Workshop scheduling and production scheduling method based on improved artificial raindrop algorithm

Abstract

The invention discloses a job-shop scheduling and production scheduling method based on an improved artificial raindrop algorithm, and the method comprises the following steps: 1, carrying out problem modeling and constraint definition, selecting a simulation platform and a job-shop scheduling model corresponding to the simulation platform, building a simulation environment containing constraints, constructing a mathematical model of job-shop scheduling, and carrying out the optimization of a job-shop scheduling model; the minimum completion time is calculated according to a plurality of cases of different scales and different processes. Through multi-strategy improvement, collaborative improvement of convergence speed, precision and robustness is realized, invalid search and waiting time of a traditional algorithm in a scheduling problem are effectively reduced, an efficient solution is provided for job-shop scheduling, and the method has a wide application prospect.

Description

Technical Field

[0001] This invention belongs to the field of production planning and scheduling technology, and in particular relates to a job shop scheduling method based on an improved artificial raindrop algorithm. Background Technology

[0002] Job shop scheduling is a classic combinatorial optimization problem. As a core problem in the field of discrete manufacturing system optimization, its essence is to achieve global optimization of production cycle, cost, or energy consumption objectives by rationally allocating equipment, processes, and time windows under limited resource constraints. Minimizing the maximum completion time is a single-objective problem with minimum time as the constraint, belonging to the Np-hard problem. With the development of the economy and society, the scale of factory production continues to expand, and the difficulty of solving problems increases exponentially. Traditional mathematical programming methods are difficult to apply in practice, and the emergence of intelligent algorithms provides an effective means to solve such problems. Optimization problems are very common in life, and combinatorial optimization problems exist in different fields. How to find the optimal solution in a short time is the direction of optimization problem development. In the early stages of optimization problem development, people used mathematical optimization methods such as integer programming to solve them. However, this method requires calculating gradients, which is computationally intensive and time-consuming for complex problems. In contrast, stochastic methods do not need to know the gradient of the solution, but instead calculate the objective function and evaluate the solution under the objective value. Heuristic algorithms are a type of stochastic method that solves problems through computer simulation. Artificial raindrop algorithm is a relatively new algorithm in recent years. It simulates the process of raindrop formation, falling and flowing in nature. The research focuses on how to balance the algorithm's exploration and development capabilities, and how to integrate problem characteristics into the algorithm design. Summary of the Invention

[0003] The purpose of this invention is to provide a job shop scheduling method based on an improved artificial raindrop algorithm to solve the technical problems mentioned in the background art.

[0004] To achieve the above objectives, the specific technical solution of the present invention is as follows: A job shop scheduling method based on an improved artificial raindrop algorithm, comprising the following steps: Step 1: Problem Modeling and Constraint Definition Select a simulation platform and its corresponding job shop scheduling model, build a simulation environment with constraints, and construct a mathematical model for job shop scheduling. Calculate the minimum completion time for multiple cases of different scales and processes. Step 2: Population Initialization N parent water vapor population individuals are generated using a chaotic mapping method, exhibiting a random and uniform distribution. Its value ranges from 0 to 1, and the population dimension is... Where n is the number of workpieces and m is the number of machines; Step 3: Encode and decode the process. For cases where the population individuals encoded with floating-point numbers do not match the actual integer machine sequence number and process number, the corresponding index sequence is obtained by vector sorting the random sequence of all dimensions of each individual, and then the corresponding processing sequence is generated by encoding. The generated processing sequence is then decoded, and the processing time of the corresponding individual is calculated by using the fitness function. Step 4: Water Vapor Aerial Search Operator Based on the existing population, for each particle, with a certain probability R, we randomly select whether to execute the aerial search operator. For individuals that meet the probability conditions, we use Levy flight to generate a random step size vector of length D, and introduce a random perturbation parameter R1. We calculate the difference between the currently selected individual and the previous generation of individuals, and generate a new individual by superimposing these random conditions. They are inserted into the population to replace the original individuals; Step 5: Raindrop Formation Process The formation of raindrops is defined as the geometric center of existing water vapor, for The water vapor matrix is ​​averaged in each column to obtain a... Raindrops of different dimensions; Step 6: Perform a raindrop descent process that takes wind direction into account. Fitness calculations are performed on the formed raindrops to determine the current iteration number. If the set iteration number condition is not met, it is considered to be in the early stage of iteration. This is achieved by introducing gravity G and air resistance drag force. drag coefficient The wind direction and angle are used to simulate the irregular trajectory of a spherical object under the influence of wind direction and airflow, thus generating a new position. If the iteration conditions are met, the raindrop dimensions can be changed in the later stages of the iteration. The value is used to simulate the vertical fall process; Step 7: Conduct the raindrop collision and new individual generation process. Based on the new position obtained in step 6 The collision strategy is updated so that raindrops, upon hitting the ground and colliding, will splash outwards in a normal distribution, creating new raindrops. The number of newly generated raindrops is completely random. For ease of calculation, the number of newly generated raindrops is defined as the population size N. All new individuals form a subpopulation. ; Step 8: Select and update raindrop flow strategies based on experience. After a collision, raindrops flow towards lower elevations. Different flow patterns are selected based on the set iteration conditions. When the iteration conditions are met, two experienced particles guide the current raindrop flow direction. The randomness of the flow is simulated by adding a perturbation term and a random step size. When the iteration conditions are not met, a flow operator with the Baldwin effect is used to encourage individuals and accelerate the evolution process. Each particle flows 3 times. The new position is updated each time, and the fitness is calculated. A greedy strategy is used to replace the current subpopulation individuals with excellent solutions and discard inferior solutions, keeping the current individual. When all individuals in the subpopulation have completed the flow, two individuals are randomly selected and added to the experience pool. At the same time, the number of particles in the experience pool is checked. If the maximum number of particles in the experience pool is met, redundant particles are deleted. Step 9: Merge the offspring and parent populations After merging the offspring population and the parent population, the fitness is calculated, and the particles with better fitness are selected as the new generation population. The population size is limited to N. Step 10: Perform iterative training Repeat steps 3 to 9, continuously select the best option through different strategies to achieve iterative training of the algorithm. During the training process, control the iterative training process according to the preset termination condition. When the preset training round number threshold is met, terminate the iterative training process, output the final solution result of the corresponding case, and generate a scheduling Gantt chart.

[0005] Preferably, in step 2, the method for generating the initial population is Circle chaotic mapping initialization.

[0006] Preferably, in step 3, the encoding method is random key encoding.

[0007] Preferably, in step 4, the selection probability R is set to 0.5, and the proposed water vapor search operator is a local search method. Based on the current water vapor particles, it is added to the generated Levy flight term and perturbation term R1 with heavy tail distribution to perform a local search.

[0008] Preferably, in step 6, the raindrop falling operator considering wind direction introduces a perturbation parameter and a tangent function to ensure that its scattering range is within... Between these points, the dimension selected during the vertical descent process is randomly chosen.

[0009] Preferably, in step 7, the new raindrops generated by the collision are normally distributed, which is simulated using the Monte Carlo method.

[0010] Preferably, in step 8, two flow modes for new raindrops are selected. The empirical flow mode is determined by a linear combination of two sub-directions d1 and d2 and flow factors τ and learning factors c1 and c2. The two particles selected from the empirical pool are randomly selected. The flow operator of the Baldwin effect determines the evolution direction by comparing the differences between different individuals. The step size for generating new solutions is determined by parameter S.

[0011] Preferably, in step 8, a bubble sorting method is adopted for updating the experience pool. The fitness values ​​of all particles in the experience pool are calculated and sorted in order from best to worst. Based on the set experience pool size N, redundant particles with poor fitness are removed, thereby maintaining the experience pool.

[0012] Preferably, in step 8, the learning factors c1 and c2 are used in a non-linear transformation manner to continuously change the learning rate and gradually transition to the preset minimum learning threshold, and the transition process is controlled by the number of iterations.

[0013] Preferably, in step 10, the job shop scheduling model case is simulated using 10 examples from la01 to la10 in the standard benchmark test set LA series.

[0014] in: In step 1, the constraints of the job shop scheduling model are: Processing sequence constraint: The processing sequence of each workpiece cannot be changed.

[0015] Machine mutual exclusion constraint: At any given time, each machine can only process one workpiece in one operation.

[0016] Processing time constraint: The completion time of a process is equal to the start time plus the machine processing time.

[0017] Time variable constraint: The processing time must be a positive number, and the first processing step of each workpiece must be 0.

[0018] in: For the set of operations, each workpiece includes One operation. Let be the processing time of the i-th workpiece on the j-th machine. For homework The start time, For homework End time, This represents the maximum completion time.

[0019] Further, in step 2, the chaotic population initialization uses Circle chaotic initialization, as shown in the formula:

[0020] Where mod represents the modulo operation.

[0021] Further, in step 4, the formula for the water vapor atmospheric search operator is:

[0022] in: This is a water vapor individual of generation G+1. and These are two different individuals within the Gth generation water vapor individual.

[0023] It follows a normal distribution with a mean of 0 and a standard deviation of 1. .

[0024] For the introduced random item, round will round the resulting random number to the nearest whole number.

[0025] For the introduction of the Levi flight process.

[0026] A further feature, in step 6, is that the formula for the descent operator considering wind direction is:

[0027] in: For newly formed raindrops, The wind direction.

[0028] g is the gravitational acceleration, taken as 9.8 m / s², and h is the fall height, i.e., the fitness value.

[0029] The drag force is caused by air resistance.

[0030] The terminal velocity of the raindrop is given by the formula:

[0031] in The drag coefficient is 0.4-0.5 for approximately spherical objects; in this paper, the value is 0.4. The density of air is taken as 1.225 kg / m³.

[0032] Further, in step 7, the raindrop collision operator formula is:

[0033] in: These are the tiny raindrops produced after the collision.

[0034] sign is the sign function. and It is a random number between 0 and 1.

[0035] It refers to any water vapor molecule in the water vapor population.

[0036] As a further feature, in step 8, the formula for the first selectable operator of the raindrop flow selection operator is:

[0037] in: This represents the position of the raindrop after the flow of the Gth generation.

[0038] The flow factor is set to 2. Preparing for the current flow of raindrops, and They are two particles randomly selected from the raindrop pool. There are two flow directions. It is a linear combination of flow directions.

[0039] Further, in step 8, the formula for the Baldwin effect raindrop flow operator is:

[0040] in: y1 represents the direction of fitness difference, i.e., the evolutionary direction. , as well as Three different particles were randomly selected. After the flow, a new position is created.

[0041] Further, in step 10, 10 simulation examples from the standard workshop scheduling test set la series, la01-la10, are used for simulation. Taking la07 as an example, its data is as follows:

[0042] In matrix J, each row represents a different workpiece, and the number in each row represents the machine number selected for that processing step. For example, the number 5 in the 15th row and 1st column means that the first process of the 15th workpiece is processed on machine number 5. Each row and column of matrix T corresponds one-to-one with matrix J, representing the processing time of its process on the corresponding machine.

[0043] The job shop scheduling method based on the improved artificial raindrop algorithm of the present invention has the following advantages:

[0044] The improved artificial raindrop algorithm proposed in this invention has significant advantages in solving the job shop scheduling problem. First, initializing the population through Circle chaotic mapping improves the spatial coverage and diversity of initial solutions, effectively avoiding premature convergence and laying the foundation for global search. Second, introducing a water vapor search operator to perturb the population, combined with Lévy flight step size and random perturbation mechanisms, enhances the algorithm's ability to escape local optima, solving the problem of the original artificial raindrop algorithm easily getting trapped in local optima in the later stages of iteration. Employing a descending operator considering wind direction simulates the irregular trajectory of raindrops affected by gravity and air resistance, expanding the search range in the development phase and improving convergence speed; simultaneously, a flow operator based on the Baldwin effect guides raindrops towards better solutions through an individual difference learning mechanism, accelerating the convergence accuracy of local searches. Furthermore, transforming the continuous optimization problem into a discrete scheduling problem through random key encoding ensures the algorithm's applicability in job shop scheduling. Overall, this invention achieves a synergistic improvement in convergence speed, accuracy, and robustness through multi-strategy improvements, effectively reducing the ineffective search and waiting time of traditional algorithms in scheduling problems, providing an efficient solution for job shop scheduling, and has broad application prospects. Attached Figure Description

[0045] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 This is a flowchart of the method of the present invention;

[0047] Figure 2 This is a schematic diagram of the raindrop change process according to an embodiment of the present invention;

[0048] Figure 3 This is a flowchart illustrating the encoding and decoding process of an embodiment of the present invention;

[0049] Figure 4 This is an evolution diagram of the Baldwin effect flow operator in an embodiment of the present invention;

[0050] Figure 5 The results show the verification of the method of this invention in the MATLAB simulation environment;

[0051] Figure 6 The results show the verification of the Particle Swarm Optimization (PSO) algorithm in the MATLAB simulation environment.

[0052] Figure 7 The results show the validation of the original artificial raindrop algorithm ARA in the MATLAB simulation environment.

[0053] Figure 8 The results show the verification of the continuous optimization function of each algorithm in the MATLAB simulation environment. Detailed Implementation

[0054] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0055] In the description of the embodiments of the present invention, it should be understood that the terms "length", "vertical", "horizontal", "top", "bottom", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of the present invention.

[0056] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0057] In the embodiments of the present invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection, an electrical connection, or a communication connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in the embodiments of the present invention according to the specific circumstances.

[0058] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0059] To better understand the purpose, structure, and function of this invention, the following detailed description of a job shop scheduling method based on an improved artificial raindrop algorithm is provided in conjunction with the accompanying drawings.

[0060] like Figure 1-8 As shown, the present invention provides a job shop scheduling method based on an improved artificial raindrop algorithm, comprising the following steps:

[0061] Step 1: Parameter Input and Population Initialization

[0062] This embodiment selects the standard test case la07 with 5 machines and 15 workpieces. First, the processing time matrix and processing sequence matrix are input as parameters into the fitness function. The artificial raindrop algorithm parameters are initialized as follows: population size N=30, problem dimension D=75 (total number of processes), maximum number of evaluations FMAX=100000, number of flows MFN=3, and flow factor. The step size is s=0.2, and the raindrop radius is R.

[0063] The initial population is generated using the Circle chaotic mapping, with the following formula:

[0064] Step 2: Aerial Search and Disturbance of Water Vapor

[0065] A random number R is generated with a probability of 0.2. If the probability is less than 0.2, the water vapor search operator is executed to perturb the population. The operator formula is:

[0066] Step 3: Encoding and Decoding

[0067] As attached Figure 3 As shown, since the artificial raindrop algorithm is a continuous optimization algorithm, it is not suitable for machine processing cases involving integers. Therefore, the most random key encoding method is used to map the generated population to the processing sequence. First, each individual in the population generated through initialization is sorted in ascending order, and their original dimension index is recorded, thus obtaining a vector sort. Mapping the individual indices after vector sorting yields an index sequence. Since the index sequence is arranged according to the corresponding dimension number, exceeding the maximum machine number, the sequence is sorted by value to generate an index sequence. The index is divided by the number of machines and rounded up, mapping to the processing order. For example, the sequence value 0.7325 corresponds to index 7, 7 / 6≈1.17 → machine 1, the first process of workpiece 3. Figure 3 This is a schematic diagram of a random key encoding with a dimension of 9. The same method is used for high-dimensional individuals.

[0068] Step 4: Raindrop Formation and Fall

[0069] The processing time for the corresponding process of each encoded individual is calculated using a fitness function and used as the fitness value. A raindrop formation operator is applied to the initialized water vapor molecules, with the raindrop defined at the geometric center of the water vapor. The formed raindrops are then subjected to a raindrop descent operator that considers wind direction to obtain their new positions. .

[0070] Step 5: Raindrop Collision and Flow

[0071] In this embodiment, the new individual position after descent Applying a collision operator to generate raindrops The number of individuals is equal to the population size N. Using the encoding and decoding method in step 3, the fitness of each newly generated raindrop is calculated. For each raindrop, a flow operator is selected: a random number R is generated, and it is checked whether it is less than 0.5. If the condition is met, the first empirical flow method is used. The formula is:

[0072] If the conditions are not met, a flow operator based on the Baldwin effect is selected, and its evolution direction and process are shown in the appendix. Figure 4 As shown, its formula is:

[0073] Calculate the new position generated by the flow The fitness value, if the fitness is better than before the flow If the fitness of a droplet is lower than its original value, it is replaced by a new individual. If the fitness is lower, the droplet is eliminated from the loop. Each droplet is limited to three flow cycles, and the flow function evaluation (FES) count increases by one for each flow cycle. Once all particles have completed their flow processes, the resulting new population becomes the offspring population.

[0074] Step 6: Generate a new generation of population and update the experience pool

[0075] In this embodiment, after completing the raindrop flow process described above, it is necessary to merge the offspring and parent populations. Specifically, after merging the two populations, all individuals are encoded as in step 3, their fitness values ​​are calculated, and the top N individuals with better performance are selected as the new generation population using bubble sort. Two random particles are then added to the experience pool. The number of individuals in the experience pool is iterated, and if it exceeds the maximum number N, redundant particles are removed in the same way.

[0076] Step 7: Determine the termination condition and output the Gantt chart.

[0077] In this embodiment, when the iterative calculations of steps 2 to 6 are completed and the current function evaluation count meets the iteration termination condition FES=100000, the algorithm stops running. The final result is then encoded and decoded in step 3 to calculate the completion time and input into the Gantt chart after production scheduling. (See attached...) Figure 5 The figure shows the scheduling effect of the improved single-objective artificial raindrop algorithm's job shop scheduling method in a Matlab simulation environment. Each workpiece is distinguished by a different color, with the center number indicating the workpiece code. The horizontal axis represents processing time, and the vertical axis represents the selected processing machine. (See attached figure.) Figure 5 As can be seen, after applying the scheduling method of this invention, the minimum completion time is 890. Figure 6 , attached Figure 7 The particle swarm optimization (PSO) algorithm and the original artificial raindrop algorithm (ARA) scored 988 and 1119 respectively. This method outperforms the other algorithms, verifying the effectiveness and robustness of the proposed operator.

[0078] Step 8: Benchmark Continuous Function Test Comparison

[0079] This implementation case verifies the effectiveness and robustness of the proposed method through step 7. The convergence and speed of the algorithm need to be verified on a continuous optimization testing platform. In this implementation method, a single-peaked test function is selected for testing, and the formula is as follows:

[0080] As attached Figure 8 As shown, the improved method outperforms the other algorithms in terms of convergence and accuracy with the same number of evaluations.

[0081] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A job shop scheduling method based on an improved artificial raindrop algorithm, characterized in that: Includes the following steps: Step 1: Problem Modeling and Constraint Definition Select a simulation platform and its corresponding job shop scheduling model, build a simulation environment with constraints, and construct a mathematical model for job shop scheduling. Calculate the minimum completion time for multiple cases of different scales and processes. Step 2: Population Initialization N parent water vapor population individuals are generated using a chaotic mapping method, exhibiting a random and uniform distribution. Its value ranges from 0 to 1, and the population dimension is... Where n is the number of workpieces and m is the number of machines; Step 3: Encode and decode the process. For cases where the population individuals encoded with floating-point numbers do not match the actual integer machine sequence number and process number, the corresponding index sequence is obtained by vector sorting the random sequence of all dimensions of each individual, and then the corresponding processing sequence is generated by encoding. The generated processing sequence is then decoded, and the processing time of the corresponding individual is calculated by using the fitness function. Step 4: Water Vapor Aerial Search Operator Based on the existing population, for each particle, with a certain probability R, we randomly select whether to execute the aerial search operator. For individuals that meet the probability conditions, we use Levy flight to generate a random step size vector of length D, and introduce a random perturbation parameter R1. We calculate the difference between the currently selected individual and the previous generation of individuals, and generate a new individual by superimposing these random conditions. They are inserted into the population to replace the original individuals; Step 5: Raindrop Formation Process The formation of raindrops is defined as the geometric center of existing water vapor, for The water vapor matrix is ​​averaged in each column to obtain a... Raindrops of different dimensions; Step 6: Perform a raindrop descent process that takes wind direction into account. Fitness calculations are performed on the formed raindrops to determine the current iteration number. If the set iteration number condition is not met, it is considered to be in the early stage of iteration. This is achieved by introducing gravity G and air resistance drag force. drag coefficient The wind direction and angle are used to simulate the irregular trajectory of a spherical object under the influence of wind direction and airflow, thus generating a new position. If the iteration conditions are met, the raindrop dimensions can be changed in the later stages of the iteration. The value is used to simulate the vertical fall process; Step 7: Conduct the raindrop collision and new individual generation process. Based on the new position obtained in step 6 The collision strategy is updated so that raindrops, upon hitting the ground and colliding, will splash outwards in a normal distribution, creating new raindrops. The number of newly generated raindrops is completely random. For ease of calculation, the number of newly generated raindrops is defined as the population size N. All new individuals form a subpopulation. ; Step 8: Select and update raindrop flow strategies based on experience. After a collision, raindrops flow towards lower elevations. Different flow patterns are selected based on the set iteration conditions. When the iteration conditions are met, two experienced particles guide the current raindrop flow direction. The randomness of the flow is simulated by adding a perturbation term and a random step size. When the iteration conditions are not met, a flow operator with the Baldwin effect is used to encourage individuals and accelerate the evolution process. Each particle flows 3 times. The new position is updated each time, and the fitness is calculated. A greedy strategy is used to replace the current subpopulation individuals with excellent solutions and discard inferior solutions, keeping the current individual. When all individuals in the subpopulation have completed the flow, two individuals are randomly selected and added to the experience pool. At the same time, the number of particles in the experience pool is checked. If the maximum number of particles in the experience pool is met, redundant particles are deleted. Step 9: Merge the offspring and parent populations After merging the offspring population and the parent population, the fitness is calculated, and the particles with better fitness are selected as the new generation population. The number of populations is limited to N. Step 10: Perform iterative training Repeat steps 3 to 9, continuously select the best option through different strategies to achieve iterative training of the algorithm. During the training process, control the iterative training process according to the preset termination condition. When the preset training round number threshold is met, terminate the iterative training process, output the final solution result of the corresponding case, and generate a scheduling Gantt chart.

2. The job shop scheduling method based on the improved artificial raindrop algorithm according to claim 1, characterized in that: In step 2, the method for generating the initial population is Circle chaotic mapping initialization.

3. The job shop scheduling method based on the improved artificial raindrop algorithm according to claim 1, characterized in that: In step 3, the encoding method is random key encoding.

4. The job shop scheduling method based on the improved artificial raindrop algorithm according to claim 1, characterized in that: In step 4, the probability R is set to 0.5, and the proposed water vapor search operator is a local search method. Based on the current water vapor particles, it is added to the generated Levy flight term and perturbation term R1 with heavy tail distribution to perform a local search.

5. A job shop scheduling method based on an improved artificial raindrop algorithm according to claim 1, characterized in that: In step 6, the raindrop falling operator considering wind direction introduces perturbation parameters and a tangent function to ensure that its scattering range is within... Between these points, the dimension selected during the vertical descent process is randomly chosen.

6. The job shop scheduling method based on the improved artificial raindrop algorithm according to claim 1, characterized in that: In step 7, the collision generates new raindrops that are normally distributed, which is simulated using the Monte Carlo method.

7. A job shop scheduling method based on an improved artificial raindrop algorithm according to claim 1, characterized in that: In step 8, two flow modes for new raindrops are selected. The empirical flow mode is determined by a linear combination of two sub-directions d1 and d2 and flow factors τ and learning factors c1 and c2. The two particles selected from the empirical pool are randomly selected. The flow operator of the Baldwin effect determines the evolution direction by comparing the differences between different individuals. The step size for generating new solutions is determined by the parameter S.

8. A job shop scheduling method based on an improved artificial raindrop algorithm according to claim 1, characterized in that: In step 8, a bubble sorting method is adopted for updating the experience pool. The fitness values ​​of all particles in the experience pool are calculated and sorted in order from best to worst. Based on the set experience pool size N, redundant particles with poor fitness are removed, thereby maintaining the experience pool.

9. A job shop scheduling method based on an improved artificial raindrop algorithm according to claim 7, characterized in that: In step 8, the learning factors c1 and c2 are used in a non-linear transformation method to continuously change the learning rate and gradually transition to the preset minimum learning threshold. The transition process is controlled by the number of iterations.

10. A job shop scheduling method based on an improved artificial raindrop algorithm according to claim 1, characterized in that: In step 10, the job shop scheduling model case is simulated using 10 examples from la01 to la10 in the standard benchmark test set LA series.

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