Multi-objective collaborative optimization hydroponic lettuce nutrient solution concentration time sequence dynamic regulation and control method

Abstract

The invention relates to a multi-objective collaborative optimization hydroponic lettuce nutrient solution concentration time sequence dynamic regulation and control method. Compared with the prior art, the defect that an optimal nutrient solution concentration scheme needed by hydroponic crop time sequence dynamic growth interacting with the environment is difficult to determine is overcome. The method comprises the following steps: constructing a time sequence group photosynthetic rate prediction model and a time sequence group moisture utilization efficiency prediction model; constructing a multi-objective optimization model; solving a Pareto solution set of the multi-objective optimization model; constructing a nutrient solution concentration time sequence regulation and control model; dynamically regulating the concentration of the hydroponic lettuce nutrient solution in a time sequence. According to the method, a non-dominated sorting multi-target genetic algorithm is adopted to solve the multi-target problem of a time sequence group photosynthetic rate prediction model and a time sequence group water utilization efficiency prediction model, and an optimal balance regulation target value is obtained by combining a uniformly distributed population strategy, non-dominated sorting, crowding degree calculation, an elitist strategy and a population updating mechanism. The problem of dynamic regulation and control of the nutrient solution concentration for plant time sequence growth is effectively solved.

Description

Technical Field

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

[0002] like Figure 2 As shown in the figure, hydroponic vegetables are one of the important vegetable cultivation methods in modern agriculture. In the hydroponic system, too low or too high nutrient solution concentration will lead to restricted plant growth, so the appropriate nutrient solution concentration is critical to plant growth. However, plants have different requirements for nutrient solution concentration in different growth stages. Low nutrient solution concentration in the early growth stage can meet plant growth, and higher nutrient solution concentration in the middle and late growth stages can significantly increase the yield of lettuce. Therefore, the dynamic regulation of nutrient solution timing is of great significance to the sustainable development of hydroponic green vegetables.

[0003] The group photosynthetic rate accurately reflects the growth status of the plant, while the group 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 their maximum values ​​at the same time. When plants increase the stomatal aperture to increase the photosynthetic rate, the transpiration rate will be accelerated, thereby reducing the water use efficiency; reducing the stomatal aperture to increase the water use efficiency will inhibit the photosynthetic rate due to the reduction in carbon dioxide supply. Therefore, the key to solving this problem is to balance and coordinate the two objectives, and obtain the optimal balance solution of the group photosynthetic rate and the group water use efficiency through a multi-objective collaborative optimization method.

[0004] As a paradigm tool for complex system optimization, multi-objective evolutionary algorithms achieve global approximation of the Pareto frontier in non-convex, high-dimensional target spaces through the co-evolution mechanism of bionic operators (selection, crossover, and mutation). As a typical representative, the non-dominated sorting multi-objective genetic algorithm works together through dual mechanisms: a hierarchical screening architecture based on the Pareto dominance relationship, a fast non-dominated sorting is used to establish the dominance level of the solution, and an elite retention strategy is combined to accelerate population convergence; a dynamic crowding distance operator is introduced to maintain the uniformity of population distribution, effectively overcoming the diversity degradation problem of traditional algorithms on complex frontiers. At present, although Chen has explored the photosynthetic rate and light energy utilization rate of hydroponic plants using a multi-objective optimization algorithm, it ignores the most basic dynamic regulation mechanism of nutrient solution concentration and population scale effect for the growth of hydroponic crops.

[0005] Therefore, how to achieve time-series dynamic regulation of the concentration of nutrient solution for hydroponic lettuce has become a technical problem that needs to be solved urgently. Summary of the invention

[0006] The purpose 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 time-series dynamic growth of hydroponic crops that interact with the environment, and to provide a multi-objective collaborative optimization method for the time-series dynamic control of the nutrient solution concentration of hydroponic lettuce to solve the above problem.

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

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

[0009] Construct a prediction model for photosynthetic rate of a time series population and a prediction model for water use efficiency of a time series population;

[0010] Construct multi-objective optimization models;

[0011] Find the Pareto solution set of multi-objective optimization models;

[0012] Constructing a time-series control model for nutrient solution concentration: Selecting the optimal equilibrium solution at the knee point in the Pareto solution set, and using a polynomial regression algorithm to construct a time-series control model for nutrient solution concentration;

[0013] Dynamically control the concentration of nutrient solution for hydroponic lettuce in time series: The nutrient solution concentration time series control model is embedded in the hydroponic intelligent monitoring and control system to dynamically control the nutrient solution concentration during the entire growth cycle of hydroponic lettuce.

[0014] The construction of the time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model comprises the following steps:

[0015] The group photosynthetic rate measuring instrument was used to obtain the group photosynthetic rate data set and the group water use efficiency data set under different nutrient solution concentrations during the whole growth period of hydroponic lettuce.

[0016] Using minimum-maximum normalization, the data is linearly mapped to the [0, 1] interval. The formula is as follows:

[0017] ,

[0018] ,

[0019] ,

[0020] ,

[0021] in, , , , They are the original cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency data. , , , They are the normalized data of cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency;

[0022] The photosynthetic rate dataset is divided into a training set in a ratio of 8:2. and test set The water use efficiency dataset is divided into a training set and a and test set ,The group photosynthetic rate dataset and the group water use efficiency dataset are both characterized by the cultivation time and the nutrient solution concentration, and the group photosynthetic rate and the group water use efficiency are used as labels;

[0023] Select radial basis function RBF kernel As the kernel function of the support vector regression SVR model, is a two-dimensional input vector, Different from The penalty coefficient C and kernel parameter γ to be optimized are optimized by 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, the parameter range is C∈[0.05, 20], γ∈[0.0001, 10]; the determination coefficient of the test set 5-fold cross validation is used as the evaluation index, and the fitness function ,in is the true value of the test set, is the model prediction value, is the true mean of the test set;

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

[0025] Each qubit is initialized to a superposition state , that is, in the ground state and A quantum population consists of 70 quantum individuals, each of which consists of 72 quantum bits, encoded as follows:

[0026] ,

[0027] in, is the state of a quantum individual. is the state of the ith qubit, and is a composite quantum state of 72 qubits, are the ground states in quantum computing, corresponding to 0 and 1 of the classical bit;

[0028] Each quantum individual is composed of a 72-bit binary string, where 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:

[0029] ,

[0030] ,

[0031] in, , The binary strings representing the penalty coefficient C and the kernel parameter γ respectively, , Respectively represent C,γ binary string converted to decimal string;

[0032] On the photosynthetic rate dataset, the decoded C and γ are used to train the support vector regression SVR model. The prediction is made on the , and the fitness value is calculated by the difference between the predicted result and the true value.

[0033] Model pair trained with parameter combinations decoded on the water use efficiency dataset Make a prediction and calculate the fitness value by the difference between the predicted result and the true value;

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

[0035] ,

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

[0037] Generation of optimal parameter combination: Continuously iterate until the maximum number of iterations is reached or the fitness converges, at which point the corresponding C and γ are the optimal parameter combination;

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

[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 , returns the two-dimensional target vector for each individual ;

[0049] Based on the prediction model of photosynthetic rate and prediction model of water use efficiency of population Calculate the photosynthetic rate ACO2 and water use efficiency WUE of each individual in the current iteration, stratify the individuals in the population according to the non-dominated sorting, quantify the density of the solutions in the same level through crowding calculation, and give priority to individuals in lower levels or with greater crowding;

[0050] A tournament selection strategy is used to screen high-quality individuals for the next generation. Two individuals are randomly selected from the population, and individuals with higher non-dominated levels are given priority. If the levels are the same, individuals with greater crowding are selected. The winning individuals serve as parents to participate in crossover and mutation.

[0051] The crossover operator is set to the SBX crossover operator. After randomly pairing the selected individuals, a crossover operation is performed with a crossover probability of 0.85 to generate new individuals. The mutation operator uses a polynomial mutation operator to introduce mutations with a mutation probability of 0.9 to maintain population diversity and prevent the population from falling into a local optimum.

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

[0053] In each generation, based on non-dominated sorting and crowding calculation, the tournament selection strategy is used to select individuals with better fitness as parents; the SBX crossover operator and polynomial mutation operation are performed on the parent individuals to generate the offspring population; the parent and offspring are merged, and the individuals in the non-dominated hierarchy (F1, F2, ...) are preferentially retained through non-dominated sorting and crowding screening; the above steps are repeated until the preset maximum number of iterations of 100 times is reached, at which time the convergence and distribution of the Pareto solution set tend to be stable, and finally the Pareto solution set of the group photosynthetic rate and the group water use efficiency is obtained;

[0054] The discrete time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model are used in the interval [ Cultivation days Repeat the above steps to obtain the Pareto solution set of the time series.

[0055] The time-series dynamic control of the concentration of the hydroponic lettuce nutrient solution comprises the following steps:

[0056] The cubic spline interpolation method is used to transform the uneven and discontinuous time series Pareto solution set into a uniform and continuously distributed time series solution set.

[0057] Since the two objectives of group photosynthetic rate and group water use efficiency are equally important, that is, the unbiased 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 of objective coordination and compromise between the two objectives of group photosynthetic rate and group water use efficiency, and the optimal balance solution of the time series is obtained. The formula of the knee point is as follows:

[0058] ,

[0059] Where a is the knee point, o is a solution of the Pareto solution set, L is the chord connecting the two endpoints, and D(o,L) is the normal distance from o to L;

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

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

[0062] The optimal parameters for constructing a prediction model include the following steps:

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

[0064] The kernel function is selected using the radial basis function kernel, the optimal parameter combination C and γ are set as the parameters of the model, and the normalized training data is input The SVR model determines the weight and bias of the optimal hyperplane based on data and parameters, thereby fitting the nonlinear relationship between input features and group photosynthetic rate, and outputting a time series group photosynthetic rate prediction model. ;

[0065] The radial basis function is used as the kernel function, and the optimal combination C and γ of the optimized group water use efficiency data set are set as the parameters of the SVR model. The normalized training data is input The SVR model fits the nonlinear relationship between input features and population water use efficiency, and outputs a time series population water use efficiency prediction model ;

[0066] Multiple training time series population photosynthetic rate prediction model and time series population water efficiency prediction model , and using 5-fold cross validation, the model with the smallest average root mean square error and the largest coefficient of determination was selected as the final model.

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

[0068] Due to the uneven distribution problem caused by the random generation of the initial population, a good point set generation method based on prime number theory is introduced. Taking 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 in the interval [0, 1) is as follows:

[0069] ,

[0070] in, is the kth individual in the population, is a modulo 1 operation, mapping the value to the interval [0, 1), p is the smallest prime number satisfying (p-3) / 2 ≥ s, s is the spatial dimension 2, that is, , N is the set population size of 70;

[0071] Map the generated good point set to the hydroponic nutrient solution concentration The actual value range of the hydroponic nutrient solution is known to be , the linear mapping formula is , the final initial population , where k is the kth individual in the population.

[0072] After the individuals in the population are stratified according to the non-dominated order, the density of the solutions in the same level is quantified by the crowding degree calculation, which includes the following steps:

[0073] After the individuals in the population are stratified according to the non-dominated order, the density of the solutions in the same level is quantified by the crowding degree calculation, which includes the following steps:

[0074] Stratify the individuals in the population according to their superiority and inferiority, and find the Pareto optimal frontier:

[0075] First, determine the dominance relationship: for any two individuals x u and x v , if x u The two objective function values ​​of are greater than or equal to x v And at least one of the objectives is strictly better, then determine x u dominatex v ;

[0076] Secondly, perform hierarchical sorting: maintain the domination number and domination set for each individual, and select all individuals that are not dominated by any individual in the first layer, that is, individuals with a domination number of zero as the Pareto frontier F1 layer;

[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 quality of the solutions gets worse as the level increases;

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

[0079] 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 distance to ensure the coverage of the Pareto front; For non-boundary individuals, calculate the difference between their adjacent solutions for each objective, normalize the differences 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 for the -th objective respectively, and are the maximum and minimum values of all individuals in the current level for 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 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 the individuals in layer F2 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, which inherits the elite solutions of the parent generation and expands the diversity of the offspring solution set.

[0087] The construction of the nutrient solution concentration time series control model comprises the following steps:

[0088] The input features Expanded to the b-order polynomial characteristic form, its model is:

[0089]

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

[0091] The dataset is divided into 80% training set and 20% test set;

[0092] A linear regression model is used to fit the polynomial features, and the extended polynomial features fit the nonlinear relationship. The coefficients of the polynomial features are learned by training the model with Python and verified on the test set to obtain the nutrient solution concentration time series control model. as follows:

[0093]

[0094] in, It’s planting time. It is the concentration of hydroponic nutrient solution.

[0095] Beneficial Effects

[0096] Compared with the prior art, the multi-objective collaborative optimization method for dynamic control of the concentration of nutrient solution for hydroponic lettuce adopts a non-dominated sorting multi-objective genetic algorithm to solve the multi-objective problems of a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model, and obtains the optimal balanced control target value by combining a uniformly distributed population strategy, non-dominated sorting, crowding calculation, elite strategy and population renewal mechanism, thereby effectively solving the problem of dynamic control of nutrient solution concentration for plant time-series growth.

[0097] The present invention first constructs a time-series population photosynthetic rate prediction model and a time-series population water use efficiency prediction model, and seeks a balanced solution that achieves the optimal coordination of population photosynthetic rate and population water use efficiency under constrained conditions in the time-series changes in the concentration of the nutrient solution required in the dynamic growth process of the plant interacting with the environment. The time-series population photosynthetic rate prediction model and the time-series population water use efficiency prediction model are used as objective functions, and the Pareto hierarchy is divided based on the fast non-dominated sorting by the non-dominated sorting multi-objective genetic algorithm, and the density of the solution set distribution is evaluated by coupling crowding; the offspring is generated by driving crossover mutation through tournament selection, and the parent-child population is fused and then stratified for screening, retaining the elite solution set with high convergence and diversity, dynamically balancing approximation and coverage, and efficiently approximating the complex Pareto front. Finally, the knee point on the Pareto frontier is selected as the optimal equilibrium solution, and a nutrient solution concentration time-series control model is constructed, which is embedded in the hydroponic intelligent monitoring and control system to dynamically control the nutrient solution concentration during the entire growth cycle of hydroponic lettuce.

[0098] The present invention verifies the time-series dynamic control method of the nutrient solution concentration of hydroponic lettuce through a 30-day cultivation experiment, and sets a nutrient solution concentration time-series control model (model group), nutrient solution concentration control to a constant value (unchanged group), and nutrient solution concentration without control treatment (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, which is 16.79% and 32.86% higher than that of the unchanged group and the blank group, respectively. The health index in the model group is also the highest, which is 9.71% higher than that of the unchanged group and 12.21% higher than that of the blank group. The fresh weight of the stem in the model group is significantly higher than that of the control group, which is 30.94% higher than that of the unchanged group and 44.91% higher than that of the blank group. The dry weight of the stem in the model group is higher than that of the control group, which is 17.55% higher than that of the control group and 22.99% higher than that of the blank group. The experiment shows that the lettuce cultivated by the control method of the present invention improves the water use efficiency and the healthy growth of plants, thereby effectively promoting the economic yield of lettuce. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0100] Figure 2 This is a field photo of the cultivation test of the present invention;

[0101] Figure 3 Visualization of the time series population photosynthetic rate prediction model of the present invention;

[0102] Figure 4 Visualization of the water use efficiency prediction model of the time series population of the present invention;

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

[0104] Figure 6 A distribution diagram of the optimal equilibrium solution of the present invention in the Pareto solution set;

[0105] Figure 7 It is a distribution diagram of the optimal time series balance solution of the present invention in the time series population photosynthetic rate prediction model;

[0106] Figure 8 It is a distribution diagram of the time series optimal balance solution of the present invention in the time series group water use efficiency prediction model;

[0107] Fig. 9 It is a visualization of the nutrient solution concentration time-series control model of the present invention;

[0108] Fig.10 This is a parameter comparison chart of the model and control group in the verification experiment of the present invention. DETAILED DESCRIPTION

[0109] In order to have a further understanding and recognition of the structural features and the effects achieved by the present invention, a preferred embodiment and accompanying drawings are used for detailed description as follows:

[0110] like Figure 1 As shown, the multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution in time series of the present invention comprises the following steps:

[0111] The first step, such as Figure 3 and Figure 4 As shown in the figure, a time series population photosynthetic rate prediction model and a time series population water use efficiency prediction model are constructed. First, the population photosynthetic rate dataset and the population water use efficiency dataset are normalized. By converting the characteristic data of different cultivation days and hydroponic nutrient solution concentrations to a unified numerical range of [0, 1], it is ensured that the contribution of the features to the subsequent support vector regression SVR model is balanced, thereby avoiding the adverse effects of different dimensions and scales on model performance. Subsequently, the dataset was randomly divided into training and test sets, and a 5-fold cross validation was 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] In order to further optimize the hyperparameters of the SVR model, especially the penalty parameter C and the kernel function parameter r, the quantum genetic algorithm QGA evolutionary optimization is introduced. Compared with the traditional genetic algorithm, QGA uses quantum bits to represent the solution space, which enables the search process to explore multiple solutions in parallel, thereby significantly enhancing the ability of global search and avoiding the limitation of traditional genetic algorithms that are prone to fall into the local optimal solution. Specifically, QGA first generates the initial population through quantum bit encoding, in which each individual is represented as a binary string of quantum state superposition. Then, a fitness function based on the test set determination coefficient is constructed, and a quantum rotating gate dynamic update strategy is designed to optimize the quality of the solution. Through quantum superposition interference, QGA can achieve effective evolution of the population, thereby avoiding the problem of premature convergence. Quantum parallelism significantly improves the efficiency of global search, allowing 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 kernel function parameter that are most suitable for the SVR model. Based on the optimal parameters of the time series photosynthetic rate dataset and the time series water use efficiency dataset, a time series photosynthetic rate prediction model and a time series water use efficiency prediction model were constructed respectively. This process not only effectively improved the prediction accuracy of the model, but also proved 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 group photosynthetic rate measuring instrument was used to obtain a group photosynthetic rate dataset and a group water use efficiency dataset under different nutrient solution concentrations during the entire growth cycle of hydroponic lettuce.

[0114] (2) Use minimum-maximum normalization to linearly map the data to the interval [0, 1], as follows:

[0115] ,

[0116] ,

[0117] ,

[0118] ,

[0119] in, , , , They are the original cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency data. , , , They are the normalized data of cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency;

[0120] The photosynthetic rate dataset is divided into a training set in a ratio of 8:2. and test set The water use efficiency dataset is divided into a training set and a and test set ,The population photosynthetic rate dataset and the population water use efficiency dataset are ,characterized by cultivation time and nutrient solution concentration, and ,the population photosynthetic rate and population water use efficiency are used 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, Different from The penalty coefficient C and kernel parameter γ to be optimized are optimized by 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, the parameter range is C∈[0.05, 20], γ∈[0.0001, 10]; the determination coefficient of the test set 5-fold cross validation is used as the evaluation index, and the fitness function ,in is the true value of the test set, is the model prediction value, is the true mean of the test set.

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

[0123] Each qubit is initialized to a superposition state , that is, in the ground state and A quantum population consists of 70 quantum individuals, each of which consists of 72 quantum bits, encoded as follows:

[0124] ,

[0125] in, is the state of a quantum individual. is the state of the ith qubit, and is a composite quantum state of 72 qubits, are the ground states in quantum computing, corresponding to 0 and 1 of the classical bit;

[0126] Each quantum individual is composed of a 72-bit binary string, where 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:

[0127] ,

[0128] ,

[0129] in, , The binary strings representing the penalty coefficient C and the kernel parameter γ respectively, , Respectively represent C,γ binary string converted to decimal string;

[0130] On the photosynthetic rate dataset, the decoded C and γ are used to train the support vector regression SVR model. The prediction is made on the , and the fitness value is calculated by the difference between the predicted result and the true value.

[0131] Model pair trained with parameter combinations decoded on the water use efficiency dataset Make a prediction and calculate the fitness value by the difference between the predicted result and the true value.

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

[0133] ,

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

[0135] (6) 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.

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

[0137] A1) Based on the optimal parameter penalty function C and kernel parameter γ of the group photosynthetic rate data set, a support vector regression SVR model is constructed.

[0138] The kernel function is selected using the radial basis function kernel, the optimal parameter combination C and γ are set as the parameters of the model, and the normalized training data is input The SVR model determines the weight and bias of the optimal hyperplane based on data and parameters, thereby fitting the nonlinear relationship between input features and group photosynthetic rate, and outputting a time series group photosynthetic rate prediction model. ;

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

[0140] A3) Multiple training time series population photosynthetic rate prediction model and time series population water efficiency prediction model , and using 5-fold cross validation, the model with the smallest average root mean square error and the largest coefficient of determination was selected as the final model.

[0141] The second step is to build a multi-objective optimization model. The time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model are used as objective functions, the coordinated optimization of plant population photosynthetic rate and population water use efficiency is the goal, and the plant cultivation days and hydroponic nutrient solution concentration are used as constraints to build a multi-objective optimization model.

[0142] There is a dynamic competitive relationship between the photosynthetic rate of the group and the water use efficiency of the group: when plants increase the stomatal aperture to increase the photosynthetic rate, the transpiration rate will be accelerated, thereby reducing the water use efficiency; reducing the stomatal aperture to increase the water use efficiency will inhibit the photosynthetic rate due to the reduction in 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 presents nonlinear time-varying characteristics—the response functions of different growth times to the environment are significantly different, and there is a physiological lag effect. Traditional single-objective optimization is difficult to solve this multi-dimensional spatiotemporal coupling problem. Compared with single-objective problems, multi-objective optimization problems can optimize multiple objectives at the same time, which is closer to actual problems and has 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 actual multi-objective problems.

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

[0144] (1) 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

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

[0146] Objective function:

[0147] ,

[0148] Constraints:

[0149] ,

[0150] 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.

[0151] The third step is to find the Pareto solution set of the multi-objective optimization model. Figure 5 , Figure 6 , Figure 7 and Figure 8 As shown in the figure, a uniformly distributed population strategy is introduced, and a non-dominated sorting multi-objective genetic algorithm is used to solve the multi-objective optimization model to obtain the Pareto solution set that balances the photosynthetic rate and water use efficiency of the population during the entire growth cycle of the plant.

[0152] The non-dominated sorting multi-objective genetic algorithm is used to solve the multi-objective optimization problems of the time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model. It can effectively solve the conflicts between multiple objectives and consider the difficulty of nutrient solution concentration control in the complex dynamic changes during plant growth. In order to ensure the global search capability and convergence speed, the uniform distribution population strategy is introduced to generate the initial population to ensure the full exploration of the solution space and avoid the population from being concentrated in a 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 frontier and determine which solutions are "non-dominated solutions", so as to find a set of balanced optimal solutions, which can overcome the limitations of the simple sorting method in the case of multiple objectives. On the basis of non-dominated sorting, the crowding degree calculation further evaluates the "crowding degree" of individuals, that is, the density of solutions in the target space. Solutions with a smaller crowding degree represent that the solutions in this area are relatively sparse, which usually means that the solution has a strong representativeness in the multi-objective space, and therefore 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. 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 repeats the above steps until the preset maximum number of iterations is 100. At this time, the convergence and distribution of the Pareto solution set tend to be stable, and finally the Pareto solution set of the group photosynthetic rate and the group water use efficiency is obtained. Finally, the discrete time series group photosynthetic rate prediction model and the time series group water use efficiency prediction model are solved by repeating the above steps on different cultivation days to obtain the time series Pareto solution set.

[0153] Compared with traditional single-objective optimization methods, non-dominated sorting multi-objective genetic algorithms have significant advantages, especially when dealing with complex multi-objective optimization problems. Traditional single-objective optimization methods can usually only optimize one specific goal, while in multi-objective optimization, there are often conflicts between different goals. Traditional methods cannot consider the relationship between multiple goals at the same time, which makes it easy to fall into local optimal solutions during the optimization process and cannot effectively explore the entire solution space. In contrast, the non-dominated sorting multi-objective genetic algorithm can comprehensively consider multiple goals under the framework of global search by introducing mechanisms such as non-dominated sorting, crowding calculation and elite strategy, and find a set of balanced Pareto optimal solutions, avoiding the degeneration of solutions and the dilemma of local optimality in single-objective optimization, and providing more powerful optimization capabilities 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 optimal point set to the concentration of the hydroponic nutrient solution The actual range of fixed cultivation days , returns the two-dimensional target vector for each individual .

[0156] The uniformly distributed population strategy is introduced as follows:

[0157] Due to the problem of uneven distribution that may be caused by random generation of the initial population, a method for generating a good point set based on prime number theory is introduced. Taking 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 in the interval [0, 1) is as follows:

[0158] ,

[0159] in, is the kth individual in the population, is a modulo 1 operation, mapping the value to the interval [0, 1), p is the smallest prime number satisfying (p-3) / 2 ≥ s, s is the spatial dimension 2, that is, , N is the set population size of 70;

[0160] Map the generated good point set to the hydroponic nutrient solution concentration The actual value range of the hydroponic nutrient solution is known to be , the linear mapping formula is , the final initial population , where k is the kth individual in the population.

[0161] (2) Based on the prediction model of photosynthetic rate and population water use efficiency prediction models The group photosynthetic rate ACO2 and group water use efficiency WUE of each individual in the current iteration are calculated. After the individuals in the population are stratified according to the Pareto dominance relationship, the crowding degree of the solution in the same level is quantified, and individuals at the lower level or with greater crowding degree are given priority.

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

[0163] A1) Stratify the individuals in the population according to their superiority and inferiority, and find the Pareto optimal frontier:

[0164] First, determine the dominance relationship: for any two individuals x u and x v , if x u The two objective function values ​​of are greater than or equal to x v And at least one of the objectives is strictly better, then determine x u Dominate xv ;

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

[0166] For the current layer F w The individuals in the domination set reduce the domination number of the individuals in their domination set one by one. If the domination number of an individual reaches zero, it will be assigned to the next level F. w+1 ; Repeat this process until all individuals are assigned to the corresponding level; finally, the population is divided into F1, F2, …, F m The hierarchical structure of , where F1 represents the global optimal solution set, and the higher the level, the lower the quality of the solution;

[0167] A2) Introducing crowding distance to quantify the sparsity of individuals in the target space and maintain the uniform distribution of solutions within the same level;

[0168] For the current level F w The individuals in the list are arranged in descending order according to the value of each objective function to generate sorted lists L1 and L2; the extreme points of each objective sorted list are identified and given infinite crowding degree. , ensuring the coverage of the Pareto frontier; for non-boundary individuals, calculate the difference between adjacent solutions on each target, normalize the difference to eliminate the dimension difference, and the total crowding distance of the individual is the sum of the normalized differences of each target:

[0169] ,

[0170] in, , They are the adjacent individuals of the i-th individual after sorting in the The value on the target, and They are the objective functions of all individuals at the current level. The maximum and minimum values ​​on .

[0171] (3) A tournament selection strategy is adopted to screen high-quality individuals for the next generation. Two individuals are randomly selected from the population, with priority given to the individual with a higher non-dominated level. If the levels are the same, the individual with a higher crowding degree is selected. The winning individual serves as the parent to participate in crossover and mutation.

[0172] (4) The crossover operator is set to the SBX crossover operator. After randomly pairing the selected individuals, a crossover operation is performed with a crossover probability of 0.85 to generate new individuals. The mutation operator uses a polynomial mutation operator to introduce mutations with a mutation probability of 0.9 to maintain population diversity and prevent the population from falling into a local optimum.

[0173] (5) Apply the elite 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 elite strategy and population update mechanism includes the following steps:

[0175] Combine 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, 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, select N optimal solutions from the combined 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; combine 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 is reached. 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 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] Step 4, as Fig. 9 shown, construct the time - series regulation model of nutrient solution concentration: 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 time - series regulation model of nutrient solution concentration.

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

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

[0184] (1) The cubic spline interpolation method is used to transform the uneven and discontinuous time series Pareto solution set into a uniform and continuously distributed time series solution set.

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

[0186] ,

[0187] Among them, a is the knee point, o is a solution of 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.

[0188] (3) Based on the optimal equilibrium solution of the time series, the optimal 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 control of the nutrient solution concentration.

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

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

[0191] A1) Input features Expanded to the b-order polynomial characteristic form, its model is:

[0192]

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

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

[0195] A3) Use linear regression model to fit polynomial features, and extend polynomial features to fit nonlinear relationships. Use Python to train the model to learn the coefficients of polynomial features and verify them on the test set to obtain the nutrient solution concentration time series control model. as follows:

[0196]

[0197] in, It’s planting time. It is the concentration of hydroponic nutrient solution.

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

[0199] The fifth step is to dynamically control the concentration of the nutrient solution for hydroponic lettuce in time: embed the nutrient solution concentration time-series control model into the hydroponic intelligent monitoring and control system to dynamically control the nutrient solution concentration during the entire growth cycle of the hydroponic lettuce.

[0200] like Fig.10As shown in the figure, the time-series dynamic control method of the nutrient solution concentration of hydroponic lettuce was verified through a 30-day cultivation experiment, and a nutrient solution concentration time-series control model (model group), nutrient solution concentration control to a constant value (unchanged group), and nutrient solution concentration without control treatment (blank group) were set for comparative analysis. The results showed that the water use efficiency of the model group was higher than that of the control group, which was increased by 16.79% and 32.86% compared with the unchanged group and the blank group, respectively. The health index in the model group was also the highest, which was 9.71% higher than that of the unchanged group and 12.21% higher than that of the blank group. The fresh weight of the stem in the model group was significantly higher than that of the control group, which increased by 30.94% compared with the unchanged group and 44.91% compared with the blank group. The dry weight of the stem in the model group was higher than that in the control group, which increased by 17.55% compared with the control group and 22.99% compared with the blank group. The experiment showed that the lettuce cultivated by the control method of the present invention improved the water use efficiency and healthy growth of plants, thereby 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 to the above embodiments. The above embodiments and descriptions only describe the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection claimed by the present invention is defined by the attached claims and their equivalents.

Claims

1. A multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution, characterized in that: The following steps are involved: 11) Construct a prediction model for photosynthetic rate of a time series population and a prediction model for water use efficiency of a time series population; 12) Construct a multi-objective optimization model; 13) Find the Pareto solution set of multi-objective optimization models; 14) Constructing a time-series control model for nutrient solution concentration: Select the knee point optimal equilibrium solution in the Pareto solution set and use the polynomial regression algorithm to construct a time-series control model for nutrient solution concentration; 15) Time-series dynamic control of nutrient solution concentration for hydroponic lettuce: The nutrient solution concentration time-series control model is embedded in the hydroponic intelligent monitoring and control system to dynamically control the nutrient solution concentration during the entire growth cycle of hydroponic lettuce.

2. The multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution according to claim 1, characterized in that: The construction of the time series population photosynthetic rate prediction model and the time series population water use efficiency prediction model comprises the following steps: 21) A group photosynthetic rate measuring instrument was used to obtain the group photosynthetic rate data set and the group water use efficiency data set under different nutrient solution concentrations during the whole growth cycle of hydroponic lettuce; 22) Use minimum-maximum normalization to linearly map the data to the [0, 1] interval. The formula is as follows: ， ， ， ， in, , , , They are the original cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency data. , , , They are the normalized data of cultivation time, nutrient solution concentration, group photosynthetic rate, and group water use efficiency; The photosynthetic rate dataset is divided into a training set in a ratio of 8:

2. and test set The water use efficiency dataset is divided into a training set and a and test set ,The group photosynthetic rate dataset and the group water use efficiency dataset are both characterized by the cultivation time and the nutrient solution concentration, and the group photosynthetic rate and the group water use efficiency are used as labels; 23) Select the radial basis function RBF kernel As the kernel function of the support vector regression SVR model, is a two-dimensional input vector, Different from The penalty coefficient C and kernel parameter γ to be optimized are optimized by 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, the parameter range is C∈[0.05, 20], γ∈[0.0001, 10]; the determination coefficient of the test set 5-fold cross validation is used as the evaluation index, and the fitness function ,in is the true value of the test set, is the model prediction value, is the true mean of the test set; 24) Initialize the quantum population. The penalty coefficient C and the kernel parameter γ to be optimized are represented by 36 quantum bits respectively, for a total of 72 quantum bits. Each qubit is initialized to a superposition state , that is, in the ground state and A quantum population consists of 70 quantum individuals, each of which consists of 72 quantum bits, encoded as follows: ， in, is the state of a quantum individual. is the state of the ith qubit, and is a composite quantum state of 72 qubits, are the ground states in quantum computing, corresponding to 0 and 1 of the classical bit; Each quantum individual is composed of a 72-bit binary string, where 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: ， ， in, , The binary strings representing the penalty coefficient C and the kernel parameter γ respectively, , Respectively represent C,γ binary string converted to decimal string; On the photosynthetic rate dataset, the decoded C and γ are used to train the support vector regression SVR model. The prediction is made on the , and the fitness value is calculated by the difference between the predicted result and the true value. Model pair trained with parameter combinations decoded on the water use efficiency dataset Make a prediction and calculate the fitness value by the difference between the predicted result and the true value; 25) In each iteration, if the current individual fitness is higher than the population average, the quantum state rotates 0.08π toward the optimal solution; otherwise, it rotates in the opposite direction. The forward update formula is as follows: ， in, is the superposition state of the quantum bit, is the ground state, corresponding to the classical bits 0 and 1; 26) Generation of optimal parameter combination: Continuously iterate until the maximum number of iterations is reached or the fitness converges, at which point the corresponding C and γ are the optimal parameter combination; 27) Construct prediction model with optimal parameters: Construct prediction model of time-series population photosynthetic rate and time-series population water use efficiency based on their respective optimal parameters.

3. The method for dynamic control of the concentration of the hydroponic lettuce nutrient solution by multi-objective collaborative optimization according to claim 1 is characterized in that: 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: 31) 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 ; 32) Construct a multi-objective optimization model as follows: Objective function: ， Constraints: ， 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.

4. The method for dynamic control of the concentration of the hydroponic lettuce nutrient solution by multi-objective collaborative optimization according to claim 1, characterized in that: 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: 41) 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 , returns the two-dimensional target vector for each individual ; 42) Based on the prediction model of photosynthetic rate and population water use efficiency prediction models Calculate the photosynthetic rate ACO2 and water use efficiency WUE of each individual in the current iteration, stratify the individuals in the population according to the non-dominated sorting, quantify the density of the solutions in the same level through crowding calculation, and give priority to individuals in lower levels or with greater crowding; 43) A tournament selection strategy is used to screen high-quality individuals for the next generation. Two individuals are randomly selected from the population, and individuals with higher non-dominated levels are given priority. If the levels are the same, individuals with greater crowding are selected. The winning individuals serve as parents to participate in crossover and mutation. 44) The crossover operator is set to the SBX crossover operator. After randomly pairing the selected individuals, a crossover operation is performed with a crossover probability of 0.85 to generate new individuals. The mutation operator uses a polynomial mutation operator to introduce mutations with a mutation probability of 0.9 to maintain population diversity and prevent the population from falling into a local optimum. 45) Apply elite strategy and population update mechanism to retain historical high-quality solutions, prevent high-quality solutions from being eliminated during evolution, and approach the real Pareto frontier; 46) In each generation, based on non-dominated sorting and crowding calculation, the tournament selection strategy is used to select individuals with better fitness as parents; the SBX crossover operator and polynomial mutation operation are performed on the parent individuals to generate the offspring population; the parent and offspring are merged, and the individuals in the non-dominated hierarchy (F1, F2, ...) are preferentially retained through non-dominated sorting and crowding screening; the above steps are repeated until the preset maximum number of iterations of 100 times is reached, at which time the convergence and distribution of the Pareto solution set tend to be stable, and finally the Pareto solution set of the group photosynthetic rate and the group water use efficiency is obtained; 47) Discrete time series population photosynthetic rate prediction model and time series population water use efficiency prediction model, in the interval [ Cultivation days Repeat the above steps to obtain the Pareto solution set of the time series.

5. The method for dynamic control of the concentration of hydroponic lettuce nutrient solution by multi-objective collaborative optimization according to claim 1, characterized in that: The time-series dynamic control of the concentration of the hydroponic lettuce nutrient solution comprises the following steps: 51) The cubic spline interpolation method is used to transform the uneven and discontinuous time series Pareto solution set into a uniform and continuously distributed time series solution set; 52) Since the two objectives of group photosynthetic rate and group water use efficiency are equally important, that is, the unbiased decision-making problem of multi-objective optimization, the knee point with cost-effectiveness and marginal utility in the Pareto solution set is selected as the optimal balance solution of objective coordination and compromise between the two objectives of group photosynthetic rate and group water use efficiency, and the optimal balance solution of the time series is obtained. The formula of the knee point is as follows: ， Where a is the knee point, o is a solution of the Pareto solution set, L is the chord connecting the two endpoints, and D(o,L) is the normal distance from o to L; 53) According to the optimal equilibrium solution of the time series, the optimal 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 nutrient solution concentration time series regulation; 54) Construction of a time-series control model for nutrient solution concentration: Taking the number of cultivation days as input and the target value of time-series control of nutrient solution concentration as output, a polynomial regression algorithm is used to construct a time-series control model for nutrient solution concentration.

6. The multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution according to claim 2, characterized in that: The optimal parameters for constructing a prediction model include the following steps: 61) Based on the optimal parameter penalty function C and kernel parameter γ of the group photosynthetic rate data set, a support vector regression SVR model was constructed. The kernel function is selected using the radial basis function kernel, the optimal parameter combination C and γ are set as the parameters of the model, and the normalized training data is input The SVR model determines the weight and bias of the optimal hyperplane based on data and parameters, thereby fitting the nonlinear relationship between input features and group photosynthetic rate, and outputting a time series group photosynthetic rate prediction model. ; 62) The radial basis function is used as the kernel function, and the optimal combination C and γ of the optimized group water use efficiency data set are set as the parameters of the SVR model. The normalized training data is input The SVR model fits the nonlinear relationship between input features and population water use efficiency, and outputs a time series population water use efficiency prediction model ; 63) Multiple training time series population photosynthetic rate prediction model and time series population water efficiency prediction model , and using 5-fold cross validation, the model with the smallest average root mean square error and the largest coefficient of determination was selected as the final model.

7. The method for dynamic control of the concentration of the hydroponic lettuce nutrient solution by multi-objective collaborative optimization according to claim 4 is characterized in that: The strategy of introducing uniformly distributed population is as follows: Construct a high-quality initial population with low deviation characteristics. The mathematical model for generating population individuals in the interval [0, 1) is as follows: ， in, is the kth individual in the population, is a modulo 1 operation, mapping the value to the interval [0, 1), p is the smallest prime number satisfying (p-3) / 2 ≥ s, s is the spatial dimension 2, that is, , N is the set population size of 70; Map the generated good point set to the hydroponic nutrient solution concentration The actual value range of the hydroponic nutrient solution is known to be , the linear mapping formula is , the final initial population , where k is the kth individual in the population.

8. The multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution according to claim 4, characterized in that: After the individuals in the population are stratified according to the non-dominated order, the density of the solutions in the same level is quantified by the crowding degree calculation, which includes the following steps: 81) Stratify the individuals in the population according to their superiority and inferiority, and find the Pareto optimal frontier: First, determine the dominance relationship: for any two individuals x u and x v , if x u The two objective function values ​​of are greater than or equal to x v And at least one of the objectives is strictly better, then determine x u Dominate x v ; Secondly, perform hierarchical sorting: maintain the domination number and domination set for each individual, and select all individuals that are not dominated by any individual in the first layer, that is, individuals with a domination number of zero as the Pareto frontier F1 layer; For the current layer F w The individuals in the domination set reduce the domination number of the individuals in their domination set one by one. If the domination number of an individual reaches zero, it will be assigned to the next level F. w+1 ; Repeat this process until all individuals are assigned to the corresponding level; finally, the population is divided into F1, F2, …, F m The hierarchical structure of , where F1 represents the global optimal solution set, and the higher the level, the lower the quality of the solution; 82) The crowding distance is introduced to quantify the sparsity of individuals in the target space and maintain the uniform distribution of the solution set within the same level; For the current level F w The individuals in the list are arranged in descending order according to the value of each objective function to generate sorted lists L1 and L2; the extreme points of each objective sorted list are identified and given infinite crowding degree. , ensuring the coverage of the Pareto frontier; for non-boundary individuals, calculate the difference between adjacent solutions on each target, normalize the difference to eliminate the dimension difference, and the total crowding distance of the individual is the sum of the normalized differences of each target: ， in, , They are the adjacent individuals of the i-th individual after sorting in the The value on the target, and They are the objective functions of all individuals at the current level. The maximum and minimum values ​​on .

9. The multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution according to claim 4, characterized in that: The application of elite strategy and population update mechanism includes the following steps: 91) Merge the N-individual parent population and the N-individual offspring population into a temporary population of size 2N; 92) Perform non-dominated sorting on the temporary population and divide it into a hierarchical sequence F1, F2, …, F m , and preferentially select individuals in the F1 layer to fill the new generation population. If the number of individuals n1 in the F1 layer ≤ N, all are retained. If n1 < N, continue to add individuals in the F2 layer until the total number is close to N; 93) When a certain level F w When the number of individuals exceeds the remaining capacity, they are sorted from high to low according to the crowding distance, and sparsely distributed individuals are given priority; 94) 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.

10. The multi-objective collaborative optimization method for dynamic control of the concentration of hydroponic lettuce nutrient solution according to claim 5, characterized in that: The construction of the nutrient solution concentration time series control model comprises the following steps: 101) Input features Expanded to the b-order polynomial characteristic form, its model is: ， in is the coefficient of the b-th term of the polynomial; 102) Divide the dataset into 80% training set and 20% test set; 103) Linear regression model is used to fit polynomial features, while extended polynomial features fit nonlinear relationships. The coefficients of polynomial features are learned by training the model in Python and verified on the test set to obtain the nutrient solution concentration time series control model. as follows: ， in, It’s planting time. It is the concentration of hydroponic nutrient solution.

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