Time-sequence dynamic regulation method for nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization

Abstract

The present invention relates to a method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce for multi-objective collaborative optimization, which solves the defect that it is difficult to determine the optimal nutrient solution concentration scheme required for the temporal dynamic growth of hydroponic crops interacting with the environment compared with the prior art. The present invention includes the following steps: constructing a prediction model for the temporal population photosynthetic rate and a prediction model for the temporal population water use efficiency; constructing a multi-objective optimization model; solving the Pareto solution set of the multi-objective optimization model; constructing a temporal regulation model for the nutrient solution concentration; and temporally dynamically regulating the nutrient solution concentration of hydroponic lettuce. The present invention uses a non-dominated sorting multi-objective genetic algorithm to solve the multi-objective problems of the prediction model for the temporal population photosynthetic rate and the prediction model for the temporal population water use efficiency, and obtains the optimal balanced regulation target value by combining the uniform distribution population strategy, non-dominated sorting, crowding degree calculation, elite strategy, and population update mechanism, effectively solving the problem of dynamic regulation of the nutrient solution concentration for the temporal growth of plants.

Description

Technical Field

[0001] The present invention relates to the technical field of smart agriculture, and specifically to a method for time-sequential dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization. Background Art

[0002] As Figure 2 shown, hydroponic vegetables are one of the important vegetable cultivation methods in modern agriculture. In a hydroponic system, too low or too high a nutrient solution concentration will cause restricted plant growth. Therefore, an appropriate nutrient solution concentration is crucial for plant growth. However, the demand for the nutrient solution concentration varies during different growth stages of plants. A low nutrient solution concentration in the early growth stage can meet the growth of plants, while a higher nutrient solution concentration in the middle and late growth stages can significantly increase the yield of lettuce. Therefore, the time-sequential dynamic regulation of the nutrient solution is of great significance for the sustainable development of hydroponic green vegetables.

[0003] The population photosynthetic rate accurately reflects the growth status of plants, while the population water use efficiency represents the productivity of hydroponic plants. Both are significantly affected by the dynamic nutrient solution concentration. However, there is a contradiction between the two, and they cannot reach the maximum value at the same time. When plants increase the stomatal aperture to improve the photosynthetic rate, it will accelerate the transpiration rate, thereby reducing the water use efficiency; reducing the stomatal aperture to improve the water use efficiency will inhibit the photosynthetic rate due to the reduced supply of carbon dioxide. Therefore, the key to solving this problem is to balance and coordinate the two objectives, and obtain the optimal balance solution of the population photosynthetic rate and the population water use efficiency through a multi-objective collaborative optimization method.

[0004] As a paradigm tool for complex system optimization, the multi-objective evolutionary algorithm realizes the global approximation of the Pareto front in a non-convex and high-dimensional objective space through the co-evolution mechanism of bionic operators (selection, crossover, mutation). As a typical representative, the non-dominated sorting multi-objective genetic algorithm works through the synergistic effect of a dual mechanism: a hierarchical screening architecture based on the Pareto dominance relationship, using fast non-dominated sorting to establish the dominance level of solutions, and combining the elitist retention strategy to accelerate the population convergence; introducing a dynamic crowding distance operator to maintain the uniformity of the population distribution, effectively overcoming the problem of diversity degradation of traditional algorithms on complex frontiers. Currently, although Chen explored the photosynthetic rate and light energy utilization rate of hydroponic plants using a multi-objective optimization algorithm, he ignored the most basic time-sequential dynamic regulation mechanism of the nutrient solution concentration of hydroponic crops and the population scale effect.

[0005] Therefore, how to achieve the time-sequential dynamic regulation of the nutrient solution concentration of hydroponic lettuce has become an urgent technical problem to be solved. Summary of the Invention

[0006] The object of the present invention is to solve the defect in the prior art that it is difficult to determine the optimal nutrient solution concentration scheme required for the temporal dynamic growth of hydroponic crops interacting with the environment, and to provide a method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization to solve the above problems.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization, comprising the following steps:

[0009] Construct a temporal population photosynthetic rate prediction model and a temporal population water use efficiency prediction model;

[0010] Construct a multi-objective optimization model;

[0011] Solve the Pareto solution set of the multi-objective optimization model;

[0012] Construct a nutrient solution concentration temporal regulation model: select the knee-point optimal balance solution in the Pareto solution set, and use the polynomial regression algorithm to construct the nutrient solution concentration temporal regulation model;

[0013] Temporally dynamically regulate the nutrient solution concentration of hydroponic lettuce: embed the nutrient solution concentration temporal regulation model into the hydroponic intelligent monitoring and regulation system to dynamically regulate the nutrient solution concentration during the entire growth period of hydroponic lettuce.

[0014] The construction of the temporal population photosynthetic rate prediction model and the temporal population water use efficiency prediction model includes the following steps:

[0015] Use a population photosynthetic rate measuring instrument to obtain the population photosynthetic rate data set and the population water use efficiency data set at different nutrient solution concentrations during the entire growth period of hydroponic lettuce;

[0016] Use min-max normalization to linearly map the data to the [0, 1] interval, and the formula is as follows:

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] Among them, 、 、 、 are the original cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency data respectively, 、 , , are the normalized data of cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency, respectively;

[0022] The population photosynthetic rate data set is divided into a training set and a test set in a ratio of 8:2, and the population water use efficiency data set is divided into a training set and a test set in a ratio of 8:2. The population photosynthetic rate data set and the population water use efficiency data set both use cultivation time and nutrient solution concentration as features and population photosynthetic rate and population water use efficiency as labels;

[0023] Select the radial basis function RBF kernel as the kernel function of the support vector regression SVR model. is a two-dimensional input vector, is a two-dimensional input vector different from . The penalty coefficient C and kernel parameter γ to be optimized are optimized using the quantum genetic algorithm QGA. The population size is determined to be 50, the maximum number of iterations is 100, the quantum rotation angle is 0.08π, and the parameter ranges are C ∈ [0.05, 20] and γ ∈ [0.0001, 10]. The coefficient of determination of the 5-fold cross-validation of the test set is used as the evaluation index, and the fitness function , where is the true value of the test set, is the predicted value of the model, is the mean of the true values of the test set;

[0024] Initialize the quantum population. The penalty coefficient C and kernel parameter γ to be optimized are represented by 36 quantum bits respectively, for a total of 72 quantum bits.

[0025] Each quantum bit is initialized to a superposition state , that is, it is simultaneously in the ground state and as a linear combination. A quantum population consists of 70 quantum individuals, and each individual consists of 72 quantum bits. The encoding is as follows:

[0026] ,

[0027] where is the state of a quantum individual, is the state of the i-th quantum bit, and are the composite quantum states of 72 quantum bits, is the ground state in quantum computing, corresponding to 0 and 1 of the classical bit respectively;

[0028] Each quantum individual is composed of a 72-bit binary string. Among them, the first 36 bits of the binary string are decoded to obtain C, and the last 36 bits are decoded to obtain γ. The decoding formulas are as follows:

[0029] ,

[0030] ,

[0031] Among them, and respectively represent the binary strings of the penalty coefficient C and the kernel parameter γ, and respectively represent the conversion of the binary strings of C and γ into decimal strings;

[0032] On the population photosynthetic rate dataset, use the decoded C and γ to train the support vector regression SVR model, and use this model to make predictions on . Calculate the fitness value through the difference between the prediction result and the true value,

[0033] Use the model trained with the parameter combination decoded on the population water use efficiency dataset to make predictions on . Calculate the fitness value through the difference between the prediction result and the true value;

[0034] In each iteration, if the fitness of the current individual is higher than the population average, the quantum state rotates 0.08π towards the optimal solution; otherwise, it rotates in the opposite direction. The forward update formula is as follows:

[0035] ,

[0036] Among them, is the superposition state of the quantum bit, is the ground state, corresponding to 0 and 1 of the classical bit;

[0037] Generation of the optimal parameter combination: Continuously iterate until the maximum iteration number is reached or the fitness converges. At this time, the corresponding C and γ are the optimal parameter combination;

[0038] Construct the prediction model with the optimal parameters: Based on the optimal parameters of the time-series population photosynthetic rate dataset and the time-series population water use efficiency dataset respectively, construct the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model.

[0039] The multi-objective optimization model is constructed by taking the time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model as the objective function, taking the coordinated optimization of the plant population photosynthetic rate and the population water use efficiency as the goal, and taking the plant cultivation days and the hydroponic nutrient solution concentration as the constraints to construct the multi-objective optimization model; including the following steps:

[0040] Prediction model of photosynthetic rate of time series population and time series population water use efficiency prediction model As the objective function, the optimal synergy between the photosynthetic rate and water use efficiency of the group is taken as the goal. Assuming that the number of days for different cultivation of plants is , the concentration of hydroponic nutrient solution is , then the optimization goal of maximizing the photosynthetic rate of the group is , the optimization goal of the optimal water use efficiency of the group is ;

[0041] Construct a multi-objective optimization model as follows:

[0042] Objective function:

[0043] ,

[0044] Constraints:

[0045] ,

[0046] in, is the decision variable, The number of days the plants are cultivated is different. It is the concentration of different hydroponic nutrient solutions for plants; is the objective function, is a population photosynthetic rate prediction model, is a population water use efficiency prediction model, , They are the lower and upper limits of the plant's entire growth cycle, respectively; , They are respectively the lower and upper limits of the concentration of hydroponic nutrient solution for plant cultivation.

[0047] The Pareto solution set for solving the multi-objective optimization model is: introducing a uniformly distributed population strategy, applying a non-dominated sorting multi-objective genetic algorithm to solve the multi-objective optimization model, and obtaining a Pareto solution set that balances the photosynthetic rate and water use efficiency of the population during the entire growth cycle of the plant; comprising the following steps:

[0048] Introduce a uniformly distributed population strategy, initialize the population, and map the generated optimal point set to the concentration of the hydroponic nutrient solution The actual range of fixed cultivation days , return the two-dimensional objective vector of each individual ;

[0049] Based on the population photosynthetic rate prediction model and the population water use efficiency prediction model Calculate the population photosynthetic rate ACO2 and population water use efficiency WUE of each individual in the current iteration. After stratifying the individuals in the population according to non-dominated sorting, calculate the density of solutions within the same level through crowding degree, and preferentially select individuals in the lower level or with a larger crowding degree;

[0050] Adopt the tournament selection strategy to screen high-quality individuals into the next generation. Randomly select two individuals from the population, preferentially select individuals with a higher non-dominated level. If the levels are the same, select individuals with a larger crowding degree. The winning individuals serve as parents to participate in crossover and mutation;

[0051] The crossover operator is set as the SBX crossover operator. After randomly pairing the selected individuals, perform crossover operations with a crossover probability of 0.85 to generate new individuals; the mutation operator adopts the polynomial mutation operator, introduce mutations with a mutation probability of 0.9, maintain the diversity of the population, and prevent the population from falling into local optima;

[0052] Apply the elitist strategy and population update mechanism to retain historical high-quality solutions, prevent high-quality solutions from being eliminated during evolution, and approach the true Pareto front;

[0053] In each generation, based on non-dominated sorting and crowding degree calculation, adopt the tournament selection strategy to screen out individuals with better fitness as parents; perform SBX crossover operator and polynomial mutation operations on the parent individuals to generate the offspring population; merge the parents and offspring, and through non-dominated sorting and crowding degree screening, preferentially retain individuals in the non-dominated levels (F1, F2,...); repeat the above steps until the preset maximum number of iterations of 100 times. At this time, the convergence and distribution of the Pareto solution set tend to be stable, and finally obtain the Pareto solution set of the population photosynthetic rate and population water use efficiency;

[0054] The discrete-time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model are repeated in the cultivation days in the interval to solve the above steps to obtain the time series Pareto solution set.

[0055] The above-mentioned time series dynamic regulation of the nutrient solution concentration of hydroponic lettuce includes the following steps:

[0056] Use the cubic spline interpolation method to transform the uneven and discontinuous time series Pareto solution set into a uniformly continuous time series solution set;

[0057] ​Since the two objectives of canopy photosynthetic rate and canopy water use efficiency are equally important, that is, a non-preferential decision-making problem of multi-objective optimization, the knee point with cost-effectiveness and boundary utility in the Pareto solution set is selected as the optimal balance solution for the objective coordination and compromise between the two objectives of canopy photosynthetic rate and canopy water use efficiency, and the optimal balance solution of time series is obtained. The formula for the knee point is as follows:

[0058] ,

[0059] where a is the knee point, o is a solution in the Pareto solution set, L is the chord connecting the two end points, and D(o,L) is the normal distance from o to L;

[0060] According to the optimal balance solution of time series, the optimal nutrient solution concentration of time series is obtained by inverse mapping based on the time series canopy photosynthetic rate prediction model and the canopy water use efficiency prediction model, that is, the target value of time series regulation of nutrient solution concentration;

[0061] Construction of the time series regulation model of nutrient solution concentration: Taking the cultivation days as the input and the target value of time series regulation of nutrient solution concentration as the output, a polynomial regression algorithm is used to construct the time series regulation model of nutrient solution concentration.

[0062] The construction of the prediction model with the optimal parameters includes the following steps:

[0063] Based on the optimal parameter penalty function C and kernel parameter γ of the canopy photosynthetic rate data set, a support vector regression (SVR) model is constructed,

[0064] The radial basis function kernel is selected as the kernel function, and the optimal parameter combination C and γ are set as the parameters of the model, and the normalized training data is input , and the SVR model determines the weights and biases of the optimal hyperplane based on the data and parameters, so as to fit the non-linear relationship between the input features and the canopy photosynthetic rate, and outputs the time series canopy photosynthetic rate prediction model ;

[0065] Using the radial basis function as the kernel function, the optimal combination C and γ of the optimized canopy water use efficiency data set are set as the parameters of the SVR model, and the normalized training data is input , and the SVR model fits the non-linear relationship between the input features and the canopy water use efficiency, and outputs the time series canopy water use efficiency prediction model ;

[0066] The time series canopy photosynthetic rate prediction model and the time series canopy water use efficiency prediction model are trained multiple times, and 5-fold cross-validation is used to select the model with the smallest mean root mean square error and the largest determination coefficient as the final model.

[0067] The strategy for introducing a uniformly distributed population is as follows:

[0068] Due to the problem of uneven distribution caused by the random generation of the initial population, a good point set generation method based on prime number theory is introduced. Based on the uniform distribution characteristics in number theory as the theoretical basis, a high-quality initial population with low deviation characteristics is constructed. The mathematical model for generating population individuals within the interval [0, 1) is as follows:

[0069] ,

[0070] where is the k-th individual of the population, is the modulo 1 operation, which maps the numerical value to the interval [0, 1). p is the smallest prime number satisfying (p - 3) / 2 ≥ s, and s is the spatial dimension of 2D, that is , and N is the set population number of 70;

[0071] Map the generated good point set to the actual value range of the hydroponic nutrient solution concentration It is known that the range of the hydroponic nutrient solution concentration is , and the linear mapping formula is , and the finally formed initial population , where k is the k-th individual of the population.

[0072] After stratifying the individuals in the population according to non-dominated sorting, the density of solutions within the same layer is quantified by calculating the crowding degree, including the following steps:

[0073] After stratifying the individuals in the population according to non-dominated sorting, the density of solutions within the same layer is quantified by calculating the crowding degree, including the following steps:

[0074] Stratify the individuals in the population according to the superiority and inferiority relationship to find the Pareto optimal front:

[0075] First, judge the dominance relationship: For any two individuals x u and x v , if the two objective function values of x u are both greater than or equal to those of x v and at least one objective is strictly better, then it is determined that x u dominates x v ;

[0076] Secondly, perform hierarchical sorting: Maintain the dominance number and dominance set for each individual. In the first layer, screen all individuals that are not dominated by any individual, that is, individuals with a dominance number of zero, as the Pareto front layer F1;

[0077] For the current layer F wFor each individual in it, gradually reduce the domination number of the individuals in its domination set. If the domination number of an individual reaches zero, classify it into the next level F. w+1 ; Repeat this process until all individuals are assigned to the corresponding levels; Finally, the population is divided into a hierarchical structure of F1, F2, …, F. m where F1 represents the global optimal solution set, and the higher the level, the lower the quality of the solution.

[0078] Introduce the crowding distance to quantify the sparsity of individuals in the objective space and maintain the uniform distribution of the solution set within the same level.

[0079] For the individuals in the current level F. w Sort the individuals in descending order according to each objective function value respectively to generate sorted lists L1 and L2; Identify the extreme points of each objective sorted list and assign them an infinite crowding distance. to ensure the coverage of the Pareto front; For non-boundary individuals, calculate the difference between adjacent solutions for each objective, normalize the difference to eliminate the dimension difference, and the total crowding distance of an individual is the sum of the normalized differences for each objective:

[0080] ,

[0081] where , are the values of the adjacent individuals of the i-th individual after sorting on the -th objective respectively, and are the maximum and minimum values of all individuals in the current level on the objective function respectively.

[0082] The application of the elite strategy and population update mechanism includes the following steps:

[0083] Merge the N-individual parent population and the N-individual offspring population into a temporary population of size 2N.

[0084] Perform non-dominated sorting on the temporary population and divide it into a hierarchical sequence of F1, F2, …, F. m , preferentially select the individuals in the F1 layer to fill the new generation population. If the number of individuals in the F1 layer n1 ≤ N, retain all of them. If n1 < N, continue to add the individuals in the F2 layer until the total number is close to N.

[0085] When the number of individuals in a certain level F. w exceeds the remaining capacity, sort them in descending order according to the crowding distance, and preferentially select the individuals with sparse distribution.

[0086] Through the above steps, N optimal solutions are selected from the merged 2N individuals to form a new generation population, inheriting the elite solutions of the parent generation and expanding the diversity of the offspring solution set.

[0087] The construction of the time - series regulation model for nutrient solution concentration includes the following steps:

[0088] Expand the input features into the form of b - th polynomial features, and its model is:

[0089]

[0090] where is the coefficient of the b - th term of the polynomial;

[0091] Divide the data set into an 80% training set and a 20% test set;

[0092] Use a linear regression model to fit the polynomial features. Since the extended polynomial features fit non - linear relationships, use Python to train the model to learn the coefficients of the polynomial features and verify them on the test set to obtain the time - series regulation model for nutrient solution concentration as follows:

[0093]

[0094] where, is the cultivation time, is the concentration of hydroponic nutrient solution.

[0095] Beneficial effects

[0096] For the method for multi - objective collaborative optimization of time - series dynamic regulation of hydroponic lettuce nutrient solution concentration in the present invention, compared with the prior art, a non - dominated sorting multi - objective genetic algorithm is used to solve the multi - objective problems of the time - series population photosynthetic rate prediction model and the time - series population water use efficiency prediction model. By combining a uniform distribution population strategy, non - dominated sorting, crowding degree calculation, elite strategy, and population update mechanism, the optimal balanced regulation target value is obtained, effectively solving the problem of dynamic regulation of nutrient solution concentration during the time - series growth of plants.

[0097] The present invention first constructs a prediction model for the temporal population photosynthetic rate and a prediction model for the temporal population water use efficiency, and seeks a balanced solution that optimizes the coordination of the population photosynthetic rate and the population water use efficiency under constrained conditions in the temporal variation of the nutrient solution concentration required during the dynamic growth process of plants interacting with the environment. Taking the prediction model for the temporal population photosynthetic rate and the prediction model for the temporal population water use efficiency as the objective functions, the non-dominated sorting multi-objective genetic algorithm is used to divide the Pareto levels based on fast non-dominated sorting, and the crowding degree is coupled to evaluate the distribution density of the solution set; the tournament selection is used to drive the crossover and mutation to generate offspring, and after fusing the parent and offspring populations, hierarchical screening is performed to retain the elite solution set with high convergence and diversity, dynamically balancing the approximation and coverage, and efficiently approaching the complex Pareto front. Finally, the knee point on the Pareto front is selected as the optimal balanced solution, a temporal regulation model for the nutrient solution concentration is constructed, and it is embedded in the hydroponic intelligent monitoring and regulation system to dynamically regulate the nutrient solution concentration during the entire growth cycle of hydroponic lettuce.

[0098] The present invention verifies the method for the temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce through a 30-day cultivation experiment, and sets up a temporal regulation model for the nutrient solution concentration (model group), regulates the nutrient solution concentration to a constant value (constant group), and does not regulate the nutrient solution concentration (blank group) for comparative analysis. The results show that the water use efficiency of the model group is higher than that of the control group, and is increased by 16.79% and 32.86% respectively compared with the constant group and the blank group. The health index in the model group is also the highest, which is increased by 9.71% compared with the constant group and 12.21% compared with the blank group. The fresh weight of the stems in the model group is significantly higher than that of the control group, increasing by 30.94% compared with the constant group and 44.91% compared with the blank group. The dry weight of the stems in the model group is higher than that of the control group, increasing by 17.55% compared with the control group and 22.99% compared with the blank group. The experiment shows that the lettuce cultivated by using the regulation method of the present invention improves the water use efficiency and the healthy growth of plants, thereby effectively promoting the economic yield of lettuce. Description of the Drawings

[0099] Figure 1 It is the method sequence diagram of the present invention;

[0100] Figure 2 It is the on-site photo of the cultivation experiment of the present invention;

[0101] Figure 3 It is the visualization of the prediction model for the temporal population photosynthetic rate of the present invention;

[0102] Figure 4 It is the visualization of the prediction model for the temporal population water use efficiency of the present invention;

[0103] Figure 5 It is the distribution diagram of the Pareto solution set obtained by solving with the non-dominated sorting multi-objective genetic algorithm of the present invention;

[0104] Figure 6 This is the distribution diagram of the optimal balance solution of the present invention in the Pareto solution set;

[0105] Figure 7 This is the distribution diagram of the optimal balance solution of the present invention in the prediction model of the temporal population photosynthetic rate;

[0106] Figure 8 This is the distribution diagram of the optimal balance solution of the present invention in the prediction model of the temporal population water use efficiency;

[0107] Figure 9 This is the visualization of the temporal regulation model of the nutrient solution concentration of the present invention;

[0108] Figure 10 This is the comparison diagram of the model and control group parameters in the verification experiment of the present invention. Detailed implementation manners

[0109] To have a further understanding and recognition of the structural features and achieved effects of the present invention, the following is a detailed description with preferred embodiments and accompanying drawings:

[0110] As Figure 1 shown, a method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to the present invention includes the following steps:

[0111] The first step, as Figure 3 and Figure 4 shown, construct a prediction model of the temporal population photosynthetic rate and a prediction model of the temporal population water use efficiency. First, data normalization processing is performed on the population photosynthetic rate dataset and the population water use efficiency dataset. By converting the characteristic data of different cultivation days and hydroponic nutrient solution concentrations into a unified [0, 1] numerical range, it is ensured that the contributions of the characteristics to the subsequent support vector regression SVR model are balanced, thus avoiding the adverse effects of different dimensions and scales on the model performance. Subsequently, the dataset is randomly divided into a training set and a test set, and 5-fold cross-validation is used to evaluate the performance of the SVR model. Cross-validation can effectively avoid overfitting and provide a more stable and reliable model evaluation.

[0112] To further optimize the hyperparameters of the SVR model, especially the penalty parameter C and the kernel function parameter r, a quantum genetic algorithm (QGA) was introduced for evolutionary optimization. Compared with the traditional genetic algorithm, QGA represents the solution space through qubits, enabling the search process to explore multiple solutions in parallel, significantly enhancing the global search ability, and avoiding the limitation of the traditional genetic algorithm being prone to falling into local optimal solutions. Specifically, QGA first generates an initial population through qubit encoding, where each individual is represented as a binary string of quantum state superposition. Then, a fitness function based on the coefficient of determination of the test set is constructed, and a quantum rotation gate dynamic update strategy is designed to optimize the solution quality. Through quantum superposition and interference effects, QGA can achieve the effective evolution of the population, thus avoiding the problem of premature convergence. Quantum parallelism significantly improves the efficiency of global search, enabling the algorithm to find better solutions in a shorter time. After multiple iterations, until the maximum number of iterations is reached or the fitness converges, QGA finally obtains the optimal hyperparameter combination, that is, the penalty parameter C and the kernel function parameter most suitable for the SVR model. Based on the optimal parameters of the time-series population photosynthetic rate dataset and the time-series population water use efficiency dataset respectively, a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model were constructed. This process not only effectively improves the prediction accuracy of the model but also proves the powerful ability of QGA in high-dimensional data optimization. Especially when facing complex nonlinear problems, the application of QGA has significant technical advantages.

[0113] (1) A population photosynthetic rate measuring instrument was used to obtain the population photosynthetic rate dataset and the population water use efficiency dataset under different nutrient solution concentrations during the entire growth period of hydroponic lettuce.

[0114] (2) Min-max normalization was used to linearly map the data to the [0, 1] interval. The formula is as follows:

[0115] ,

[0116] ,

[0117] ,

[0118] ,

[0119] where , , , are the original cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency data respectively, , , , They are the data of normalized cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency respectively;

[0120] The population photosynthetic rate dataset is divided into a training set and a test set at a ratio of 8:2, and the population water use efficiency dataset is divided into a training set and a test set at a ratio of 8:2. The population photosynthetic rate dataset and the population water use efficiency dataset both use cultivation time and nutrient solution concentration as features and population photosynthetic rate and population water use efficiency as labels.

[0121] (3)Select the radial basis function RBF kernel as the kernel function of the support vector regression SVR model. is a two-dimensional input vector, is a two-dimensional input vector different from . The penalty coefficient C and kernel parameter γ to be optimized are optimized using the quantum genetic algorithm QGA. The population size is determined to be 50, the maximum number of iterations is 100, the quantum rotation angle is 0.08π, and the parameter ranges are C ∈ [0.05, 20] and γ ∈ [0.0001, 10]. The coefficient of determination of 5-fold cross-validation of the test set is used as the evaluation index, and the fitness function where is the true value of the test set, is the predicted value of the model, is the mean of the true values of the test set.

[0122] (4)Initialize the quantum population. The penalty coefficient C and kernel parameter γ to be optimized are represented by 36 quantum bits respectively, for a total of 72 quantum bits.

[0123] Each quantum bit is initialized to a superposition state , that is, a linear combination of the ground state and at the same time. A quantum population consists of 70 quantum individuals, and each individual consists of 72 quantum bits. The encoding is as follows:

[0124] ,

[0125] where is the state of a quantum individual, is the state of the i-th quantum bit, and are the composite quantum states of 72 quantum bits, is the ground state in quantum computing, corresponding to 0 and 1 of the classical bit respectively;

[0126] Each quantum individual is composed of a 72-bit binary string. Among them, the first 36 bits of the binary string are decoded to obtain C, and the last 36 bits are decoded to obtain γ. The decoding formulas are as follows:

[0127] ,

[0128] ,

[0129] Among them, 、 respectively represent the binary strings of the penalty coefficient C and the kernel parameter γ, 、 respectively represent the conversion of the binary strings of C and γ into decimal strings;

[0130] On the population photosynthetic rate dataset, use the decoded C and γ to train the support vector regression SVR model, and use this model to make predictions, and calculate the fitness value through the difference between the prediction result and the true value.

[0131] Use the model trained with the parameter combination decoded on the population water use efficiency dataset to make predictions, and calculate the fitness value through the difference between the prediction result and the true value.

[0132] (5) In each iteration, if the fitness of the current individual is higher than the population average, the quantum state rotates 0.08π towards the optimal solution; otherwise, it rotates in the opposite direction. The forward update formula is as follows:

[0133] ,

[0134] Among them, is the superposition state of the quantum bit, is the ground state, corresponding to 0 and 1 of the classical bit.

[0135] (6) Generation of the optimal parameter combination: Continuously iterate until the maximum iteration number is reached or the fitness converges. At this time, the corresponding C and γ are the optimal parameter combination.

[0136] (7) Based on the optimal parameters of the time-series population photosynthetic rate dataset and the time-series population water use efficiency dataset, construct a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model. The steps are as follows:

[0137] A1) Based on the optimal parameter penalty function C and kernel parameter γ of the population photosynthetic rate dataset, construct a support vector regression SVR model,

[0138] Select the radial basis function kernel as the kernel function, set the optimal parameter combination C and γ as the parameters of the model, and input the normalized training data , the SVR model determines the weights and biases of the optimal hyperplane based on data and parameters, thereby fitting the non-linear relationship between the input features and the population photosynthetic rate, and outputting a time-series population photosynthetic rate prediction model. ;

[0139] A2) Using the radial basis function as the kernel function, set the optimal combination C and γ of the optimized population water use efficiency dataset as the parameters of the SVR model, and input the normalized training data. , the SVR model fits the non-linear relationship between the input features and the population water use efficiency, and outputs a time-series population water use efficiency prediction model. ;

[0140] A3) Train the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model multiple times, and use 5-fold cross-validation to select the model with the smallest mean root mean square error and the largest determination coefficient as the final model.

[0141] The second step is to construct a multi-objective optimization model. Take the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model as the objective functions, aim at the collaborative optimization of the plant population photosynthetic rate and the population water use efficiency, and construct a multi-objective optimization model with the plant cultivation days and the hydroponic nutrient solution concentration as the constraint conditions.

[0142] There is a dynamic competitive relationship between the population photosynthetic rate and the population water use efficiency: when plants increase the stomatal aperture to improve the photosynthetic rate, it will accelerate the transpiration rate, thereby reducing the water use efficiency; reducing the stomatal aperture to improve the water use efficiency will inhibit the photosynthetic rate due to the reduction of carbon dioxide supply. In addition, the nutrient solution environment of the hydroponic system is the metabolic basis for plant growth and has a significant impact on plant growth and development. At the same time, plant growth shows non-linear time-varying characteristics - the response functions to the environment are significantly different at different growth times, and there is a physiological lag effect. Traditional single-objective optimization is difficult to solve this multi-dimensional spatio-temporal coupling problem. Compared with single-objective problems, multi-objective optimization problems can optimize multiple objectives simultaneously, are closer to practical problems, and have practical application significance. The multi-objective evolutionary algorithm can globally search for potential optimal solutions and obtain the entire solution set in a single run, which can effectively improve the solution speed. Therefore, it is widely used to solve practical multi-objective problems.

[0143] Constructing a multi-objective optimization model includes the following steps:

[0144] (1) Using the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model is the objective function, aiming at the collaborative optimization of the population photosynthetic rate and the population water use efficiency. Assuming that the different cultivation days of the plants are , and the concentration of the hydroponic nutrient solution is , then the optimization objective for the maximum population photosynthetic rate is , and the optimization objective for the optimal population water use efficiency is

[0145] (2)Construct a multi-objective optimization model as follows:

[0146] Objective function:

[0147] ,

[0148] Constraints:

[0149] ,

[0150] Among them, is the decision variable, is the different cultivation days of the plants, is the different concentrations of the hydroponic nutrient solution of the plants; is the objective function, is the prediction model of the population photosynthetic rate, is the prediction model of the population water use efficiency, , are the lower and upper limits of the entire growth period of the plants respectively; , are the lower and upper limits of the cultivation of the hydroponic nutrient solution concentration of the plants respectively.

[0151] The third step is to solve the Pareto solution set of the multi-objective optimization model. As Figure 5 , Figure 6 , Figure 7 and Figure 8 shown, introduce the uniform distribution population strategy, and apply the non-dominated sorting multi-objective genetic algorithm to solve the multi-objective optimization model to obtain the Pareto solution set that balances the population photosynthetic rate and the population water use efficiency within the entire growth period of the plants.

[0152] The non-dominated sorting multi-objective genetic algorithm is used to solve the multi-objective optimization problems of the temporal population photosynthetic rate prediction model and the temporal population water use efficiency prediction model. It can effectively solve the conflicts between multiple objectives and simultaneously consider the difficult problem of nutrient solution concentration regulation in the complex dynamic changes during the plant growth process. To ensure the global search ability and convergence speed, a uniformly distributed population strategy is introduced to generate the initial population, ensuring sufficient exploration of the solution space and avoiding the population concentrating in a certain local area, thereby improving the optimization efficiency. The non-dominated sorting method is used to sort the individuals in the population according to the dominance relationship, which can effectively divide the Pareto front and determine which solutions are "non-dominated solutions", so as to find a set of balanced optimal solutions and overcome the limitations of the simple sorting method in the multi-objective case. On the basis of non-dominated sorting, the crowding degree calculation further evaluates the "crowding degree" of individuals, that is, the density of the solution in the objective space. A solution with a smaller crowding degree represents a sparser solution in this area, usually meaning that the solution has a stronger representativeness in the multi-objective space, so it has a higher selection probability, effectively avoiding the concentration of solutions and the loss of diversity. The population is updated through the tournament selection strategy, SBX crossover operator and polynomial mutation operator, and the elite strategy is applied to ensure the retention of high-quality solutions, that is, the best individuals in each generation will directly enter the next generation. This strategy can effectively avoid the loss of excellent solutions during the iteration process and improve the convergence and stability of the algorithm. The population continuously repeats the above steps until the preset maximum number of iterations of 100 times is reached. At this time, the convergence and distribution of the Pareto solution set tend to be stable, and finally the Pareto solution set of the population photosynthetic rate and the population water use efficiency is obtained. Finally, the discrete temporal population photosynthetic rate prediction model and the temporal population water use efficiency prediction model repeat the above steps at different cultivation days to obtain the temporal Pareto solution set.

[0153] Compared with the traditional single-objective optimization method, the non-dominated sorting multi-objective genetic algorithm has significant advantages, especially when dealing with complex multi-objective optimization problems. The traditional single-objective optimization method usually can only optimize a specific objective. In multi-objective optimization, there are often conflicts between different objectives. The traditional method cannot consider the mutual relationship of multiple objectives at the same time, resulting in being prone to falling into local optimal solutions during the optimization process and unable to effectively explore the entire solution space. In contrast, the non-dominated sorting multi-objective genetic algorithm can comprehensively consider multiple objectives under the framework of global search by introducing mechanisms such as non-dominated sorting, crowding degree calculation and elite strategy, find a set of balanced Pareto optimal solutions, avoid the degradation of solutions and the dilemma of local optimality in single-objective optimization, and provide more powerful optimization ability and flexibility in practical applications.

[0154] It includes the following steps:

[0155] (1) Introduce a uniformly distributed population strategy, initialize the population, and map the generated good point set to the hydroponic nutrient solution concentration The actual range, fixed cultivation days , return the two-dimensional target vector of each individual .

[0156] Introduce the uniform distribution population strategy as follows:

[0157] Due to the problem of uneven distribution that may be caused by the random generation of the initial population, introduce the good point set generation method based on prime number theory. Based on the uniform distribution characteristics in number theory as the theoretical basis, construct a high-quality initial population with low deviation characteristics. The mathematical model for generating population individuals within the interval [0, 1) is as follows:

[0158] ,

[0159] where, is the k-th individual of the population, is the modulo 1 operation, which maps the value to the interval [0, 1). p is the smallest prime number satisfying (p - 3) / 2 ≥ s, and s is the spatial dimension of 2D, that is , and N is the set population number of 70;

[0160] Map the generated good point set to the actual value range of the hydroponic nutrient solution concentration ; The known range of the hydroponic nutrient solution concentration is , and the linear mapping formula is , and the finally formed initial population , where k is the k-th individual of the population.

[0161] (2) Based on the population photosynthetic rate prediction model and the population water use efficiency prediction model Calculate the population photosynthetic rate ACO2 and the population water use efficiency WUE of each individual in the current iteration. After stratifying the individuals in the population according to the Pareto dominance relationship, quantify the crowding degree of the solutions within the same layer, and preferentially select individuals in the lower layer or with a greater crowding degree.

[0162] After stratifying the individuals in the population according to the Pareto dominance relationship, quantifying the crowding degree of the solutions within the same layer includes the following steps:

[0163] A1) Stratify the individuals in the population according to the superiority and inferiority relationship to find the Pareto optimal front:

[0164] First, perform the dominance relationship judgment: For any two individuals x u and x v , if the two objective function values of x u are both greater than or equal to those of x v and at least one objective is strictly better, then it is determined that x u dominates xv ;

[0165] Secondly, perform hierarchical sorting: maintain the domination number and domination set for each individual. In the first layer, screen all individuals that are not dominated by any other individual, that is, individuals with a domination number of zero as the Pareto front F1 layer;

[0166] For individuals in the current layer F w , gradually reduce the domination numbers of individuals within their domination sets. If an individual's domination number becomes zero, classify it into the next layer F w+1 ; repeat this process until all individuals are assigned to the corresponding layers; finally, the population is divided into a hierarchical structure of F1, F2, …, F m , where F1 represents the global optimal solution set, and the higher the layer, the lower the quality of the solutions;

[0167] A2) Introduce the crowding distance to quantify the sparsity of individuals in the objective space and maintain the distribution uniformity of the solution set within the same layer;

[0168] For individuals in the current layer F w , sort them in descending order according to each objective function value respectively to generate sorted lists L1 and L2; identify the extreme points of each objective sorted list and assign them an infinite crowding distance to ensure the coverage of the Pareto front; for non-boundary individuals, calculate the differences between adjacent solutions for each objective, normalize the differences to eliminate the dimension differences, and the total crowding distance of an individual is the sum of the normalized differences for each objective:

[0169] ,

[0170] where , are the values of the adjacent individuals of the i-th individual after sorting for the -th objective respectively, and are the maximum and minimum values of all individuals in the current layer for the objective function respectively.

[0171] (3) Adopt the tournament selection strategy to screen high-quality individuals into the next generation. Randomly select two individuals from the population, and preferentially select individuals with a higher non-domination level. If the levels are the same, select the individual with a larger crowding distance. The winning individual serves as a parent to participate in crossover and mutation.

[0172] (4) Set the crossover operator as the SBX crossover operator. After randomly pairing the selected individuals, perform crossover operations with a crossover probability of 0.85 to generate new individuals; adopt the polynomial mutation operator for the mutation operator, introduce mutations with a mutation probability of 0.9 to maintain population diversity and prevent the population from falling into local optima.

[0173] (5) Apply the elitist strategy and population update mechanism to retain historical high-quality solutions, prevent high-quality solutions from being eliminated during evolution, and approach the true Pareto front.

[0174] Applying the elitist strategy and population update mechanism includes the following steps:

[0175] Merge the N-individual parent population and the N-individual offspring population into a temporary population of size 2N;

[0176] Perform non-dominated sorting on the temporary population and divide it into a hierarchical sequence F1, F2, …, F m , preferentially select individuals in layer F1 to fill the new generation population. If the number of individuals in layer F1, n1 ≤ N, then retain all of them. If n1 < N, continue to add individuals in layer F2 until the total number is close to N;

[0177] When the number of individuals in a certain layer F w exceeds the remaining capacity, sort them in descending order of crowding distance, and preferentially select individuals with sparse distribution;

[0178] Through the above steps, N optimal solutions are selected from the merged 2N individuals to form a new generation population, which inherits the elite solutions of the parent generation and expands the diversity of the offspring solution set.

[0179] (6) In each generation, based on non-dominated sorting and crowding degree calculation, adopt the tournament selection strategy to screen out individuals with better fitness as parents; perform the SBX crossover operator and polynomial mutation operation on the parent individuals to generate an offspring population; merge the parents and offspring, and through non-dominated sorting and crowding degree screening, preferentially retain individuals in the non-dominated levels (F1, F2, …); repeat the above steps until the preset maximum number of iterations, 100 times, at which time the convergence and distribution of the Pareto solution set tend to be stable, and finally obtain the Pareto solution set of the population photosynthetic rate and the population water use efficiency.

[0180] (7) For the discrete-time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model, repeat the above steps to solve on the cultivation days in the interval to obtain the time series Pareto solution set.

[0181] Fourth step, as Figure 9 shown, construct the nutrient solution concentration time series regulation model: Select the knee point in the Pareto solution set as the optimal balance solution for coordination and compromise between the population photosynthetic rate and the population water use efficiency targets, and use the polynomial regression algorithm to construct the nutrient solution concentration time series regulation model.

[0182] In the multi-objective optimization problem, the population photosynthetic rate and the population water use efficiency are regarded as equally important objectives, that is, this problem is a non-preferential decision-making problem, and an objective solution needs to be selected as a coordinated and compromised equilibrium solution. To make a reasonable choice without introducing subjective preferences, the knee point with cost-effectiveness and boundary utility in the Pareto front is considered an ideal decision point. The knee point represents a solution that naturally balances multiple objectives. Its selection not only avoids human intervention but also provides a solution with high practical value in the optimization process. First, cubic spline interpolation is performed on the time-series Pareto solution set to generate a uniformly and continuously distributed time-series solution set. By selecting the knee point with the maximum vertical normal distance as the optimal balance solution, a solution with the best compromise characteristics in the objective space is effectively found, thus achieving an effective balance between the population photosynthetic rate and the population water use efficiency. Based on the selected optimal balance solution, inverse mapping is performed using the time-series population photosynthetic rate prediction model and the population water use efficiency prediction model to obtain the corresponding time-series nutrient solution concentration, that is, the target value of the time-series regulation of the nutrient solution concentration. Using the cultivation days as input features, they are extended to the form of quartic polynomial features to form a high-dimensional feature space to capture the non-linear relationship between the input and the output. Then the data set is divided into a training set and a test set, and a linear regression model is used to fit the extended polynomial features. Through the polynomial regression model, a time-series regulation model of the nutrient solution concentration is constructed, providing a reliable theoretical support for the regulation of the nutrient solution concentration during the plant growth process.

[0183] The time-series dynamic regulation of the nutrient solution concentration for hydroponic lettuce includes the following steps:

[0184] (1) Use the cubic spline interpolation method to transform the uneven and discontinuous time-series Pareto solution set into a uniformly and continuously distributed time-series solution set.

[0185] (2) Since the two objectives of the population photosynthetic rate and the population water use efficiency are equally important, that is, a non-preferential decision-making problem for multi-objective optimization, select the knee point with cost-effectiveness and boundary utility in the Pareto solution set as the optimal balance solution for objective coordination and compromise between the two objectives of the population photosynthetic rate and the population water use efficiency, and obtain the time-series optimal balance solution. The formula for the knee point is as follows:

[0186] ,

[0187] where a is the knee point, o is a solution in a Pareto solution set, L is the chord connecting the two end points, and D(o,L) is the normal distance from o to L.

[0188] (3) According to the time-series optimal balance solution, inverse map to obtain the time-series best nutrient solution concentration, that is, the target value of the time-series regulation of the nutrient solution concentration, based on the time-series population photosynthetic rate prediction model and the population water use efficiency prediction model.

[0189] (4)Construction of the time - series regulation model for nutrient solution concentration: Taking the cultivation days as the input and the target value of the time - series regulation of nutrient solution concentration as the output, a polynomial regression algorithm is used to construct the time - series regulation model for nutrient solution concentration;

[0190] The construction of the time - series regulation model for nutrient solution concentration includes the following steps:

[0191] A1) Expand the input feature into the form of b - th order polynomial features, and its model is:

[0192]

[0193] where is the coefficient of the b - th term of the polynomial;

[0194] A2) Divide the data set into an 80% training set and a 20% test set;

[0195] A3) Use a linear regression model to fit the polynomial features. Since the extended polynomial features fit non - linear relationships, use Python to train the model to learn the coefficients of the polynomial features and verify them on the test set to obtain the time - series regulation model for nutrient solution concentration as follows:

[0196]

[0197] where, is the cultivation time, is the concentration of the hydroponic nutrient solution.

[0198] Here, the time - series regulation model for nutrient solution concentration can be embedded in the hydroponic intelligent monitoring and regulation system to dynamically regulate the concentration of the nutrient solution during the entire growth cycle of hydroponic lettuce.

[0199] Step 5, Dynamically regulate the concentration of the hydroponic lettuce nutrient solution in time series: Embed the time - series regulation model for nutrient solution concentration into the hydroponic intelligent monitoring and regulation system to dynamically regulate the concentration of the nutrient solution during the entire growth cycle of hydroponic lettuce.

[0200] Such as Figure 10As shown, through a 30-day cultivation experiment, the temporal dynamic regulation method of the nutrient solution concentration for hydroponic lettuce was verified. A temporal regulation model of the nutrient solution concentration (model group), a constant nutrient solution concentration (constant group), and a non-regulated nutrient solution treatment (blank group) were set up for comparative analysis. The results showed that the water use efficiency of the model group was higher than that of the control group, and it was increased by 16.79% and 32.86% compared with the constant group and the blank group respectively. The health index in the model group was also the highest, which was increased by 9.71% compared with the constant group and 12.21% compared with the blank group. The fresh weight of the stems in the model group was significantly higher than that of the control group, increased by 30.94% compared with the constant group, and increased by 44.91% compared with the blank group. The dry weight of the stems in the model group was higher than that of the control group, increased by 17.55% compared with the control group, and increased by 22.99% compared with the blank group. The experiment showed that the lettuce cultivated by using the regulation method of the present invention improved the water use efficiency and the healthy growth of plants, thus effectively promoting the economic yield of lettuce.

[0201] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification is only the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization, characterized in that, It includes the following steps: 11) Construct a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model; The construction of the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model includes the following steps: 111) Use a population photosynthetic rate measuring instrument to obtain a population photosynthetic rate dataset and a population water use efficiency dataset under different nutrient solution concentrations during the entire growth period of hydroponic lettuce respectively; 112) Use min-max normalization to linearly map the data to the interval [0, 1]. The formula is as follows: ， ， ， ， Among them, , , , are the original data of cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency respectively, , , , are the normalized data of cultivation time, nutrient solution concentration, population photosynthetic rate, and population water use efficiency respectively; Divide the dataset of population photosynthetic rate into a training set and a test set at a ratio of 8:

2. and a test set Divide the dataset of population water use efficiency into a training set and a test set at a ratio of 8:

2. and a test set Use the cultivation time and nutrient solution concentration as features, and the population photosynthetic rate and population water use efficiency as labels for both the dataset of population photosynthetic rate and the dataset of population water use efficiency. 113) Select the radial basis function RBF kernel as the kernel function of the support vector regression SVR model, is a two-dimensional input vector, is a two-dimensional input vector different from . The penalty coefficient C and kernel parameter γ to be optimized are optimized by the quantum genetic algorithm QGA. The population size is determined to be 50, the maximum number of iterations is 100, the quantum rotation angle is 0.08π, and the parameter ranges are C ∈ [0.05, 20] and γ ∈ [0.0001, 10]; the coefficient of determination of 5-fold cross-validation of the test set is used as the evaluation index, and the fitness function , where is the true value of the test set, is the predicted value of the model, is the mean value of the true values of the test set; 114) Initialize the quantum population. The penalty coefficient C and the kernel parameter γ to be optimized are represented by 36 quantum bits respectively, with a total of 72 quantum bits. Each qubit is initialized to a superposition state , that is, simultaneously in the ground state and A linear combination of. A quantum population consists of 70 quantum individuals, each of which consists of 72 qubits and is encoded as follows: ， Among them, is the state of a quantum individual, is the state of the i-th qubit, and is the composite quantum state of 72 qubits, is the ground state in quantum computing, corresponding to 0 and 1 of classical bits respectively; Each quantum individual is composed of a 72-bit binary string. Among them, the first 36 bits of the binary string are decoded to obtain C, and the last 36 bits are decoded to obtain γ. The decoding formula is as follows: ， ， Among them, and represent the binary strings of the penalty coefficient C and the kernel parameter γ respectively, and represent the conversion of the binary strings of C and γ into decimal strings respectively; On the dataset of population photosynthetic rate, the obtained C and γ are used to train the support vector regression (SVR) model, and this model is used to make predictions on . The fitness value is calculated based on the difference between the predicted result and the true value. The model trained with the parameter combination decoded on the dataset of population water use efficiency predicts and calculates the fitness value through the difference between the prediction result and the true value. 115) In each iteration, if the fitness of the current individual is higher than the population average, the quantum state rotates 0.08π in the direction of the optimal solution; otherwise, it rotates in the opposite direction. The forward update formula is as follows: ， Among them, is the superposition state of qubits, is the ground state, corresponding to 0 and 1 of classical bits; 116) Generation of the optimal parameter combination: Continuously iterate until the maximum number of iterations is reached or the fitness converges. At this time, the corresponding C and γ are the optimal parameter combination; 117) Construct a prediction model with the optimal parameters: Based on the optimal parameters of the time-series population photosynthetic rate dataset and the time-series population water use efficiency dataset respectively, construct a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model; 12) Construct a multi-objective optimization model; 13) Solve the Pareto solution set of the multi-objective optimization model; The solution of the Pareto solution set of the multi-objective optimization model is as follows: Introduce a uniform distribution population strategy, and apply the non-dominated sorting multi-objective genetic algorithm to solve the multi-objective optimization model to obtain the Pareto solution set that balances the population photosynthetic rate and the population water use efficiency during the entire growth period of the plant; it includes the following steps: 131) Introduce the uniformly distributed population strategy, initialize the population, map the generated good point set to the actual range of the hydroponic nutrient solution concentration, fix the cultivation days , and return the two-dimensional objective vector of each individual ; ; 132) Based on the population photosynthetic rate prediction model and the population water use efficiency prediction model Calculate the population photosynthetic rate ACO2 and the population water use efficiency WUE of each individual in the current iteration. After stratifying the individuals in the population according to non-dominated sorting, calculate the crowding degree to quantify the density of solutions within the same level, and preferentially select individuals in the lower level or with a greater crowding degree; 133) Adopt a tournament selection strategy to screen high-quality individuals into the next generation. Randomly select two individuals from the population, and preferentially select individuals with a higher non-dominated level. If the levels are the same, select the individual with a larger crowding degree. The winning individual serves as the parent to participate in crossover and mutation; 134) The crossover operator is set as the SBX crossover operator. After randomly pairing the selected individuals, perform crossover operations with a crossover probability of 0.85 to generate new individuals; the mutation operator adopts a polynomial mutation operator, and introduces mutations with a mutation probability of 0.9 to maintain population diversity and prevent the population from falling into local optima; 135) Apply an elite strategy and a population update mechanism to retain historical high-quality solutions, prevent high-quality solutions from being eliminated during evolution, and approach the true Pareto front; 136) In each generation, based on non-dominated sorting and crowding degree calculation, the tournament selection strategy is adopted to screen out individuals with better fitness as the parental generation; the SBX crossover operator and polynomial mutation operation are performed on the parental individuals to generate the offspring population; the parental generation and the offspring are combined, and through non-dominated sorting and crowding degree screening, individuals in the non-dominated levels (F1, F2, …) are preferentially retained; repeat the above steps until the preset maximum number of iterations of 100 times is reached. At this time, the convergence and distribution of the Pareto solution set tend to be stable, and finally, the Pareto solution set of the population photosynthetic rate and the population water use efficiency is obtained; 137) The discrete-time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model are solved by repeating the above steps for the cultivation days in the interval to obtain the time series Pareto solution set, where and are the lower and upper limits of the entire growth period of the plant, respectively; 14) Construct a time-series regulation model for nutrient solution concentration: Select the knee-point optimal balance solution in the Pareto solution set, and use the polynomial regression algorithm to construct a time-series regulation model for nutrient solution concentration; 141) Use the cubic spline interpolation method to transform the uneven and discontinuous time-series Pareto solution set into a uniformly continuous distributed time-series solution set; 142) Since the two objectives of the population photosynthetic rate and the population water use efficiency are equally important, that is, the non-preference decision-making problem of multi-objective optimization, select the knee points with cost-effectiveness and boundary utility in the Pareto solution set as the optimal balance solution for the objective coordination and compromise between the two objectives of the population photosynthetic rate and the population water use efficiency, and obtain the optimal balance solution of the time series. The formula for the knee point is as follows: ， where a is the knee point, o is a solution in a Pareto solution set, L is the chord connecting the two end points, and D(o, L) is the normal distance from o to L; 143) According to the optimal balance solution of the time series, the best nutrient solution concentration of the time series is obtained by inverse mapping based on the time-series population photosynthetic rate prediction model and the population water use efficiency prediction model, that is, the target value of the time-series regulation of the nutrient solution concentration; 144) Construction of the time-series regulation model for nutrient solution concentration: Taking the cultivation days as the input and the target value of the time-series regulation of the nutrient solution concentration as the output, use the polynomial regression algorithm to construct a time-series regulation model for nutrient solution concentration; The construction of the time-series regulation model for nutrient solution concentration includes the following steps: 1441) Expand the input features into the b-th degree polynomial feature form, and its model is: ； wherein is the coefficient of the b-th term of the polynomial; 1442) Divide the data set into an 80% training set and a 20% test set; 1443) Use a linear regression model to fit polynomial features, while the extended polynomial features fit non-linear relationships. Use Python to train the model to learn the coefficients of the polynomial features and verify them on the test set to obtain the time-series regulation model of nutrient solution concentration as follows: ； Among them, is the cultivation time, is the concentration of the hydroponic nutrient solution; 15) Dynamically regulate the nutrient solution concentration of hydroponic lettuce in time series: Embed the time-series regulation model for nutrient solution concentration into the hydroponic intelligent monitoring and regulation system to dynamically regulate the nutrient solution concentration during the entire growth period of hydroponic lettuce.

2. The time-sequence dynamic regulation method for the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to claim 1, characterized in that The constructed multi-objective optimization model is: Taking the time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model as the objective functions, with the goal of the coordinated optimization of the plant population photosynthetic rate and the population water use efficiency, and constructing a multi-objective optimization model with the plant cultivation days and the hydroponic nutrient solution concentration as the constraint conditions; including the following steps: 21) Prediction model of photosynthetic rate of time series population and time series population water use efficiency prediction model As the objective function, the optimal synergy between the photosynthetic rate and water use efficiency of the group is taken as the goal. Assuming that the number of days for different cultivation of plants is , the concentration of hydroponic nutrient solution is , then the optimization goal of maximizing the photosynthetic rate of the group is , the optimization goal of the optimal water use efficiency of the group is ; 22) Construct a multi-objective optimization model as follows: Objective function: ， Constraint conditions: ， Among them, is a decision variable, is the different cultivation days of the plants, is the different hydroponic nutrient solution concentrations of the plants; is the objective function, is the population photosynthetic rate prediction model, is the population water use efficiency prediction model, and are the lower limit and upper limit of the entire growth period of the plants, respectively; and are the lower limit and upper limit of the cultivation of the hydroponic nutrient solution concentration of the plants, respectively.

3. A method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to claim 1, characterized in that The construction of the prediction model with optimal parameters includes the following steps: 31) Based on the optimal parameter penalty function C and kernel parameter γ of the population photosynthetic rate data set, construct a support vector regression SVR model, The kernel function is selected as the radial basis function kernel, and the optimal parameter combination C and γ are set as the parameters of the model, and the normalized training data is input , Based on the data and parameters, the SVR model determines the weights and biases of the optimal hyperplane, thereby fitting the nonlinear relationship between the input features and the population photosynthetic rate, and outputs the time-series population photosynthetic rate prediction model ; 32) Using the radial basis function as the kernel function, set the optimal combination C and γ of the optimized population water use efficiency dataset as the parameters of the SVR model, and input the normalized training data , the SVR model fits the non-linear relationship between the input features and the population water use efficiency, and outputs the time series population water use efficiency prediction model ; 33) Train the temporal population photosynthetic rate prediction model multiple times and the temporal population water use efficiency prediction model , and use 5-fold cross-validation to select the model with the smallest mean root mean square error and the largest determination coefficient as the final model.

4. A method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to claim 1, characterized in that, The introduction of the uniformly distributed population strategy is as follows: Construct a high-quality initial population with low deviation characteristics. The mathematical model for generating population individuals within the interval [0, 1) is as follows: ， Among them, is the k-th individual of the population, is the modulo 1 operation that maps the value to the interval [0, 1). p is the smallest prime number satisfying (p - 3) / 2 ≥ s, where s is the spatial dimension of 2D, that is , and N is the set population number of 70; Map the generated good point set to the actual value range of the hydroponic nutrient solution concentration ; Given that the range of the hydroponic nutrient solution concentration is , the linear mapping formula is , and the finally formed initial population , where k is the k-th individual of the population.

5. A method for temporal dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to claim 1, characterized in that, After stratifying the individuals in the population according to non-dominated sorting, quantifying the density of solutions within the same layer by crowding degree calculation includes the following steps: 51) Stratify the individuals in the population according to the superiority and inferiority relationship to find the Pareto optimal front: First, perform dominance relation judgment: For any two individuals x u and x v , if the two objective function values of x u are both greater than or equal to those of x v and at least one objective is strictly better, then it is determined that x u dominates x v ; Secondly, perform hierarchical sorting: maintain the domination number and domination set for each individual. In the first layer, screen all individuals that are not dominated by any individual, that is, individuals with a domination number of zero as the Pareto front F1 layer; For the individuals in the current layer F w Reduce the domination number of the individuals in their domination sets one by one. If the domination number of an individual reaches zero, include it in the next level F w+1 ; Repeat this process until all individuals are assigned to the corresponding levels; Finally, the population is divided into a hierarchical structure of F1, F2, …, F m , where F1 represents the global optimal solution set, and the higher the level, the worse the quality of the solution; 52) Introduce the crowding distance to quantify the sparsity of individuals in the objective space and maintain the uniform distribution of the solution set within the same layer; For the individuals in the current level F w Sort them in descending order according to each objective function value respectively to generate sorted lists L1 and L2; identify the extreme points of each objective sorted list and assign them infinite crowding degree , to ensure the coverage of the Pareto front; for non-boundary individuals, calculate the difference between adjacent solutions for each objective, normalize the difference to eliminate the dimension difference, and the total crowding distance of an individual is the sum of the normalized differences of each objective: ， Among them, , are the values of the adjacent individuals of the i-th individual after sorting on the th target, and are the maximum and minimum values of all individuals at the current level on the objective function respectively.

6. A method for time-sequential dynamic regulation of the nutrient solution concentration of hydroponic lettuce with multi-objective collaborative optimization according to claim 1, characterized in that, The application of the elitist strategy and the population update mechanism includes the following steps: 61) Merge the N-individual parent population and the N-individual offspring population into a temporary population of size 2N; 62) Perform non-dominated sorting on the temporary population and divide it into a hierarchical sequence F1, F2, …, F m , preferentially select individuals in layer F1 to fill the new generation population. If the number of individuals in layer F1, n1 ≤ N, retain all of them. If n1 < N, continue to add individuals in layer F2 until the total number is close to N; 63) When the number of individuals at a certain level F w exceeds the remaining capacity, sort them in descending order of crowding distance and preferentially select individuals with sparse distribution; 64) Through the above steps, screen out N optimal solutions from the merged 2N individuals to form a new generation of population, which inherits the elite solutions of the parent generation and expands the diversity of the offspring solution set.

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