A multi-objective crop planting optimization method considering fuzzy uncertainty

Abstract

A multi-objective optimization method for crop planting considering fuzzy uncertainty includes the following steps: Step 1: Obtain historical data; Step 2: Construct a corresponding fuzzy parameter set based on the historical data; Step 3: Describe the planting area of ​​various crops on different plots as variables, and construct the expression relationship between their total planting area and total yield; Step 4: Construct a fuzzy multi-objective optimization model for crop planting based on the fuzzy parameter set; Step 5: Introduce plot area constraints, crop suitability constraints, crop rotation constraints, and minimum planting area constraints into the fuzzy multi-objective optimization model; Step 6: Obtain the clarified multi-objective optimization model; Step 7: Obtain a Pareto optimal planting scheme set; Step 8: Select the target planting scheme from the Pareto optimal planting scheme set and output the planting area configuration results of various crops on different plots. This invention can obtain a planting method that better conforms to actual production conditions.

Description

Technical Field

[0001] This invention belongs to the field of agricultural planting planning and agricultural resource optimization and allocation technology, specifically involving a multi-objective crop planting optimization method that considers fuzzy uncertainty. Background Technology

[0002] The rational formulation of crop planting plans is a crucial aspect of agricultural production management, directly impacting land resource utilization efficiency, agricultural production returns, and the scientific nature of the planting structure. As agricultural production becomes increasingly large-scale, experience-based crop planting methods are no longer adequate for the complex and ever-changing market environment and production conditions, necessitating the use of optimization models to improve crop planting methods.

[0003] Most existing crop planting optimization methods focus on a single objective, using linear and nonlinear programming models to allocate crop planting areas for different plots. These methods rarely consider the balance between benefits and risks, making it difficult to provide planting entities with decision support that balances economic benefits and risk control when production conditions change adversely. Furthermore, these methods generally treat parameters such as crop yield per unit area and planting costs as deterministic values, modeling them based on empirical estimates. In actual agricultural production, these parameters are often affected by various factors such as regional differences in planting conditions, exhibiting significant uncertainty and ambiguity. If deterministic parameters are still used in the optimization modeling process, the resulting planting method will deviate significantly from the actual situation, making it difficult to meet the adaptability requirements of actual agricultural production.

[0004] Therefore, how to construct a multi-objective planting optimization method that takes into account both profit and risk objectives, and how to reasonably characterize the fuzzy and uncertain factors existing in the crop planting process, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] In order to overcome the problems existing in the prior art, the purpose of this invention is to provide a multi-objective crop planting optimization method that considers fuzzy uncertainty. This method can establish a multi-objective optimization model that takes into account both benefits and risks, and on this basis, fuzzy characterize the key uncertain factors in the crop planting process, thereby obtaining a planting method that is more in line with actual production conditions.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-objective crop planting optimization method considering fuzzy uncertainty includes the following steps; Step 1: Obtain historical data on the sales volume, sales price, yield per unit area, planting cost per unit area, plot area, plot type, and suitability of various crops within the target planting area; Step 2: Based on the historical data, the yield per unit area, sales price, and planting cost per unit area of ​​various crops are fuzzified to construct a corresponding set of fuzzy parameters; Step 3: Describe the planting area of ​​various crops on each plot as variables, and construct the relationship between their total planting area and total yield; Step 4: Construct a fuzzy multi-objective optimization model for crop planting based on the fuzzy parameter set, including a profit objective and a risk objective. The profit objective is used to characterize the overall economic benefit of the crop planting scheme, and the risk objective is used to characterize the degree of profit fluctuation of the planting scheme under the influence of fuzzy uncertain parameters. Step 5: Introduce plot area constraints, crop suitability constraints, crop rotation constraints, and minimum planting area constraints into the fuzzy multi-objective optimization model to ensure that the obtained planting scheme meets the actual agricultural production requirements. Step 6: De-clarification of the fuzzy multi-objective optimization model, converting the fuzzy objective function and fuzzy parameters into a computable deterministic expression to obtain the de-clarified multi-objective optimization model; Step 7: Solve the clarified multi-objective optimization model using a multi-objective optimization algorithm to obtain the Pareto optimal planting scheme set; Step 8: Based on the preset profit and risk preferences, select the target planting scheme from the Pareto optimal planting scheme set, and output the planting area allocation results of various crops on different plots.

[0007] In step 1, the crop planting information and plot information within the target planting area are first organized and preprocessed. The basic data for crops are: Historical yield per unit area of ​​crops is recorded as ;No. The historical sales price of crops is recorded as ;No. The unit area planting cost of crops is denoted as ;No. The expected market demand for crops is denoted as ;in, , This indicates the total number of crop varieties; The basic data of the land parcel is: The total area of ​​the plot is denoted as ;No. The land parcel type is denoted as ;No. Plot of land to the first The suitability parameters for planting crops are denoted as ;in, , Indicates the total number of land parcels; Species suitability parameters The definition is as follows: In addition, to eliminate the influence between data of different dimensions, the basic data of crops and plots are standardized for a certain indicator. Its standardized value The range standardization method is used to calculate: in, and These represent the maximum values ​​of the indicator in the sample.

[0008] The specific steps of step 2 are as follows: Step 1: The above-mentioned basic crop data are uncertain parameters, which are characterized by triangular fuzzy numbers; for the ... For planting crops, the triangular fuzzy number of the yield per unit area is denoted as: The triangular fuzzy number of its selling price is denoted as: The triangular fuzzy number representing the unit area planting cost is denoted as: ; where superscript Indicates the lower limit value, superscript Indicates the most likely value, indicated by a superscript. Indicates the upper limit value; Step 2: For any triangular fuzzy number Its membership function is defined as: in, Let represent the lower limit, most likely value, and upper limit of the triangular fuzzy number, respectively, and satisfy . ; This indicates that the corresponding parameter can take any value within its range. express For triangular fuzzy numbers Membership degree; Step 3. Based on historical statistical values, construct triangular fuzzy numbers as follows: in, They represent the first Fuzzy fluctuation coefficients for crop yield, price, and cost.

[0009] In step 3, decision variables are defined. : Indicates the first Planting crops in the first The planting area on the plot of land, Therefore, the total planted area of ​​crops is: ; No. The total output of crops is: ,in, Indicates the first Total fuzzy yield of crops, Indicates the first Planting crops in the first The planting area on the plot of land, Indicates the first Fuzzy numbers representing the yield per unit area of ​​crops.

[0010] set up ,in Let represent the lower limit, most likely value, and upper limit of the yield per unit area, respectively. Then, the... The total fuzzy yield of crops is represented as: .

[0011] In step 4, the profit objective function is first constructed, and the first... The vague sales revenue of agricultural products is recorded as When total output does not exceed market demand When the total output exceeds market demand, all crops are sold at normal prices; when the total output exceeds market demand, the excess is sold at a discount or disposed of as unsold goods. Therefore, the first The fuzzy representation of income from growing crops is as follows: ; in For the first The overproduction discount factor for crops; when When, it means that the overproduction is completely unsold; when At that time, it meant that the excess production would be sold at a discounted price; the next time... The approximate cost of planting crops is: The total cost of fuzzy planting is: The total fuzzy revenue function is: The first objective function is: ; Secondly, a risk objective function is constructed, using the width of the fuzzy return interval as a risk characterization index; let the total fuzzy return... The triangular fuzzy representation is as follows: Then its risk objective function is defined as: .in, The width of the fuzzy return range represents the range where the return is more susceptible to parameter fluctuations, and thus carries higher risk. Therefore, the second objective function is: ; Finally, the following multi-objective crop planting optimization model is established: , ,in, The target profit value after clarification. This represents the risk value for fluctuations in returns.

[0012] In step 5, the following constraints are set: (1) Land area constraint: For each plot of land, the total area allocated to each type of crop cannot exceed the total area of ​​that plot. ; (2) Suitability constraint: If the first The plot of land is not suitable for planting. If crops are planted, the corresponding planting area is zero. ; (3) Minimum planting area constraint: To avoid the planting area being too scattered, a minimum planting area threshold is set. : ; (4) Total crop planting area constraints: For a certain type of crop, the total planting area is limited according to the market size: ,in, and They represent the first Minimum and maximum permitted planting areas for crops; (5) Crop rotation constraint: Considering multi-year planning, in order to prevent the same crop from being planted continuously on the same plot of land, a 0-1 variable is adopted. Indicates the first Year Is the plot of land planted with the first Crop planting: Then the rotation constraint is: (6) Nonnegativity constraint: .

[0013] In step 6, since the NSGA-II algorithm requires a deterministic objective function as input, the fuzzy objective function needs to be clarified. The centroid method is used to clarify triangular fuzzy numbers. For any triangular fuzzy number: Its clarification results The calculation is as follows: ; Therefore, the total fuzzy gain The target value for the clarification benefit is: The risk target value is: At this point, the multi-objective model can be transformed into a deterministic bi-objective optimization model: , .

[0014] The specific steps of step 7 are as follows: Step 1: Population Initialization: Set the population size as The maximum number of iterations is The crossover probability is The mutation probability is Randomly generate the initial population: , among which each individual This corresponds to a complete plan for allocating planting area for crops across different plots: The initial individual is then subjected to constraint checks, including plot area constraints, crop suitability constraints, and minimum planting area constraints. If the constraints are not met, a repair operator is used to correct them so that they are called feasible solutions. Step 2: Calculate the individual objective function value: For each individual Calculate the profit target based on steps 4 to 6. and risk objectives : , ; Step 3: Determine non-dominant relationships for all individuals in the population: If individual The following conditions must be met: And there is at least one target. satisfy: Then it is called an individual. Dominant Individual Since the optimization objective of this invention is to maximize profits and minimize risks, the following should be considered simultaneously when making non-dominance judgments: as well as If both of the above conditions are met, and at least one condition is strictly true, then Dominate Based on dominance relationships, the population is divided into multiple non-dominated layers: ,in, This is the first non-dominated layer, i.e., the Pareto optimal layer; Step 4: Calculate congestion level: To maintain the diversity of Pareto solutions in the payoff-risk space, crowding distance is calculated for individuals within the same non-dominated layer; for individuals within the same non-dominated layer, crowding distance is calculated according to their payoff objectives. and risk objectives The values ​​are sorted. For non-boundary individuals, their values ​​are sorted according to the first... The crowding distance on each target can be expressed as: ,individual The total congestion distance is: ,in, and They represent the first and second digits in the same non-dominated layer. The maximum and minimum values ​​of the objective function are considered. A larger crowding distance indicates fewer other solutions around the individual, suggesting better distribution representativeness in the Pareto front. Therefore, within the same undominated layer, individuals with larger crowding distances are preferentially retained to avoid over-concentration of optimization results in a particular region.

[0015] Step 5: Use the crowding comparison operator to select parent individuals to participate in crossover and mutation: The crossover operation generates new individuals. If real number encoding is used, a simulated binary crossover operator can be employed. The mutation operation can be represented as: ,in, This represents a small-scale random perturbation. To prevent mutated individuals from violating area or suitability constraints, a repair operation is performed on the new individuals. For example, if the total allocated area of ​​a plot of land exceeds its area limit, it is scaled proportionally. ; Step 6: Merge the parent population with the offspring population to obtain a joint population: The joint population was re-sorted using a fast non-dominated ranking and crowding calculation, and the top-ranked populations were selected based on the principles of prioritizing non-dominated layers and crowding. Individuals constitute the next generation of the population: ; Step 7: If the current iteration count reaches the maximum iteration count Or the Pareto front of the population changes less than a preset threshold for several consecutive generations. If the iteration fails, stop; otherwise, return to Step 2 and continue iterating. The Pareto front change is expressed as: ,when The algorithm is considered to have converged at that time.

[0016] In step 8, the individuals in the first non-dominated layer obtained in step 7 are output as the Pareto optimal planting scheme set; if the final Pareto optimal scheme set is: , where each scheme Each corresponds to a set of profit target values and risk target value Finally, the final implementation plan is selected from the Pareto solution set based on the decision-maker's preferences. (1) Prioritize profit: ; (2) Risk Priority: ; (3) Construct a comprehensive evaluation function: ; in, Indicates the first The overall evaluation value of the Pareto candidate planting schemes; Representation scheme Clearly define the target revenue value; Representation scheme Risk target value; Weights for return preferences; These represent the maximum and minimum values ​​of the objective value of the Pareto solution set, respectively; These represent the maximum and minimum risk objective values ​​in the Pareto solution set, respectively. The scheme with the highest overall evaluation value is ultimately selected. .

[0017] The beneficial effects of this invention are: Compared with existing crop planting planning methods based on deterministic parameters, the beneficial effects of this invention are mainly reflected in the following aspects: (1) By fuzzing the key parameters such as crop yield per unit area, sales price and planting cost per unit area in step 2, the uncertainty and fuzziness in the agricultural production process can be better represented, thereby avoiding the problem of large deviation from the actual situation when using deterministic parameters for modeling, and improving the model's adaptability to complex agricultural production environments.

[0018] (2) By constructing a multi-objective optimization model that takes into account both profit and risk objectives in step 4, and by introducing constraints on plot area, crop suitability, crop rotation and minimum planting area in step 5, the planting plan can be made to meet the actual agricultural production requirements while taking into account both economic benefits and risk control, thereby improving the scientific nature, robustness and feasibility of the planting plan.

[0019] (3) By clarifying the fuzzy objective function and fuzzy parameters in step 6, and solving them by using a multi-objective optimization algorithm in step 7, the computability of the model can be improved while retaining the ability to describe uncertainty. This results in a Pareto optimal planting scheme set that balances benefits and risks, thus providing decision-makers with a variety of options.

[0020] (4) By selecting the target planting scheme from the Pareto optimal planting scheme set according to the preset profit preference and risk preference in step 8, different decision-making needs such as profit priority, risk priority or comprehensive balance can be met, thereby improving the applicability of the present invention in actual agricultural production decision-making and helping to improve land resource utilization efficiency and comprehensive agricultural economic benefits. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a multi-objective crop planting optimization method that considers fuzzy uncertainty according to the present invention. Detailed Implementation

[0022] The present invention will now be described in further detail with reference to the accompanying drawings.

[0023] As shown in the figure, the flowchart includes the following steps in sequence: acquisition of historical data and land parcel data, data preprocessing and standardization, fuzzy parameter construction, definition of decision variables, construction of a dual-objective model of benefit and risk, introduction of constraints, fuzzy model clarification, NSGA-II multi-objective optimization solution, and selection of the final planting scheme based on benefit preference and risk preference, and output of configuration results.

[0024] Example Background: Problem C of the 2024 National Undergraduate Mathematical Modeling Contest.

[0025] Specific steps: Step 1: First, organize and preprocess the crop planting information and plot information within the target planting area.

[0026] In this example, the basic data for crops is defined as: the first Historical yield per unit area of ​​crops is recorded as ;No. The historical sales price of crops is recorded as ;No. The unit area planting cost of crops is denoted as ;No. The expected market demand for crops is denoted as The basic data of the land parcel is defined as: the first The total area of ​​the plot is denoted as ;No. The land parcel type is denoted as ;No. Plot of land to the first The suitability parameters for planting crops are denoted as .in, .

[0027] Land suitability parameters Defined as: .

[0028] For example, grain crops (excluding rice) can be grown on flat land, terraced fields, and hillsides. Rice is grown in irrigated land under single-season conditions. .

[0029] For the sales price range, this example uses the average of the range as the historical sales price, that is: Expected market demand The actual total yield of each crop in 2023 is calculated as follows: ,in, Indicates the 2023rd The first piece of land The planting area for crops This indicates the yield per acre of the crop under the corresponding plot type and season. Furthermore, to eliminate the influence between data of different dimensions, the basic data for crops and plots are standardized for a given indicator. Its standardized value The range standardization method is used to calculate: in, and These represent the maximum values ​​of the indicator in the sample. After this step, the standardized crop parameter dataset and plot dataset are obtained.

[0030] Step 2: Based on the historical data described in Step 1, fuzzify the yield per unit area, sales price, and planting cost per unit area of ​​various crops to construct a corresponding set of fuzzy parameters.

[0031] The specific steps are as follows: Step 1: Regarding the first Plant crops and construct them separately: , , Among them, superscript , , These represent the lower limit, the most likely value, and the upper limit, respectively.

[0032] Step 2: Arbitrary triangular fuzzy number The membership function is: Step 3: In this example, the triangular fuzzy number is constructed proportionally based on historical statistical values. For the... Crops grown include: in, They represent the first Fuzzy fluctuation coefficients for crop yield, price, and cost.

[0033] In this example, the yield fluctuation coefficient of grain crops is selected based on national agricultural policy standards. Price volatility coefficient Cost fluctuation coefficient ; Yield fluctuation coefficient of vegetable crops Price volatility coefficient Cost fluctuation coefficient Yield fluctuation coefficient of edible fungi crops Price volatility coefficient Cost fluctuation coefficient For example, for soybeans, the historical yield is 400 jin / mu, the historical selling price is 3.25 yuan / jin, and the historical planting cost is 400 yuan / mu. Then its triangular fuzzy number can be expressed as: , , After this step, a fuzzy parameter set for all 41 crops is obtained.

[0034] Step 3: Define decision variables : Indicates the first Planting crops in the first The planting area on the plot of land, Then the first The total planting area for crops is: ;No. The total output of crops is: ,because It is an fuzzy number, therefore Also a fuzzy number, represented as: For example, if soybeans are planted in plot A4 (40 mu), plot B3 (20 mu), and plot C2 (15 mu) in a certain year, the total soybean planting area is 75 mu, and the corresponding total fuzzy yield can be directly calculated using the formula above.

[0035] Step 4: Construct a fuzzy multi-objective optimization model for crop planting based on the aforementioned fuzzy parameter set. For this example, firstly, a profit objective function is constructed, and the first... The vague sales revenue of agricultural products is recorded as When total output does not exceed market demand. When all crops are sold at normal prices, and when total production exceeds market demand, the excess is sold at a discount. Then, the... The fuzzy income from growing crops is: ,in For the first In this example, the overproduction discount factor for crops is set at 100% for grain crops. Vegetable crops Edible fungi crops . No. The approximate cost of planting crops is: The total cost of fuzzy planting is: The total fuzzy revenue function is: The first objective function is: .

[0036] Secondly, a risk objective function is constructed, using the width of the fuzzy return interval as a risk characterization index. Let the total fuzzy return... The triangular blur is: Then its risk objective function is: .in, This represents the width of the fuzzy return range. The wider the range, the greater the impact of parameter fluctuations on the return, and the higher the risk. Therefore, the second objective function is: .

[0037] Finally, the following multi-objective crop planting optimization model is established: , ,in, The target profit value after clarification. This represents the risk value for fluctuations in returns.

[0038] Step 5: Introduce constraints into the fuzzy multi-objective optimization model. For this example, constraints are introduced including plot area, crop suitability, minimum planting area, total crop planting scale, crop rotation, and non-negativity. Details are as follows: (1) Land area constraint: For each plot of land, the sum of the areas allocated to various crops cannot exceed the total area of ​​the plot, i.e. ; (2) Crop suitability constraints: If the first The plot of land is not suitable for planting. If crops are planted, the corresponding planting area is zero. ; (3) Minimum planting area constraint: To avoid the planting area being too scattered, a minimum planting area threshold is set. Open-air plots mu, greenhouse plots mu, that is: ; (4) Total Crop Planting Scale Constraints: The total planting area for each crop is limited based on market size. For the first... Planting crops, with ,in and They represent the first The minimum and maximum allowable planting area for crops. In this example, Based on expected market demand Compared with historical yield per mu The ratio is determined, that is: ,in We choose 0.15 as the allowable market redundancy factor.

[0039] (5) Crop rotation constraint: To prevent the same crop from being planted continuously on the same plot of land, a 0-1 variable is introduced. , indicating the first Year Is the plot of land planted with the first Crop planting: The rotation constraint is: .

[0040] (6) Nonnegativity constraint: This ensures that the planting scheme obtained from the solution simultaneously meets the area restrictions, the suitability requirements, and the laws of agricultural planting management.

[0041] Step 6: De-clarification of the fuzzy multi-objective optimization model involves converting the fuzzy objective function and fuzzy parameters into a computable deterministic expression, thus obtaining the de-clarified multi-objective optimization model. Since the NSGA-II algorithm requires a deterministic objective function as input, this example uses the centroid method to de-clarify the triangular fuzzy numbers. For any triangular fuzzy number: The result of the clarification is as follows: Therefore, the total fuzzy gain The target value for the clarification benefit is: The risk target value is: Thus, the original fuzzy bi-objective optimization model is transformed into a deterministic bi-objective optimization model: , .

[0042] Step 7: Solve the clarified bi-objective optimization model using the NSGA-II multi-objective optimization algorithm. In this example, the population size is set. The maximum number of iterations is The crossover probability is The mutation probability is The specific steps are as follows: Step 1: Population Initialization. Randomly generate the initial population: , among which each individual A corresponding planting area allocation scheme: The system performs constraint checks on the initial individuals. If the area constraint, suitability constraint, or minimum planting area constraint is violated, a repair operator is used to correct it.

[0043] Step 2: Calculate the individual objective function value. For each individual... Calculate the two corresponding objective function values ​​according to steps 4 to 6: , .

[0044] Step 3: Determine the non-dominant relationship for all individuals in the population. If an individual... The following conditions must be met: And there is at least one target. satisfy: Then it is called an individual. Dominant Individual Based on dominance relationships, the population is divided into multiple non-dominated layers: ,in, This is the first non-dominated layer, i.e., the Pareto optimal layer.

[0045] Step 4: Calculate crowding degree. Calculate the crowding distance for individuals in the same non-dominated layer to maintain the uniformity of the solution set distribution. For the The nth objective function, after being sorted by objective value in ascending order, the nth... The crowding distance for each individual is calculated as follows: The total congestion distance is: ,in, and These represent the first and second digits of the non-dominated layer, respectively. The maximum and minimum values ​​of each objective function.

[0046] Step 5. A crowding comparison operator is used for selection, choosing parent individuals to participate in crossover and mutation. New individuals are generated after the crossover operation, using real-number encoding and a simulated binary crossover operator. The mutation operation can be represented as: ,in, This represents a small-scale random perturbation. To prevent mutated individuals from violating area or suitability constraints, a repair operation is performed on the new individuals. For example, if the total allocated area of ​​a plot of land exceeds its area limit, it is scaled proportionally. .

[0047] Step 6: Merge the parent population with the offspring population to obtain a joint population: The joint population was re-sorted using a fast non-dominated ranking and crowding calculation, and the top-ranked populations were selected based on the principles of prioritizing non-dominated layers and crowding. Individuals constitute the next generation of the population: .

[0048] Step 7: If the current iteration count reaches the maximum iteration count Or the Pareto front of the population changes less than a preset threshold for several consecutive generations. If the iteration fails, stop; otherwise, return to Step 2 to continue iterating and solving.

[0049] Step 8: Based on preset profit and risk preferences, select the target planting plan from the Pareto optimal planting plan set. The Pareto optimal plan set obtained in Step 7 is... , where each scheme Each corresponds to a set of profit target values and risk target value In this example, we prioritize comprehensive evaluation and construct a comprehensive evaluation function: Using Python to solve the problem, and considering the comprehensive evaluation, the final profit is 3.8112 million yuan.

[0050] Land parcel name Land parcel type Planting season Configuration results A1 dry land single season 80.00 mu of soybeans A2 dry land single season Millet 55.00 mu A3 dry land single season 35.00 mu of oats A4 dry land single season Millet 72.00 mu A5 dry land single season Soybeans: 64.67 mu; Oats: 3.33 mu A6 dry land single season 21.90 mu of barley; 19.21 mu of soybeans; 13.89 mu of climbing beans. B1 Terraced fields single season 60.00 mu of corn B10 Terraced fields single season 25.00 mu of wheat B11 Terraced fields single season 30.05 mu of mung beans; 29.95 mu of wheat B12 Terraced fields single season 41.00 mu of mung beans; 4.00 mu of sorghum B13 Terraced fields single season 31.73 mu of mung beans; 3.27 mu of millet. B14 Terraced fields single season 20.00 mu of wheat B2 Terraced fields single season 46.00 mu of sorghum B3 Terraced fields single season 40.00 mu of wheat B4 Terraced fields single season 28.00 mu of wheat B5 Terraced fields single season 25.00 mu of millet B6 Terraced fields single season Wheat: 83.37 mu; Black beans: 2.63 mu B7 Terraced fields single season Corn: 41.52 mu; Climbing soybeans: 13.48 mu B8 Terraced fields single season 38.21 mu of corn; 5.79 mu of mung beans. B9 Terraced fields single season Millet 50.00 mu C1 hillside single season 10.78 mu of black beans; 4.22 mu of red beans C2 hillside single season 13.00 mu of red beans C3 hillside single season 15.00 mu of black beans C4 hillside single season 18.00 mu of red beans C5 hillside single season 27.00 mu of red beans C6 hillside single season 20.00 mu of black beans D1 Irrigated land single season 15.00 mu of rice D2 Irrigated land single season 10.00 mu of rice D3 Irrigated land Season 1 8.15 mu of cowpeas; 4.85 mu of sword beans; 1.00 mu of green peppers. D3 Irrigated land Season 2 14.00 mu of white radishes D4 Irrigated land Season 1 Tomatoes: 5.69 mu; Spinach: 0.31 mu D4 Irrigated land Season 2 6.00 mu of carrots D5 Irrigated land single season 10.00 mu of rice D6 Irrigated land single season 12.00 mu of rice D7 Irrigated land Season 1 10.20 mu of bok choy; 8.03 mu of sword beans; 1.99 mu of green beans; 1.00 mu of cauliflower; 0.77 mu of potatoes. D7 Irrigated land Season 2 19.45 mu of Chinese cabbage; 2.55 mu of carrots D8 Irrigated land Season 1 Potatoes: 8.80 mu; tomatoes: 8.19 mu; romaine lettuce: 1.03 mu; chili peppers: 0.69 mu; lettuce: 0.66 mu; celery: 0.31 mu; bok choy: 0.31 mu D8 Irrigated land Season 2 14.75 mu of white radishes; 5.25 mu of red radishes F1 Smart Greenhouse Season 1 0.60 mu of potatoes F1 Smart Greenhouse Season 2 0.60 mu of potatoes F2 Smart Greenhouse Season 1 0.60 mu of potatoes F2 Smart Greenhouse Season 2 0.60 mu of potatoes F3 Smart Greenhouse Season 1 0.60 mu of potatoes F3 Smart Greenhouse Season 2 0.60 mu of potatoes F4 Smart Greenhouse Season 1 0.60 mu of potatoes F4 Smart Greenhouse Season 2 0.60 mu of potatoes The specific planting method obtained is shown above.

Claims

1. A multi-objective crop planting optimization method considering fuzzy uncertainty, characterized in that, Includes the following steps; Step 1: Obtain historical data on the sales volume, sales price, yield per unit area, planting cost per unit area, plot area, plot type, and suitability of various crops within the target planting area; Step 2: Based on the historical data, the yield per unit area, sales price, and planting cost per unit area of ​​various crops are fuzzified to construct a corresponding set of fuzzy parameters; Step 3: Describe the planting area of ​​various crops on each plot as variables, and construct the relationship between their total planting area and total yield; Step 4: Construct a fuzzy multi-objective optimization model for crop planting based on the fuzzy parameter set, including a profit objective and a risk objective. The profit objective is used to characterize the overall economic benefit of the crop planting scheme, and the risk objective is used to characterize the degree of profit fluctuation of the planting scheme under the influence of fuzzy uncertain parameters. Step 5: Introduce plot area constraints, crop suitability constraints, crop rotation constraints, and minimum planting area constraints into the fuzzy multi-objective optimization model to ensure that the obtained planting scheme meets the actual agricultural production requirements. Step 6: De-clarification of the fuzzy multi-objective optimization model, converting the fuzzy objective function and fuzzy parameters into a computable deterministic expression to obtain the de-clarified multi-objective optimization model; Step 7: Solve the clarified multi-objective optimization model using a multi-objective optimization algorithm to obtain the Pareto optimal planting scheme set; Step 8: Based on the preset profit and risk preferences, select the target planting scheme from the Pareto optimal planting scheme set, and output the planting area allocation results of various crops on different plots.

2. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 1, characterized in that, In step 1, the crop planting information and plot information within the target planting area are first organized and preprocessed. The basic data for crops are: Historical yield per unit area of ​​crops is recorded as ;No. The historical sales price of crops is recorded as ;No. The unit area planting cost of crops is denoted as ;No. The expected market demand for crops is denoted as ;in, , This indicates the total number of crop varieties; The basic data of the land parcel is: The total area of ​​the plot is denoted as ;No. The land parcel type is denoted as ;No. Plot of land to the first The suitability parameters for planting crops are denoted as ;in, , Indicates the total number of land parcels; Species suitability parameters The definition is as follows: In addition, to eliminate the influence between data of different dimensions, the basic data of crops and plots are standardized for a certain indicator. Its standardized value The range standardization method is used to calculate: in, and These represent the maximum values ​​of the indicator in the sample.

3. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 2, characterized in that, The specific steps of step 2 are as follows: Step 1: The above-mentioned basic crop data are uncertain parameters, which are characterized by triangular fuzzy numbers; for the ... For planting crops, the triangular fuzzy number of the yield per unit area is denoted as: The triangular fuzzy number of its selling price is denoted as: The triangular fuzzy number representing the unit area planting cost is denoted as: ; where superscript Indicates the lower limit value, superscript Indicates the most likely value, indicated by a superscript. Indicates the upper limit value; Step 2: For any triangular fuzzy number Its membership function is defined as: in, Let represent the lower limit, most likely value, and upper limit of the triangular fuzzy number, respectively, and satisfy . ; This indicates that the corresponding parameter can take any value within its range. express For triangular fuzzy numbers Membership degree; Step 3. Based on historical statistical values, construct triangular fuzzy numbers as follows: in, They represent the first Fuzzy fluctuation coefficients for crop yield, price, and cost.

4. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 3, characterized in that, In step 3, decision variables are defined. : Indicates the first Planting crops in the first The planting area on the plot of land, Therefore, the total planted area of ​​crops is: ; No. The total output of crops is: ,in, Indicates the first Total fuzzy yield of crops, Indicates the first Planting crops in the first The planting area on the plot of land, Indicates the first Fuzzy numbers representing the yield per unit area of ​​crops. set up ,in Let represent the lower limit, most likely value, and upper limit of the yield per unit area, respectively. Then, the... The total fuzzy yield of crops is represented as: 。 5. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 4, characterized in that, In step 4, the profit objective function is first constructed, and the first... The vague sales revenue of agricultural products is recorded as ; When total output does not exceed market demand When the total output exceeds market demand, all crops are sold at normal prices; when the total output exceeds market demand, the excess is sold at a discount or disposed of as unsold goods. Therefore, the first The fuzzy representation of income from growing crops is as follows: ； in For the first The overproduction discount factor for crops; when When, it means that the overproduction is completely unsold; when At that time, it meant that the excess production would be sold at a discounted price; the next time... The approximate cost of planting crops is: The total cost of fuzzy planting is: The total fuzzy revenue function is: The first objective function is: ; Secondly, a risk objective function is constructed, using the width of the fuzzy return interval as a risk characterization index; let the total fuzzy return... The triangular fuzzy representation is as follows: Then its risk objective function is defined as: .in, The width of the fuzzy return range represents the range where the return is more susceptible to parameter fluctuations, and thus carries higher risk. Therefore, the second objective function is: ; Finally, the following multi-objective crop planting optimization model is established: , ,in, The target profit value after clarification. This represents the risk value for fluctuations in returns.

6. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 5, characterized in that, In step 5, the following constraints are set: (1) For each plot of land, the sum of the areas allocated to various crops cannot exceed the total area of ​​that plot: ; (2) If the first The plot of land is not suitable for planting. If crops are planted, the corresponding planting area is zero. ; (3) To avoid the planting area being too scattered, a minimum planting area threshold is set. : ; (4) For a certain type of crop, the total planting area is limited according to the market size: ,in, and They represent the first Minimum and maximum permitted planting areas for crops; (5) Considering multi-year planning, in order to prevent the same crop from being planted continuously on the same plot of land, a 0-1 variable is adopted. Indicates the first Year Is the plot of land planted with the first Crop planting: Then the rotation constraint is: (6) Nonnegativity constraint: .

7. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 6, characterized in that, In step 6, the fuzzy objective function is clarified. The centroid method is used to clarify triangular fuzzy numbers. For any triangular fuzzy number: Its clarification results The calculation is as follows: ； Therefore, the total fuzzy gain The target value for the clarification benefit is: The risk target value is: At this point, the multi-objective model can be transformed into a deterministic bi-objective optimization model: ， 。 8. The multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 7, characterized in that, The specific steps of step 7 are as follows: Step 1: Set the population size as The maximum number of iterations is The crossover probability is The mutation probability is Randomly generate the initial population: , among which each individual This corresponds to a complete plan for allocating planting area for crops across different plots: The initial individual is then subjected to constraint checks, including plot area constraints, crop suitability constraints, and minimum planting area constraints. If the constraints are not met, a repair operator is used to correct them so that they are called feasible solutions. Step 2: For each individual Calculate the profit target based on steps 4 to 6. and risk objectives : ， ； Step 3: Determine non-dominant relationships for all individuals in the population: If individual The following conditions must be met: And there is at least one target. satisfy: Then it is called an individual. Dominant Individual When making non-dominant judgments, the following should also be considered: as well as If both of the above conditions are met, and at least one condition is strictly true, then Dominate ; Based on dominance relationships, the population is divided into multiple non-dominated layers: ,in, This is the first non-dominated layer, i.e., the Pareto optimal layer; Step 4: Calculate crowding distance for individuals within the same non-dominated stratum; for individuals within the same non-dominated stratum, calculate crowding distance according to their respective benefit objectives. and risk objectives Sort the values; For non-boundary individuals, their first... The crowding distance on each target can be expressed as: ,individual The total congestion distance is: ,in, and They represent the first and second digits in the same non-dominated layer. The maximum and minimum values ​​of the objective function; the larger the crowding distance, the fewer other solutions there are around the individual, and the better the distribution representativeness of it in the Pareto front; Within the same non-dominated layer, individuals with larger crowding distances are preferentially retained to avoid excessive concentration of optimization results in a certain area; Step 5: After the crossover operation, a new individual is generated. If real number encoding is used, a simulated binary crossover operator is employed. The mutation operation can be represented as: ,in, For small-scale random perturbations; perform repair operations on new individuals, scaling proportionally: ; Step 6: The joint population was re-sorted using a fast non-dominated ranking and crowding calculation, and the top-ranked populations were selected based on the principles of prioritizing non-dominated layers and crowding. Individuals constitute the next generation of the population: ; Step 7: If the current iteration count reaches the maximum iteration count Or the Pareto front of the population changes less than a preset threshold for several consecutive generations. If the iteration fails, stop; otherwise, return to Step 2 and continue iterating. The Pareto front change is expressed as: ,when The algorithm is considered to have converged at that time.

9. A multi-objective crop planting optimization method considering fuzzy uncertainty according to claim 8, characterized in that, In step 8, the individuals in the first non-dominated layer obtained in step 7 are output as the Pareto optimal planting scheme set; if the final Pareto optimal scheme set is: , where each scheme Each corresponds to a set of profit target values and risk target value Finally, the final implementation plan is selected from the Pareto solution set based on the decision-maker's preferences. (1) Prioritize profit: ; (2) Risk Priority: ; (3) Construct a comprehensive evaluation function: ； in, Indicates the first The overall evaluation value of the Pareto candidate planting schemes; Representation scheme Clearly define the target revenue value; Representation scheme Risk target value; Weights for return preferences; These represent the maximum and minimum values ​​of the objective value of the Pareto solution set, respectively; These are the maximum and minimum values ​​of the risk objective value in the Pareto solution set, respectively. The final solution with the highest overall evaluation value was selected. .

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