boundary among all possible solutions.

[0088] In one embodiment, such as Figure 5 As shown, the Pareto front plot for multi-objective optimization is analyzed, with the horizontal axis representing the relative yield objective f1 (dimensionless) and the vertical axis representing the water and fertilizer efficiency objective f2 (dimensionless). Figure 5 The gray dots represent all candidate solutions, and the red lines connect them to the identified Pareto front. The front shape illustrates the conflict between high yield and high efficiency; pursuing higher relative yield inevitably leads to a decrease in efficiency, and vice versa. Experimental results show that multi-objective optimization methods can provide a set of non-dominated solutions, allowing decision-makers to choose appropriate water and fertilizer strategies based on their preferences.

[0089] In a specific implementation, S3 is as follows: After obtaining the Gaussian process surrogate model, the Gaussian process surrogate model is used as a fast evaluator to search for non-dominated solutions between high yield and high efficiency in the continuous water and fertilizer space.

[0090] To reduce invalid searches in obviously unreasonable regions, this invention introduces root zone water and nitrogen stress perception weights, direction-guided sampling covariance matrix, and event-driven pheromone volatilization mechanism into the continuous ant colony optimization process. The specific steps are as follows: S3.1 Initialize the ant colony and establish an elite profile set. This step addresses the blindness of the initial search in ant colony optimization (ACO) algorithms. By introducing root zone water and nitrogen stress perception at the outset of the search and combining it with fast non-dominated sorting, the computational resources of the initial ant population are preferentially allocated to areas with efficient water and nutrient synergy and high-yield or high-efficiency potential. This quickly identifies promising search directions and establishes an initial elite solution set, laying the foundation for subsequent targeted searches. The specific steps are as follows: 1) Initial ant populations were generated using Latin hypercube sampling within feasible ranges for irrigation, nitrogen, phosphorus, and potassium application rates.

[0091] In one implementation, each individual ant corresponds to a candidate original water-fertilizer combination vector. , where subscript Indicates the first The initial number of ant individuals can be set from 20 to 100 based on the calculation budget.

[0092] It should be noted that Latin hypercube sampling is a stratified sampling method that divides the range of values ​​of each variable into several non-overlapping sub-intervals with equal probability, randomly selects a sample point in each sub-interval, and then randomly pairs and combines the sample points of each variable. This can achieve a more uniform coverage of the multidimensional space with a smaller number of samples.

[0093] 2) For each individual ant, apply the evaluation process in S2.3 to obtain the relative yield objective function value. and the objective function value of integrated water and fertilizer efficiency Perform a fast non-dominated sort on all individual ants to obtain the non-dominated hierarchy. ,in, Indicates the first The non-dominant level of an individual ant in the current population; the smaller the value, the closer it is to the current Pareto front.

[0094] In one embodiment, as an example, suppose there are three ant individuals A, B, and C. A's two objective function values ​​are both better than or equal to B's, and at least one is strictly better; therefore, A dominates B. If A and C do not dominate each other, then they are in the same non-dominated level. It refers to the level at which an individual is dominated by other individuals in the population, with the level of the most frontier non-dominated individuals being level 1.

[0095] In one embodiment, such as Figure 6 As shown, the evolutionary graphs of the elite set (initial population, 5th iteration, and 10th iteration) are analyzed. The coordinate axes of the three subgraphs are relative yield target f1 (dimensionless) and water and fertilizer efficiency f2 (dimensionless), with different point colors representing different iteration stages. From the initial population to the 10th iteration, the elite set gradually converges towards the Pareto front, and its distribution range continuously shifts towards the high f1 region. Experimental results show that the root zone water and nitrogen stress perception and direction-guided sampling mechanism can effectively drive the search towards the optimal tradeoff boundary within a finite number of iterations.

[0096] 3) Recalculate the effective water-nitrogen coupling index of the root zone under the current plot conditions for each individual ant, and construct the root zone water-nitrogen stress perception factor accordingly.

[0097] In practical implementation, the root zone water and nitrogen stress sensing factor can be denoted as "the lower limit constant plus a linear amplification term of the effective water and nitrogen coupling index in the root zone". Specifically, we take... .in, Indicates the first The root zone water and nitrogen stress perception factor of an individual ant, with a value range of [value missing]. arrive ; This represents the minimum retention weight, which can be between 0.1 and 0.3. This can prevent the individual weight from becoming 0 directly when the effective water-nitrogen coupling index in the root zone is very low, thus retaining a small amount of exploration capability. Indicates the first Each ant represents a set of candidate water and fertilizer solutions. The effective water-nitrogen coupling index in the root zone.

[0098] 4) Combine the non-dominated hierarchy with the root zone water and nitrogen stress sensing factor to obtain the initial heuristic weights.

[0099] In specific implementation, for the first The initial heuristic weights of an individual ant are calculated as follows: ; in, Indicates the first The initial heuristic weights for each ant individual, ranging from 0 to 1.0, satisfy the following conditions: ; This is the hierarchical attenuation coefficient, with a value ranging from 0.5 to 1.0; The initial number of individual ants; Represents the natural exponential function; Individuals at lower (more frontier) non-dominated levels receive higher base weights, multiplied by... The weight allocation of effective individuals for water and nitrogen synergy in the root zone was further strengthened.

[0100] 5) Based on the non-dominated hierarchy and crowding level, retain a group of high-quality individuals of controlled size to form the current elite archive. ,in, This represents the elite archive set, used to store high-quality and widely distributed candidate solutions in the current iteration. It can be set to 20 to 60.

[0101] Specifically, all ant individuals are first arranged in ascending order of non-dominant hierarchy, and within the same hierarchy, they are arranged in descending order of crowding. Individuals are selected layer by layer starting from the first hierarchy. When adding all individuals to a hierarchy would cause the total number of elite archives to exceed a preset limit, only a few individuals with the highest crowding in that hierarchy are selected to fill the limit, and the remaining individuals are discarded. Here, crowding refers to the distance between an individual and its neighboring individuals in the target space; the greater the distance, the sparser the distribution.

[0102] In one embodiment, for example, the elite archive set has an upper limit of 3. There are individuals A and B in the first level and individuals C and D in the second level. Since there are 2 individuals in the first level, A and B are directly retained, leaving 1 slot. In the second level, the crowding of C and D is compared. If the crowding of C is greater than that of D, it means that C is more sparsely populated, so C is retained. Finally, the elite archive set consists of A, B and C.

[0103] S3.2 Construct the direction-guided sampling covariance matrix and generate new candidate solutions. Conventional continuous ant colony optimization typically employs an approximately isotropic local sampling method, which makes it difficult to reflect "which direction is more likely to improve the predicted yield at the current position".

[0104] This step utilizes a Gaussian process surrogate model to perform local gradient estimation on the relative output objective function, and embeds the gradient direction into the sampling covariance matrix. The specific steps are as follows: 1) From the Elite Archives A guide individual is randomly selected based on the current heuristic weights, denoted as: ;in, This represents the current guiding individual used to generate new candidate solutions; Indicates the amount of irrigation water to guide an individual; Indicates the amount of nitrogen applied to guide an individual; Indicates the amount of phosphorus to guide an individual's application; This indicates the amount of potassium to be applied to guide an individual.

[0105] 2) Estimate the gradient direction of the relative output objective function at the guide individual.

[0106] In practical implementation, guiding individuals Each decision dimension The specific steps are as follows: a) Set the perturbation step size for this dimension. The feasible range of this dimension can be taken. ; b) Construct a positive perturbation solution (Only in the first) Dimensions increase ) and negative perturbation solution (Only in the first) Dimension reduction ) c) Calculate the relative output objective function values ​​for the two new vectors respectively. and ; d) Calculate the first Approximate partial derivatives of dimension: ; e) Combine the partial derivatives of the four dimensions to obtain the gradient direction vector. Dimension , This indicates a transpose calculation.

[0107] In one embodiment, for example, the feasible range of irrigation volume is taken as follows: perturbation step size The positive perturbation solution is The negative perturbation solution is If calculated , The partial derivative of the irrigation amount dimension is approximately .

[0108] 3) Determine the basic sampling scale based on the overall dispersion of the elite archives.

[0109] In practice, the specific steps for calculating the base sampling scale are as follows: a) Calculate the average of the absolute differences: for each dimension Calculation guides individuals With Elite Archives All other individuals The average of the absolute differences in this dimension ; b) Determine the baseline standard deviation: Multiply the average of the absolute differences of each dimension by a scaling factor. (Recommended) ), thus obtaining the basic sampling scale, i.e., the basic standard deviation. It can be divided into four basic standard deviations based on the decision-making dimensions. , , and , The basic standard deviation of irrigation volume This represents the basic standard deviation of nitrogen application rate. This represents the basic standard deviation of the phosphorus application rate. This represents the basic standard deviation of the potassium application rate; c) Setting a lower limit: To prevent the sampling radius from converging to zero prematurely, a lower limit is set for each basic standard deviation. The feasible range of this dimension can be taken. ; d) Construct the fundamental diagonal covariance matrix Write the squares of the four basic standard deviations in sequence. On the diagonal of a diagonal matrix, form .

[0110] In one embodiment, for example, for the irrigation amount dimension, the leading individual value is 40mm, and the other two individual values ​​in the elite archive are 35mm and 45mm, then the mean absolute difference (irrigation amount dimension) is... ;Pick ,but If the feasible range of irrigation volume is The lower limit is set as the feasible range. Right now ; Therefore, it is retained. .

[0111] 4) Superimpose the gradient directions onto the basic diagonal covariance matrix to construct the direction-guided sampling covariance matrix, which is calculated as follows: ; in, This represents the direction-guided sampling covariance matrix corresponding to the individual being guided; This represents the gradient direction amplification factor, with a value ranging from 1.0 to 5.0. It degenerates into isotropic sampling; Represents the gradient vector The modulus length; This represents a numerically stable term to prevent the denominator from being zero, and can be taken as... ; Represents the gradient vector The transpose of the sample distribution is used; when a certain direction is estimated to be more likely to increase the relative output objective function, the sample distribution is extended along that direction.

[0112] In one embodiment, for example, if the gradient direction near the individual mainly manifests as "increasing irrigation amount" and "moderately increasing nitrogen application amount" to improve the relative yield objective function value more quickly, while the gradient directions of phosphorus application amount and potassium application amount are small, then the direction-guided sampling covariance matrix will show more obvious stretching in the irrigation amount dimension and nitrogen application amount dimension, and new candidate solutions are more likely to expand along the direction of "water and nitrogen synergistic yield increase".

[0113] 5) Using the guide individual as the mean and the direction-guided sampling covariance matrix as the covariance, new candidate solutions are obtained by sampling from the four-dimensional multivariate Gaussian distribution. If a certain dimension exceeds the feasible interval, the mirror bounce or boundary truncation method is used for correction.

[0114] In one implementation, when a dimension is greater than the upper limit, the excess portion is reflected back into the interval in a symmetrical manner. When a dimension is less than the lower limit, it is also reflected in a symmetrical manner. Based on this, a new candidate original water and fertilizer combination vector that satisfies the agronomic boundary constraints is obtained.

[0115] It should be noted that the generation of new solutions in the continuous ant colony optimization in this step no longer relies entirely on empirical local random perturbations. Instead, it uses a Gaussian process surrogate model to directionally stretch the sampling distribution in the direction of the local response in the current region. This can improve the search efficiency for potential high-yield areas and reduce ineffective random trials in flat areas without increasing the cost of real field trials.

[0116] S3.3 Execute pheromone evaporation and incremental update based on the number of days of maintenance without stress. Agricultural irrigation decisions are characterized by events. Different irrigation schemes have different root zone stress-free maintenance days. Although the objective function value of a scheme with a short maintenance time may be not low at a certain moment, its sustainability is poor and it is not suitable to retain high weights in the long term during optimization.

[0117] This step incorporates the theoretical number of days of stress-free maintenance into the pheromone evaporation process to achieve differentiated weight updates. The specific steps are as follows: 1) For each individual in the elite archives Following the same method as in S2.1, calculate the effective root zone water volume and the theoretical number of days to sustain without stress under the current site conditions. ,in, Indicates the first volume of the elite archives The theoretical number of days an individual can sustain stress-free transpiration under current conditions.

[0118] 2) The pheromone volatility coefficient can be calculated based on the theoretical number of days without stress. It can be calculated by multiplying the baseline volatility by a drought amplification term, as follows: ; in, Indicates the first The pheromone volatility coefficient of an individual; This represents the basic volatility, with a value ranging from 0.1 to 0.3. This represents the drought amplification factor, with a value ranging from 0.5 to 2.0; This means limiting the result to between 0 and 1. This represents the input to the stage function, if The result is 0; if The result is 1 if the result is 1 otherwise. ; This represents the function that takes the minimum value; theoretically, the shorter the number of days without stress, the faster the pheromones evaporate.

[0119] In one embodiment, for example, if the maximum number of days of stress-free maintenance allowed at the current reproductive stage is 7 days, and the theoretical number of days of stress-free maintenance for a certain elite individual is only 2 days, then... , The pheromone volatility coefficient is approximately This shows that although the scheme may temporarily enter the elite archive, its weight will decrease faster than the scheme that lasts longer.

[0120] 3) Perform pheromone volatilization on all individuals in the elite archives.

[0121] Specifically, if the current weight of an individual before it evaporates is... The intermediate weight update method after evaporation is as follows: ,in, This represents the intermediate weight after evaporation.

[0122] 4) Perform pheromone increment allocation on the newly generated candidate solutions.

[0123] In practice, new candidate solutions are merged with the current elite archive individuals, then re-evaluated and ranked; if a new candidate solution enters a new non-dominated frontier, a fixed increment is directly assigned. If a new candidate solution, although not entering the non-dominated frontier, improves at least one of the relative yield objective function or the water and fertilizer efficiency objective function relative to its guided individual by more than a threshold. Then, allocate small increments, and the upper limit of the small increment can be set to... ,and ;in, This represents the increment of rewards on the non-dominated frontier, which is dimensionless. This indicates the upper limit of the improvement reward, and is dimensionless. This represents the effective improvement threshold, which is dimensionless and can be taken as 0.01.

[0124] In one embodiment, as an example, suppose , , If a new candidate solution is merged with the elite archive set and enters the non-dominated frontier, it gains an increment. Another new candidate solution did not enter the non-dominated frontier, but its relative output objective function value with respect to the guiding individual increased from 0.88 to 0.90 (an increase). Then it gains an increment. .

[0125] 5) After merging the intermediate weights after evaporation with the reward increments of new candidate solutions, normalize them again, and update the elite archive set according to the principle of "non-dominated hierarchy priority, congestion degree second priority". Individuals that are completely dominated and densely distributed are deleted, while non-dominated and sparsely distributed individuals are retained to ensure the coverage of the Pareto front.

[0126] It should be noted that the retention strength of elite individuals in this step depends not only on the current objective function value, but also on how long the scheme can maintain a stress-free water supply under the current plot conditions. This makes the optimization process more biased towards water and fertilizer schemes that "perform well at present and have strong sustainability", rather than schemes that "look good in the short term but quickly enter the risk of water shortage".

[0127] S3.4 Iteratively update and output the final Pareto frontier policy set. To establish a complete iterative optimization closed loop, this step drives the entire ant population to converge toward the multi-objective optimal trade-off boundary (Pareto front) of the water-fertilizer scheme by repeatedly executing a series of operations: new solution generation, evaluation, pheromone updating, and elite file maintenance. This outputs a uniformly distributed set of optimal solutions representing different trade-off preferences, providing a high-quality candidate pool for the final decision. The specific steps are as follows: 1) Using the updated elite profile set as the basis for guiding individual selection in the next round, repeat S3.2 and S3.3. In each iteration, generate new candidate solutions, evaluate the objective function, perform pheromone evaporation and reward, and update the elite profile set.

[0128] 2) When the maximum number of iterations is reached Or the maximum number of proxy model calls The iteration stops when the time is right, where, This represents the maximum number of iterations, which can be between 50 and 200. This indicates the maximum number of times the Gaussian process proxy model can be invoked, which can be between 2000 and 10000, and is used to control the overall computational budget.

[0129] 3) Extract all non-dominated candidate solutions from the elite archive set at the termination time to form the final Pareto frontier strategy set. ,in, This represents the final Pareto frontier strategy set, where each strategy includes irrigation amount, nitrogen application amount, phosphorus application amount, potassium application amount, predicted relative yield, and predicted water and fertilizer efficiency.

[0130] In one embodiment, for example, ultimately It includes 3 options: Option A is The predicted relative yield is 0.92, and the efficiency is 0.75; Option B is... The predicted relative yield is 0.95, and the efficiency is 0.68; Option C is... The predicted relative yield is 0.85 and the efficiency is 0.88.

[0131] In a specific implementation, S4 is as follows: After completing the training of the Gaussian process surrogate model and constructing the multi-objective continuous ant colony optimization method, this invention can be deployed in a field integrated water and fertilizer decision-making system to output an executable water and fertilizer prescription in each irrigation decision cycle. The specific steps are as follows: 1) Collect real-time field status data at the current irrigation decision point. The real-time status data should include at least the current soil volumetric moisture content, the expected effective rainfall, the reference crop evapotranspiration, the crop coefficient at the current growth stage, the depth of the main root activity layer, and the maximum number of days of stress-free maintenance allowed at the current growth stage.

[0132] In one implementation, if the plot is equipped with a soil moisture sensor, the most recent stable measurement value is read directly; if no sensor is installed, the most recent manual soil moisture measurement value or the crop model estimate value can be used.

[0133] 2) Using the current field status data as input, combined with the auxiliary status parameters of the plot, construct the enhanced feature vector at the current decision moment, call the evaluation process of S2.3 and the multi-objective continuous ant colony optimization process of S3 to generate the final Pareto front strategy set corresponding to the current plot. Each scheme in the strategy set corresponds to a set of executable irrigation amount, nitrogen amount, phosphorus amount and potassium amount at the current moment.

[0134] 3) The final Pareto frontier strategy set is further screened based on business objectives or management constraints.

[0135] In practical implementation, a minimum relative output threshold can be set. and in satisfying The scheme with the highest water and fertilizer efficiency objective function value can be selected from the options. Alternatively, maximum available irrigation volume, maximum fertilizer budget, or environmental constraint upper limits can be set, and the scheme with the highest relative yield objective function value among the schemes that meet the constraints can be selected. This indicates the minimum acceptable relative production threshold.

[0136] 4) Output recommended water and fertilizer prescriptions.

[0137] Specifically, the recommended water and fertilizer prescription should include at least the recommended irrigation volume. Recommended nitrogen application rate Recommended phosphorus application rate Recommended potassium application rate Predicting relative output And predicting the overall efficiency of water and fertilizer ,in, This represents the vector of the ultimately selected recommended original water and fertilizer combination.

[0138] In one embodiment, for example, the final prescription is output as: recommended irrigation amount. Recommended nitrogen application rate Recommended phosphorus application rate Recommended potassium application rate The plan is expected to achieve a relative yield of 0.92 and a comprehensive water and fertilizer efficiency of 0.75.

[0139] 5) When entering the next irrigation decision cycle, the latest field status data is read again and the above steps are repeated to achieve dynamic updating of water and fertilizer prescription output. If new production samples are accumulated in this season, the new samples are incorporated into the historical water and fertilizer test sample set, and the Gaussian process surrogate model is retrained according to the preset cycle to continuously improve the model's adaptability.

[0140] It should be noted that the final output of this invention is a set of non-dominated schemes dynamically calculated under the constraints of the current field conditions, and can be screened according to different objectives such as prioritizing high yield, water conservation, fertilizer reduction, or comprehensive benefits. Based on this, it can adapt to the decision-making preferences of different operators, while ensuring that the prescription generation process is always based on the common foundation of the current root zone's actual absorption state and historical experimental patterns.

[0141] In one embodiment, for example, in a spring cornfield in Northeast China, the current growth stage is the tasseling stage, and the crop coefficient is... Field sensors showed a soil volumetric moisture content of 0.21, a root depth of 500 mm, and a field capacity of 0.33. No effective rainfall is forecast for the next week, and the daily reference crop evapotranspiration is 5.2 mm. The system initiated a decision-making process. a) The system reads the status data and invokes the optimization process; b) The system outputs a Pareto frontier policy set containing 30 schemes; c) When the manager selects the "water-saving priority" mode, the system automatically selects the option with the highest water and fertilizer efficiency among all options with a relative yield prediction of not less than 0.85; The system outputs a final prescription with a single irrigation amount of 35 mm, a nitrogen application rate of 140 kg / ha, a phosphorus application rate of 50 kg / ha, and a potassium application rate of 65 kg / ha. The predicted relative yield of this scheme is 0.92, and the comprehensive water and fertilizer efficiency is 0.75. The system then sends this prescription to the integrated water and fertilizer control terminal for execution.

[0142] Example 2 A system for recommending integrated water and fertilizer management strategies based on multi-objective optimization includes a module for executing processing instructions for each step in a method for recommending integrated water and fertilizer management strategies based on multi-objective optimization, comprising: Sample collection and processing module: used to arrange multiple sets of water and fertilizer treatments, record relevant parameters, organize water and fertilizer vectors, convert relative yields, clean up outliers and unify units to build a sample set, and save water and fertilizer limits; Feature construction and model training module: used to construct effective water-nitrogen coupling enhancement features in the root region, establish an improved Matern kernel function Gaussian process surrogate model and construct a multi-objective function; Multi-objective optimization module: used to initialize ant population, establish elite profile set, construct sampling covariance matrix to generate candidate solutions, update pheromones and iteratively output Pareto front policy set; Decision Deployment Module: Used to deploy models and optimization methods, collect real-time data in each irrigation decision cycle, output executable water and fertilizer prescriptions and update them dynamically.

[0143] Although the specific embodiments of the invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the invention. Based on the technical solutions of the invention, various modifications or variations that can be made by those skilled in the art without creative effort are still within the scope of protection of the invention.

Claims

1. A method for recommending integrated water and fertilizer management strategies based on multi-objective optimization, characterized in that, Includes the following steps: S1. Arrange multiple water and fertilizer treatments, record irrigation amount, nitrogen, phosphorus and potassium application amount, yield and auxiliary parameters to obtain water and fertilizer samples, organize the data of each sample into water and fertilizer vectors, convert the relative yield, clean up outliers and unify units to construct water and fertilizer sample set, and save water and fertilizer limits at the same time. S2. Construct effective water-nitrogen coupling enhancement features in the root zone based on water-fertilizer vectors, use them as input, and then establish an improved Matern kernel function Gaussian process surrogate model with fractal scale and threshold penalty. Construct a multi-objective function from the posterior prediction of the Gaussian process surrogate model. S3. Using the Gaussian process surrogate model as a fast evaluator, multi-objective continuous ant colony optimization is performed. First, the ant population is initialized and an elite profile set is established. Then, the direction-guided sampling covariance matrix is ​​constructed and new candidate solutions are generated. Then, pheromone evaporation and incremental updates based on the number of days of maintenance without stress are executed. After iterative updates, the final Pareto front strategy set is output. S4. The trained Gaussian process agent model and the constructed multi-objective continuous ant colony optimization method are deployed in the field water and fertilizer integrated decision system, and an executable water and fertilizer prescription is output in each irrigation decision cycle.

2. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 1, characterized in that, S1 is as follows: Multiple water and fertilizer treatment combinations were set up in the field test plots corresponding to the target crop, and the amount of irrigation per treatment combination was recorded. Nitrogen application rate Phosphorus application rate Potassium application rate And record the corresponding yield after harvest; For each experimental sample, auxiliary state parameters at the time of sample formation were recorded. These auxiliary state parameters included field capacity. Soil volumetric moisture content at the time of decision-making Depth of the main active layer of the root system Effective rainfall during the decision-making cycle , reference crop evapotranspiration Crop coefficient at the current growth stage The maximum number of days of stress-free maintenance allowed during the current reproductive stage. Recommended nitrogen application rate for the current growth stage ; The single irrigation amount for each sample Nitrogen application rate Phosphorus application rate Potassium application rate Organize the data into the original water and fertilizer combination vector, and convert the measured yield of each sample into a relative yield; Outlier cleanup and unit standardization were performed on all samples. Samples with obvious missing irrigation, fertilizer, or yield data were deleted. Time alignment was performed on soil moisture content and meteorological data collected by sensors. Abnormal records outside the agronomic allowable range were manually reviewed to obtain the water and fertilizer sample set. At the same time, feasible upper and lower limits for irrigation, nitrogen, phosphorus and potassium application rates should be maintained.

3. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 1, characterized in that, S2 is as follows: S2.1 Based on the water-fertilizer combination vector and auxiliary state parameters of each sample, calculate the average effective water coefficient and nitrogen availability factor of the root zone to obtain the effective water-nitrogen coupling index of the root zone. Then, concatenate the effective water-nitrogen coupling index of the root zone to the water-fertilizer combination vector to form an enhanced feature vector. S2.2 Calculate the difference between irrigation amount, nitrogen application amount, phosphorus application amount, potassium application amount and effective water-nitrogen coupling index in the root zone for any two enhanced feature vectors. When the difference exceeds the preset threshold, add local distance penalty to establish an improved Matrn kernel function and train a Gaussian process surrogate model on it. S2.3 Extract the posterior predicted mean from the Gaussian process surrogate model, and construct the relative yield objective function and the water and fertilizer efficiency objective function accordingly.

4. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 3, characterized in that, S2 The specific calculation process for the enhanced feature vector is as follows: Read the water and fertilizer combination vector of a single sample and the auxiliary state parameters corresponding to that sample. Based on the current water storage capacity of the soil and the external water supply, calculate the effective water volume in the root zone. First, subtract the current soil volumetric water content from the field water holding capacity, and then multiply by the depth of the main active layer of the root system to calculate the maximum water replenishment depth in the root zone. Then calculate the total water supply within the decision period. Take the smaller value between the maximum water replenishment depth in the root zone and the total water supply to obtain the effective water volume in the root zone. Finally, add it to the single irrigation amount to obtain the total water supply within the decision period. The effective root zone water volume is then divided by the potential transpiration intensity at the current stage to obtain the theoretical number of days without stress. The potential transpiration intensity is represented by the product of the reference crop evapotranspiration and the crop coefficient at the current growth stage. The theoretical number of days without stress is then divided by the maximum allowable number of days without stress at the current growth stage, limiting the result to... arrive Between these values, the root zone average effective water coefficient is obtained; Next, the ratio of the applied nitrogen amount to the recommended nitrogen amount is substituted into the saturated mapping function to obtain the nitrogen availability factor; the average effective water coefficient of the root zone is multiplied by the nitrogen availability factor to obtain the effective water-nitrogen coupling index of the root zone; finally, the original water-fertilizer combination vector is concatenated with the effective water-nitrogen coupling index of the root zone to form an enhanced feature vector.

5. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 3, characterized in that, S2 The objective function is constructed as follows: The differences in each dimension of any two enhanced feature vectors are normalized using independent length scales. Then, the base anisotropy distance is calculated, and a threshold is set. If the base anisotropy distances for irrigation, phosphorus, and potassium application exceed the threshold, a threshold penalty is added. Then, the Matrn algorithm is applied. The kernel function calculates the covariance between samples, obtaining the value at the corresponding position in the kernel function matrix; Then, construct the covariance matrix based on the pairwise kernel function values ​​of all samples, and add the observation noise variance and small jitter terms to the diagonal of the covariance matrix. Finally, train all the hyperparameters of the improved Matern kernel function. For any candidate water and fertilizer combination vector, combined with the soil moisture and meteorological conditions of the current decision-making plot, the corresponding enhanced feature vector is obtained through the S2.1 operation. The kernel function value between the candidate enhanced feature vector and the enhanced feature vector of all samples is calculated to form a covariance vector. Then, combined with the covariance matrix obtained in the training phase, the posterior prediction mean and posterior prediction variance of the candidate scheme are obtained according to the Gaussian process regression posterior prediction formula. The posterior prediction mean is used as the first objective function, namely the relative yield objective function. The posterior prediction mean is then combined with the normalized resource input penalty term to obtain the second objective function, namely the water and fertilizer comprehensive efficiency objective function. The relative yield objective function and the water and fertilizer comprehensive efficiency objective function are used as evaluation indicators for subsequent optimization.

6. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 1, characterized in that, The initialization of the ant colony and the establishment of the elite profile set in S3 are as follows: Within the feasible range of irrigation, nitrogen, phosphorus, and potassium application rates, an initial ant population was generated using Latin hypercube sampling. For each individual ant, the evaluation process in step S2 was called to obtain the relative yield objective function value and the water and fertilizer integrated efficiency objective function value. Then, a fast non-dominated sort was performed on all individual ants to obtain the non-dominated hierarchy. Next, the effective water and nitrogen coupling index of the root zone under the current plot conditions was recalculated for each individual ant, and a root zone water and nitrogen stress perception factor was constructed based on this. The non-dominated hierarchy was then combined with the root zone water and nitrogen stress perception factor to obtain the initial heuristic weights. Finally, a set of high-quality individuals with controlled size was retained based on the non-dominated hierarchy and crowding to form the current elite archive set.

7. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 6, characterized in that, The calculation process for new candidate solutions, pheromone evaporation, and incremental updates in S3 is as follows: A guide individual is randomly selected from the elite archive set according to the current heuristic weights. The gradient direction of the relative output objective function is estimated at the guide individual. The basic sampling scale is then determined based on the overall dispersion of the elite archive set. The gradient direction is then superimposed on the basic diagonal covariance matrix to construct the directional guided sampling covariance matrix. Finally, new candidate solutions are obtained by sampling from the four-dimensional multivariate Gaussian distribution with the guide individual as the mean and the directional guided sampling covariance matrix as the covariance. For each individual in the elite archive set, the effective water volume in the root zone and the theoretical number of days of no-stress maintenance are calculated under the current plot conditions. Then, the pheromone volatilization coefficient is calculated based on the theoretical number of days of no-stress maintenance. Pheromones are then volatilized for all individuals in the elite archive set. Next, pheromone increments are allocated to newly generated candidate solutions. Specifically, the new candidate solutions are merged with the individuals in the current elite archive set, re-evaluated, and sorted. If a new candidate solution enters a new non-dominated frontier, a fixed increment is directly allocated. If a new candidate solution, although not entering a non-dominated frontier, improves at least one of the relative yield objective function or water and fertilizer efficiency objective function relative to its guiding individual by more than a threshold, a small increment is allocated. Finally, the intermediate weights after volatilization are merged with the reward increments of the new candidate solutions and re-normalized. The elite archive set is then updated according to the principle of non-dominated level priority and crowding degree second priority.

8. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 7, characterized in that, The calculation process of the final Pareto frontier policy set in S3 is as follows: Using the updated elite archive set as the basis for guiding individual selection in the next round, the calculation process of new candidate solutions, pheromone evaporation and incremental updates is repeated. In each iteration, new candidate solutions are generated, the objective function is evaluated, pheromone evaporation and rewards are executed, and the elite archive set is updated. When the maximum number of iterations or the maximum number of proxy model calls is reached, the iteration stops. All non-dominated candidate solutions are extracted from the elite archive set at the termination time to form the final Pareto front strategy set.

9. The method for recommending integrated water and fertilizer control strategies based on multi-objective optimization according to claim 1, characterized in that, S4 is as follows: Real-time field status data is collected at the current irrigation decision point. Using the current field status data as input and combined with the auxiliary status parameters of the plot, an enhanced feature vector for the current decision point is constructed. Steps S2 and S3 are called to generate the final Pareto front strategy set corresponding to the current plot. Then, the final Pareto front strategy set is screened a second time according to the business objectives or management constraints to output the recommended water and fertilizer prescription. When entering the next irrigation decision cycle, the latest field status data is read again and the aforementioned steps are repeated to achieve dynamically updated water and fertilizer prescription output.

10. A water and fertilizer integration control strategy recommendation system based on multi-objective optimization, characterized in that, The module includes a module for executing the processing instructions for each step in the method for recommending a multi-objective optimization-based integrated water and fertilizer control strategy as described in any one of claims 1-9, comprising: Sample collection and processing module: used to arrange multiple sets of water and fertilizer treatments, record relevant parameters, organize water and fertilizer vectors, convert relative yields, clean up outliers and unify units to build a sample set, and save water and fertilizer limits; Feature construction and model training module: used to construct effective water-nitrogen coupling enhancement features in the root region, establish an improved Matern kernel function Gaussian process surrogate model and construct a multi-objective function; Multi-objective optimization module: used to initialize ant population, establish elite profile set, construct sampling covariance matrix to generate candidate solutions, update pheromones and iteratively output Pareto front policy set; Decision Deployment Module: Used to deploy models and optimization methods, collect real-time data in each irrigation decision cycle, output executable water and fertilizer prescriptions and update them dynamically.

Images