Soil cadmium ion removal method based on hybrid simulated annealing cuckoo algorithm

Abstract

The invention discloses a soil cadmium ion removal method based on a hybrid simulated annealing cuckoo algorithm. The method comprises the following steps: setting related algorithm parameters; initializing a population, and generating an initial solution set; a multi-objective optimization model is established, and cadmium removal efficiency and soil health are balanced; exploring a global optimal solution through the long jump characteristic of Levy flight; carrying out fitness calculation and sorting, evaluating a current population and screening an elite solution; simulating an annealing disturbance triggering condition; the cadmium migration characteristic change caused by environment change in actual restoration is simulated; crossover and variation are carried out, and population diversity is enhanced through genetic manipulation; population updating, termination condition judgment, algorithm termination opportunity determination and optimal scheme output. According to the method, through algorithm optimization, the optimal organic acid application amount and the optimal cadmium ion concentration reduction can be achieved, the maximum benefit of the remediation process is ensured, the cadmium removal efficiency is improved by 25%-30%, the remediation period is shortened by 40%, the organic acid application amount is dynamically balanced through an intelligent algorithm, and the soil pH fluctuation is smaller than 0.5.

Description

Technical Field

[0001] The present invention relates to the field of soil heavy metal pollution remediation, and particularly to a method for removing cadmium ions from soil based on a hybrid simulated annealing cuckoo algorithm. Background Art

[0002] Cadmium (Cd), as a toxic heavy metal element, is one of the important factors of soil pollution and widely exists in fields such as mining, metallurgical industry, battery manufacturing, and agricultural fertilization. The long-term accumulation of cadmium will not only affect soil fertility but also enter the human body through the food chain, causing serious harm to human health. Cadmium has strong biological toxicity, which can interfere with the growth and development of plants and affect the immune system, kidney function, and bone health of animals and humans. Therefore, developing efficient soil remediation technologies to remove cadmium pollution from soil has become an important research topic in the fields of environmental science and agroecology.

[0003] Currently, the treatment methods for soil cadmium pollution mainly include chemical remediation, physical remediation, and biological remediation, etc. Each method has its own advantages and disadvantages and shows different remediation effects under different circumstances. In recent years, the application of organic acids has also provided new ideas for phytoremediation. Organic acids, such as citric acid, malic acid, and oxalic acid, etc., can react with heavy metal ions in the soil to form complex compounds, increase the solubility of these metal ions, and make them more easily absorbed by plants. By adding organic acids, not only can the absorption ability of plants to heavy metals be enhanced, but also the chemical properties of the soil can be improved. However, relying solely on the effect of organic acids is often limited, and it may cause soil acidification and affect the growth of plants. Therefore, relying solely on organic acid treatment cannot effectively solve the cadmium pollution problem. Therefore, developing a comprehensive remediation method that can both improve the absorption efficiency of plants to cadmium and avoid the negative impacts of organic acids on the soil and plants has become an urgent problem to be solved. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide a method for removing cadmium ions from soil based on a hybrid simulated annealing cuckoo algorithm.

[0005] Technical Solution: The present invention forms a hybrid simulated annealing cuckoo algorithm by combining the cuckoo algorithm and the simulated annealing algorithm, and regulates the acetic acid concentration and the oxalic acid spraying frequency through the mutual fusion of the algorithms to optimize the balance between the cadmium ion concentration reduction efficiency and the total amount of organic acid application, including the following steps:

[0006] (1) Set relevant algorithm parameters;

[0007] (2) Initialize the population, generate an initial solution set, covering possible organic acid application strategies;

[0008] (3) Propose a multi-objective optimization model to balance cadmium removal efficiency and soil health;

[0009] (4) Explore the global optimal solution through the long jump characteristics of Levy flight;

[0010] (5) Fitness calculation and sorting, evaluate the current population and screen for elite solutions;

[0011] (6) Simulate the triggering conditions of annealing perturbation;

[0012] (7) When the algorithm determines that it has fallen into a local optimum, trigger the perturbation operation to simulate the change in cadmium migration characteristics caused by environmental changes during actual remediation;

[0013] (8) Crossover and mutation, enhance population diversity through genetic operations;

[0014] (9) Population update, merge the new and old solution sets and screen the next generation of populations;

[0015] (10) Termination condition judgment, determine the termination time of the algorithm, and output the optimal solution.

[0016] Further, the step (1) includes:

[0017] Set the step size factor α, and the dynamic adjustment formula is: where ΔC Cd is the current cadmium concentration reduction value, and the step size factor adaptively shrinks with the remediation progress to avoid late-stage oscillations;

[0018] The Levy index β = 1.5, which is used to control the heavy-tailed distribution characteristics of Levy flight;

[0019] The discovery probability P a = 0.25, which is used for mutation operations to avoid the population falling into a local optimum;

[0020] The maximum number of iterations N max = 100, which limits the running time of the algorithm to prevent infinite loops;

[0021] Set the annealing parameters, the initial temperature T0 = 0.5, and the attenuation coefficient k = 0.1, to control the perturbation amplitude to decrease with iterations;

[0022] The fitness improvement threshold θ = 0.01, which is used to judge the critical condition for triggering simulated annealing.

[0023] Further, the definition of the initial solution set in the step (2) includes:

[0024] Each solution set contains the acetic acid concentration C1 and the oxalic acid spraying frequency F1, which are randomly generated from the following intervals respectively:

[0025] C1 ∈ [0.1, 0.5] mol / L: Take into account plant tolerance and cadmium dissolution efficiency;

[0026] F1 ∈ [2, 4] times / week: Balance the spraying cost and the repair effect;

[0027] The population size n = 50: Improve the global search ability through an initial solution set with sufficient diversity.

[0028] Furthermore, the multi-objective optimization model in step (3) includes objective function 1 and objective function 2,

[0029] Objective function 1 is expressed as:

[0030]

[0031] where f1(X i ) is to maximize the cadmium removal amount, the plant enrichment amount A 植物 = biomass * cadmium enrichment coefficient, the biomass is obtained by harvesting and weighing the plants, and the cadmium enrichment coefficient is the ratio of the cadmium concentration in the plants measured in the laboratory to the cadmium concentration in the soil; A max is the maximum cadmium enrichment ability of the plants measured in the laboratory; the denominator introduces a pH offset penalty term. When the soil pH deviates from neutral, the objective function value is reduced, reflecting the immediate regulation of soil health during the repair process;

[0032] Objective function 2 is expressed as:

[0033]

[0034] where f3(X i ) is to balance the organic acid usage efficiency, and at the same time constrain the total amount of organic acid C max = 0.5 mol / L, F max = 4 times / week, to avoid soil compaction caused by excessive use.

[0035] Comprehensive fitness function:

[0036] f(X i ) = 0.4 * f1(X i ) - 0.1 * f2(X i )

[0037] Taking cadmium removal as the core goal, with a weight of 0.6, soil health as 0.3, and cost control as 0.1.

[0038] Furthermore, the update formula for the Levy flight global search parameters in step (4):

[0039]

[0040] ΔC Cd represents the direction of guiding the search. The more the cadmium concentration decreases, the smaller the step size; when the pH deviates from neutral, increase the adjustment amplitude of the oxalic acid frequency;

[0041] Levy distribution generation:

[0042] The calculation of σ is based on the Gamma function and the β value to ensure that the step size conforms to the characteristics of the heavy-tailed distribution.

[0043] Furthermore, step (5) includes: calculating f(X i ) for each solution. The larger the value, the better the comprehensive performance. Retain the top 10% of the high-fitness solutions. Combining with the actual scenario of soil remediation, the calculation of the fitness function f(X i ) needs to be based on the soil cadmium concentration, pH value, and plant biomass data monitored in real time. After each round of iteration, soil samples are collected through a plant planting instrument to measure the cadmium concentration and pH value, update the parameters of the objective function, and dynamically adjust the search direction of the algorithm.

[0044] Furthermore, the triggering condition for the simulated annealing perturbation in step (6) is that if the dynamic detection algorithm stagnates, a local perturbation is triggered; if the fitness improvement Δf(X i ) < 0.01 in 8 consecutive iterations, it is determined to be trapped in a local optimum; set the threshold θ = 0.01 and calibrate it through experimental data to balance the sensitivity and false positive rate.

[0045] Furthermore, step (7) applies a random perturbation to the non-elite solutions to jump out of the local optimum.

[0046] Perturbation formula: C new = C old * (1 + η * rand(-1, 1))

[0047] F new = F old * (1 + η * rand(-1, 1))

[0048] The annealing coefficient η = T0 * e -k*t exponentially decays with the number of iterations t. The perturbation amplitude is large at the beginning and gradually converges later; the random direction rand(-1, 1) generates uniformly distributed random numbers to ensure the diversity of the perturbation directions.

[0049] Furthermore, step (8) includes a crossover operation and a mutation operation.

[0050] Crossover operation: In uniform crossover, randomly select the gene loci of elite solutions and non-elite solutions and exchange some parameters.

[0051] Mutation operation: With a probability P a = 0.25, apply a Gaussian perturbation X′ i = X i + N(0, 0.1). The crossover operation simulates the experience sharing in multi-site remediation.

[0052] Further, the termination conditions of the step (10) include:

[0053] a. Reaching the maximum number of iterations N max = 100;

[0054] b. The global optimal solution has no significant change for 15 consecutive times Δf best < 0.005, and output the optimal acetic acid concentration and oxalic acid spraying frequency.

[0055] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The present invention adopts the hybrid cuckoo search algorithm (SA-CS) to optimize the application amount of organic acids and the cadmium removal effect, which can be dynamically adjusted according to the actual conditions of the soil and plants, effectively improving the efficiency of the cadmium removal process; Through algorithm optimization, the optimal application amount of organic acids and the optimal reduction of cadmium ion concentration can be achieved, ensuring the maximum benefit of the remediation process, with the cadmium removal efficiency increased by 25%-30%, the remediation cycle shortened by 40%, the intelligent algorithm dynamically balancing the amount of organic acids used, and the soil pH fluctuation less than 0.5. Brief Description of the Drawings

[0056] Figure 1 is a flowchart of the present invention. Detailed Embodiments

[0057] The technical solutions of the present invention will be further described below with reference to the drawings.

[0058] The efficient heavy metal removal for cadmium ion-enriched soil mainly includes planting ryegrass and rape on the land rich in cadmium ions, combined with specific organic acid treatment, to improve the cadmium enrichment efficiency of the subsequent crop sunflower in the system;

[0059] Regularly add low-concentration organic acids to the plant irrigation system to promote the absorption and accumulation of cadmium by rape, and detect the cadmium ion concentration in the soil with the help of a soil and plant sample analyzer; Introduce the soil remediation agent sunflower to effectively absorb the residual cadmium ions in the soil, and then use the hybrid cuckoo search algorithm to control the total amount of organic acids added to achieve the optimal absorption effect; Under the detection of the soil and plant sample analyzer, detect whether the soil after removal has achieved the purpose of efficiently reducing the cadmium ion concentration in the soil.

[0060] As Figure 1 shown, the present invention regulates the acetic acid concentration C1 and the oxalic acid spraying frequency F1 through the mutual fusion of algorithms, and optimizes the balance between the cadmium ion concentration reduction efficiency and the total amount of organic acid application. The specific optimization process is as follows:

[0061] (1) Set relevant algorithm parameters:

[0062] The step size factor α, and the dynamic adjustment formula is: where ΔC Cd is the current reduction value of cadmium concentration, and the step factor adaptively shrinks with the progress of remediation to avoid late-stage oscillation;

[0063] The Lévy index β = 1.5, which is used to control the heavy-tailed distribution characteristics of Lévy flight to ensure large-range jump search;

[0064] The discovery probability P a = 0.25, which is used for mutation operation to avoid the population falling into local optimum;

[0065] The maximum number of iterations N max = 100, which limits the running time of the algorithm to prevent infinite loop;

[0066] Set the annealing parameters, the initial temperature T0 = 0.5, and the attenuation coefficient k = 0.1 to control the perturbation amplitude decreasing with iteration;

[0067] The fitness improvement threshold θ = 0.01, which is used to judge the critical condition for triggering simulated annealing.

[0068] (2) Initialize the population, generate the initial solution set, covering possible organic acid application strategies:

[0069] Definition of the solution; each solution contains acetic acid concentration C1 and oxalic acid spraying frequency F1, which are randomly generated from the following intervals respectively:

[0070] C1 ∈ [0.1, 0.5] mol / L: Taking into account plant tolerance and cadmium dissolution efficiency;

[0071] F1 ∈ [2, 4] times / week: Balancing spraying cost and remediation effect.

[0072] The population size n = 50: Improving the global search ability through an initial solution set with sufficient diversity

[0073] (3) Propose a multi-objective optimization model to balance cadmium removal efficiency and soil health. Set up the objective function as follows:

[0074] Objective function 1:

[0075]

[0076] where f1(X i ) is to maximize the cadmium removal amount, and the plant enrichment amount A 植物 = biomass * cadmium enrichment coefficient. The biomass is obtained by harvesting and weighing the plants, and the cadmium enrichment coefficient is the ratio of the cadmium concentration in the plants measured in the laboratory to the soil cadmium concentration. A maxis the maximum cadmium enrichment capacity of plants determined in the laboratory; a pH offset penalty term is introduced in the denominator, which reduces the objective function value when the soil pH deviates from neutral (6.5), reflecting the immediate regulation of soil health during the remediation process.

[0077] Objective function 2:

[0078]

[0079] Among them, f3(X i ) is to balance the use efficiency of organic acids and at the same time constrain the total amount of organic acids (C max = 0.5 mol / L, F max = 4 times / week) to avoid soil compaction caused by excessive use.

[0080] Comprehensive fitness function (weighted summation):

[0081] f(X i ) = 0.4 * f1(X i ) - 0.1 * f2(X i )

[0082] Taking cadmium removal as the core objective (weight 0.6), taking into account soil health (0.3) and cost control (0.1).

[0083] (4) Levy flight global search, exploring the global optimal solution through the long jump characteristics of Levy flight.

[0084] Parameter update formula:

[0085]

[0086] ΔC Cd is used to guide the search direction. The more the cadmium concentration decreases, the smaller the step size; when the pH deviates from neutral, increase the adjustment amplitude of oxalic acid frequency.

[0087] Levy distribution generation: The calculation of σ is based on the Gamma function and β value to ensure that the step size conforms to the heavy-tailed distribution characteristics.

[0088] (5) Fitness calculation and sorting, evaluating the current population and screening elite solutions. Calculate f(X i ) for each solution. The larger the value, the better the comprehensive performance. Retain the top 10% of the high-fitness solutions (i.e., the top 5) to avoid the loss of excellent genes. Combining with the actual scenario of soil remediation, the fitness function f(X i) The calculation needs to be based on the real-time monitored soil cadmium concentration, pH value and plant biomass data to ensure that the algorithm optimization is synchronized with the on-site remediation progress. After each iteration, soil samples are collected through the plant cultivation instrument to measure the cadmium concentration and pH value, update the parameters of the objective function, and dynamically adjust the search direction of the algorithm.

[0089] (6) Simulated annealing perturbation triggering condition: If the dynamic detection algorithm stalls, local perturbation is triggered. If the fitness improvement Δf(X i ) < 0.01 in 8 consecutive iterations, it is determined to fall into the local optimum. Set the threshold θ = 0.01 and calibrate it through experimental data to balance the sensitivity and misjudgment rate.

[0090] (7) When the algorithm determines that it has fallen into the local optimum, a perturbation operation is triggered to simulate the change in cadmium migration characteristics caused by environmental changes (such as rainfall and temperature fluctuations) during actual remediation. The acetic acid concentration and oxalic acid frequency after perturbation need to be verified by soil sensors to ensure that the adjusted strategy still meets the plant tolerance threshold and avoid excessive acidification or resource waste. At this time, a random perturbation is applied to the non-elite solutions to jump out of the local optimum.

[0091] Perturbation formula: C new = C old * (1 + η * rand(-1, 1))

[0092] F new = F old * (1 + η * rand(-1, 1))

[0093] Annealing coefficient η = T0 * e -k*t Exponentially decays with the number of iterations t. The perturbation amplitude is large in the initial stage and gradually converges in the later stage. The random direction rand(-1, 1) generates uniformly distributed random numbers to ensure the diversity of perturbation directions.

[0094] (8) Crossover and mutation to enhance the population diversity through genetic operations.

[0095] Crossover operation: In uniform crossover, randomly select the gene loci (oxalic acid concentration) of the elite solution and the non-elite solution, and exchange some parameters. For example, the parent solutions [C1, F1] and [C2, F2] generate the offspring [C1, F2] and [C2, F1].

[0096] Mutation operation: Probability P a = 0.25; Apply Gaussian perturbation X′ i = X i+N(0, 0.1) to avoid population homogenization. The crossover operation simulates the experience sharing in multi-plot remediation. For example, combining the acetic acid concentration parameter with high cadmium absorption efficiency and the low-frequency oxalic acid spraying strategy to explore better solutions. The mutation operation introduces Gaussian noise to simulate the parameter fine-tuning caused by equipment errors or environmental fluctuations during actual application, enhancing the robustness of the algorithm.

[0097] (9) Population update, merging the old and new solution sets and screening the next-generation population. Merge the elite solutions, perturbed solutions, and crossover solutions into 100 candidate solutions. Sort them by fitness and retain the top 50 optimal solutions to ensure a constant population size.

[0098] (10) Termination condition judgment, determining the termination time of the algorithm and outputting the optimal solution.

[0099] Termination conditions: 1. Reach the maximum number of iterations N max = 100; 2. The global optimal solution has no significant change for 15 consecutive times (Δf best < 0.005), output the optimal acetic acid concentration C1 and oxalic acid spraying frequency F1 to ensure the maximization of the cadmium ion concentration reduction efficiency and the immediate regulation of soil health.

Claims

1. A method for removing cadmium ions from soil based on a hybrid simulated annealing cuckoo algorithm, characterized in that, The cuckoo algorithm and the simulated annealing algorithm are combined to form a hybrid simulated annealing cuckoo algorithm. By the mutual integration of the algorithms, the acetic acid concentration and the oxalic acid spraying frequency are regulated to optimize the balance between the cadmium ion concentration reduction efficiency and the total amount of organic acid application, including the following steps: (1) Set relevant algorithm parameters; (2) Initialize the population, generate an initial solution set, covering possible organic acid application strategies; (3) Propose a multi-objective optimization model to balance cadmium removal efficiency and soil health; (4) Explore the global optimal solution through the long jump characteristics of Levy flight; (5) Fitness calculation and sorting, evaluate the current population and screen elite solutions; (6) Simulate the annealing perturbation trigger condition; (7) When the algorithm determines that it has fallen into a local optimum, trigger a perturbation operation to simulate the change in cadmium migration characteristics caused by environmental changes in actual remediation; (8) Crossover and mutation, enhance population diversity through genetic operations; (9) Population update, merge the old and new solution sets and screen the next generation of populations; (10) Judgment of termination conditions, determine the termination time of the algorithm, and output the optimal solution.

2. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, characterized in that The step (1) includes: Set the step size factor α, and the dynamic adjustment formula is: where ΔC Cd is the current reduction value of cadmium concentration, and the step size factor adaptively shrinks with the progress of remediation to avoid late oscillation; The Levy index β = 1.5, which is used to control the heavy-tailed distribution characteristics of Levy flight; Discovery probability P a = 0.25, which is used for mutation operation to prevent the population from falling into local optimum; The maximum number of iterations N max = 100, which limits the running time of the algorithm and prevents infinite loops; Set the annealing parameters, the initial temperature T0 = 0.5, the attenuation coefficient k = 0.1, and control the perturbation amplitude to decrease with iteration; The fitness improvement threshold θ = 0.01, which is used to judge whether to trigger the critical condition of simulated annealing.

3. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, characterized in that The definition of the initial solution set in the step (2) includes: Each solution set contains the acetic acid concentration C1 and the oxalic acid spraying frequency F1, which are randomly generated from the following intervals respectively: C1 ∈ [0.1, 0.5] mol / L: Taking into account plant tolerance and cadmium dissolution efficiency; F1 ∈ [2, 4] times / week: Balancing spraying cost and remediation effect; The population size n = 50: Improve the global search ability through an initial solution set with sufficient diversity.

4. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, characterized in that, The multi-objective optimization model in the step (3) includes objective function 1 and objective function 2, Objective function 1 is expressed as: Among them, f1(X i ) is to maximize the cadmium removal amount, and the plant enrichment amount A 植物 = biomass * cadmium enrichment coefficient. The biomass is obtained by harvesting and weighing the plants, and the cadmium enrichment coefficient is the ratio of the cadmium concentration in the plants determined in the laboratory to the cadmium concentration in the soil; A max is the maximum cadmium enrichment capacity of the plants determined in the laboratory; a pH offset penalty term is introduced in the denominator. When the soil pH deviates from neutral, the objective function value is reduced, reflecting the immediate regulation of soil health during the remediation process; Objective function 2 is expressed as: Among them, f3(X i ) is to balance the use efficiency of organic acids while restricting the total amount of organic acids C max = 0.5 mol / L, F max = 4 times / week to avoid soil compaction caused by excessive use. Comprehensive fitness function: f(X i ) = 0.4 * f1(X i ) - 0.1 * f2(X i ) Taking cadmium removal as the core objective, with a weight of 0.6, soil health as 0.3, and cost control as 0.

1.

5. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, wherein The Levy flight global search parameter update formula in the step (4): ΔC Cd Indicates the direction of the guiding search. The greater the decrease in cadmium concentration, the smaller the step size; When the pH deviates from neutral, increase the adjustment amplitude of the oxalic acid frequency; Levy distribution generation: The calculation of σ is based on the Gamma function and the β value to ensure that the step size conforms to the heavy-tailed distribution characteristics.

6. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, characterized in that The said step (5) includes: calculating f(X i ) for each solution, where the larger the value, the better the comprehensive performance. Retain the top 10% of the high-fitness solutions. Combining with the actual scenario of soil remediation, the calculation of the fitness function f(X i ) needs to be based on the data of soil cadmium concentration, pH value and plant biomass monitored in real time. After each round of iteration, collect soil samples through a plant cultivation instrument, measure the cadmium concentration and pH value, update the parameters of the objective function, and dynamically adjust the search direction of the algorithm.

7. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, wherein The triggering condition of the simulated annealing perturbation in step (6) is that if the dynamic detection algorithm stagnates, local perturbation is triggered; if the fitness improvement Δf(X i ) < 0.01 in 8 consecutive iterations, it is determined to fall into a local optimum; a threshold θ = 0.01 is set and calibrated through experimental data to balance the sensitivity and false positive rate.

8. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, wherein In the step (7), apply a random perturbation to non-elite solutions to jump out of the local optimum, Disturbance formula: C new = C old *(1 + η * rand(-1, 1)) F new = F old *(1 + η*rand(-1, 1)) Annealing coefficient η = T0 * e -k*t Exponentially decays with the number of iterations t, with a large initial perturbation amplitude and gradually converges in the later stage; the random direction rand(-1, 1) generates uniformly distributed random numbers to ensure the diversity of perturbation directions.

9. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, wherein The step (8) includes a crossover operation and a mutation operation, Crossover operation: In uniform crossover, randomly select the gene loci of elite solutions and non-elite solutions and exchange some parameters; Mutation operation: probability P a = 0.25 applies Gaussian perturbation X' to some of the solutions i = X i + N(0, 0.1). The crossover operation simulates experience sharing in multi-site remediation.

10. The method for removing cadmium ions from soil based on the hybrid simulated annealing cuckoo algorithm according to claim 1, characterized in that, The termination conditions in the step (10) include: a. Reach the maximum number of iterations N max = 100; b. The global optimal solution has not changed significantly for 15 consecutive times, Δf best <0.005, output the optimal acetic acid concentration and oxalic acid spraying frequency.

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