Zero-latency flow shop scheduling method based on discrete coding red mouth blue magpie optimization algorithm

Abstract

The invention discloses a zero-latency flow shop scheduling method based on a discrete coding red mouth blue magpie optimization algorithm, and belongs to the technical field of flow shop scheduling. According to the method, on the basis of a discrete coding Red-billed Blue-Tapie optimization algorithm (DRBMO), the zero-latency flow shop scheduling problem with the goal of minimizing the maximum completion time is solved. The method mainly comprises the following steps: proposing a method based on INEH, random and reverse learning to generate a high-quality initial population; dividing the population into a large group and a small group according to the fitness value; discretizing a continuous position updating formula of the algorithm, and updating the position of the individual by using the discretized updating formula; variable neighborhood search is carried out, an adaptive parameter q and two neighborhood structures are given, the global search capability in the earlier stage of iteration is high, and the local search capability in the later stage is high; substitution operation: reserving one of the same individuals in the population, and randomly generating other repeated individuals; and checking a termination condition, if the termination condition is satisfied, stopping iteration, and outputting an optimal individual as an optimal scheduling scheme, otherwise, re-dividing the population.

Description

Technical Field

[0001] The invention relates to the technical field of flow shop scheduling, in particular to a zero-wait flow shop scheduling method based on a discrete coding red-billed blue magpie optimization algorithm. Background Art

[0002] The zero-wait flow shop scheduling problem is a typical production scheduling problem in the manufacturing industry. It involves multiple workpieces that need to go through multiple processing procedures in sequence, and the waiting time between each process of each workpiece must be zero. The requirement of zero waiting makes this problem more complicated than the traditional flow shop scheduling problem, and it is a typical NP-hard problem. Although traditional scheduling methods, such as mathematical programming and heuristic algorithms, can solve some simple scheduling problems, for large-scale or high-complexity zero-wait flow shop scheduling problems, the computational complexity is high, the solution efficiency is low, and it is often difficult to obtain the global optimal solution. Therefore, it is necessary to design an algorithm that can efficiently solve the zero-wait flow shop scheduling problem.

[0003] The Red-billed Blue Magpie Optimization Algorithm is an emerging heuristic optimization algorithm inspired by the foraging behavior of the Red-billed Blue Magpie. The algorithm has strong global search capabilities and fast convergence speed, and has been successfully applied to many combinatorial optimization problems. However, the Red-billed Blue Magpie Optimization Algorithm is mainly used to solve continuous optimization problems. For discrete optimization problems, especially discrete variables such as the processing sequence of workpieces and processes involved in scheduling problems, traditional continuous coding optimization algorithms are often difficult to apply directly. It is necessary to design a new method that can efficiently solve the zero-wait flow shop scheduling problem. Summary of the invention

[0004] The present invention proposes a zero-wait flow shop scheduling method based on a discrete coding red-billed blue magpie optimization algorithm. By improving the red-billed blue magpie optimization algorithm, it can effectively handle the zero-wait flow shop scheduling problem and meet the zero-wait constraint condition, thereby obtaining a better scheduling solution. The method provides an innovative idea and effective solution for solving the zero-wait flow shop scheduling problem.

[0005] The purpose of the present invention is to provide a zero-wait flow shop scheduling solution method based on a discrete coding red-billed blue magpie optimization algorithm, aiming to solve the problems of weak global search ability of the red-billed blue magpie optimization algorithm in the early stage of iteration, weak local search ability in the later stage and easy to fall into local optimality, and to provide an optimal scheduling solution for the zero-wait flow shop scheduling problem.

[0006] The technical solution of the present invention comprises the following steps:

[0007] Step 1: Parameter initialization, MAXT is the maximum number of iterations, t is the current number of iterations, P is the population size, N is the number of workpieces, and M is the number of machines;

[0008] Step 2: Population initialization. Encoding is performed through discrete encoding, and a population initialization method based on an improved NEH heuristic algorithm (INEH), random initialization, and opposition-based learning is proposed. First, 0.3P individuals are generated using the INEH method. Second, 0.2P individuals are generated using the random initialization method. Finally, 0.5P individuals are generated from the generated 0.5P individuals using the opposition-based learning method.

[0009] Step 3: Population division. Calculate the fitness values of the individuals in the population, and divide the individuals in the population into a large group and a small group according to the fitness values. At the same time, record the minimum fitness value in the population as gbest, and the individual corresponding to the minimum fitness value as

[0010] Step 4: Update the position of the red-billed blue magpie. First, the red-billed blue magpie searches for food and updates its position. Second, the red-billed blue magpie attacks the prey and updates its position. If the fitness value of the individual after the position update is smaller than the fitness value of the individual before the update, then replace the individual before the update with the updated individual.

[0011] Step 5: Variable neighborhood search operation. Give an adaptive parameter q, generate a random number k in the range of 0 to 1. If k < q, search according to the transformed neighborhood structure; otherwise, search according to the left-right flip neighborhood structure.

[0012] Step 6: Substitution operation. Calculate the fitness values of the individuals in the population. If there are two or more identical individuals in the population, only retain one and remove the remaining duplicate individuals. Let the number of removed individuals be P1. At this time, the population size becomes P - P1. Finally, to keep the population size unchanged, replace the removed P1 duplicate individuals with randomly generated P1 individuals.

[0013] Step 7: Calculate the fitness values of the individuals in the population, and sort them in ascending order according to the fitness values. Record the minimum fitness value as pbest, and the individual corresponding to it as If pbest < gbest, then let gbest = pbest.

[0014] Step 8: Determine whether the iteration termination condition is satisfied. If it is satisfied, stop the iteration and give the optimal scheduling plan; otherwise, return to Step 3.

[0015] Preferably, in Step 2, the discrete encoding means that one individual is a scheduling plan, and a red-billed blue magpie individual can be represented as π = {π1, π2, …, π N}(π1 is workpiece 1, π N is workpiece N), and the workpieces are processed in sequence according to the order of the workpieces in the individual π.

[0016] The present invention proposes a population initialization method of an improved NEH heuristic algorithm (INEH), random initialization and reverse learning. The detailed steps of the INEH algorithm can be described as follows:

[0017] The first step is to calculate the total processing time T of all processes in workpiece i (i = 1, 2, ..., N) according to the processing time matrix i ;

[0018] The second step is to i Arrange the N artifacts in descending order according to the value;

[0019] The third step is to select the first two workpieces, assuming that the first two workpieces are workpiece i and workpiece j, calculate the workpiece waiting time of the two processing methods of workpiece i, workpiece j and workpiece j, workpiece i, and select the processing method with the smallest waiting time (assuming that it is workpiece i and workpiece j) as the optimal sequence ij;

[0020] Step 4: Select T from step 2 i The workpiece k with the third largest value is inserted into the optimal sequence ij of the third step, and the workpiece waiting time of the three processing methods ij k, i kj and k ij is calculated. The processing method with the smallest waiting time (set as workpiece i, workpiece j, workpiece k) is selected as the optimal sequence ij k;

[0021] Step 5: Use the method in step 4 to insert the remaining workpieces in step 2 into the optimal sequence one by one in order until all workpieces are arranged;

[0022] The random initialization method refers to randomly arranging all integers between [1, N];

[0023] The initialization method based on reverse learning refers to the above-mentioned INEH-based and randomly generated 0.5P individuals according to X (0.5P+i) =fliplr(X i )(i=1,2,…,0.5P,fliplr is the i 0.5P individuals are generated by flipping the sequence in left and right) as individuals generated based on reverse learning.

[0024] Preferably, in step three, the population division includes the following steps:

[0025] In the first step, let the size of the population be P, and P is an even number, and sort the individuals in P in ascending order according to the fitness value F (maximum completion time);

[0026] In the second step, the population before sorting is X = (X1, X2, ..., X n ), after sorting, X'=(X1',X'2,…,X'n ), and after sorting, F(X1')≤F(X'2)≤…≤F(X' n );

[0027] The third step is to divide the first 70% of individuals in the sorted population into large groups, and the last 30% of individuals into small groups.

[0028] Preferably, in step 4, the location update in the food search phase includes the following steps:

[0029] In the first step, randomly select an individual in the large group as parent 1, randomly select an individual in the small group as parent 2, and randomly select two workpiece numbers from parent 1, which are recorded as I1 in the processing order. The remaining workpieces are recorded as I2 in the processing order. Find the processing order of the workpiece in I1 in parent generation 2, recorded as I3;

[0030] The second step is to determine whether the workpiece processing sequence in I1 and I3 is the same. If so, randomly select an individual from the large population as the parent generation 1, and then randomly select two workpiece sequence numbers I1 from the parent generation 1 until the workpiece processing sequence in I1 and I3 are different. If not, replace the corresponding workpiece positions in the parent generation 2 with the two workpiece sequences in I1, and obtain the child generation 1, which is recorded as off1. Replace the corresponding workpiece positions in the parent generation 2 with the workpiece sequence in I2, and obtain the child generation 2, which is recorded as off2.

[0031] The third step is to repeat the first and second steps until P offspring individuals are generated, and replace the original population with the generated new population.

[0032] The position update in the attack prey phase includes the following steps:

[0033] In the first step, let the number of workpieces be N, and randomly generate an integer a between [1, N];

[0034] The second step is to randomly generate a different integers b, where b is the workpiece number, and copy the workpieces with workpiece number b in parent generation 1 and parent generation 2 to child generation 1 and child generation 2 respectively, while ensuring that their order and position in the child generation are the same as in the parent generation;

[0035] The third step is to copy the remaining workpiece numbers in parent generation one and parent generation two to child generation two and child generation one in sequence.

[0036] Preferably, in step five, the adaptive parameter t is the current iteration number, MAXT is the maximum iteration number, and q is a parameter that changes from 1 to 0, which makes the algorithm execute the transformation neighborhood structure with a high probability in the early stage to improve the global search ability of the algorithm, and execute the left-right flip neighborhood structure with a high probability in the later stage to improve the local search ability of the algorithm;

[0037] The two neighborhood structures are a transformation neighborhood structure and a left-right flip neighborhood structure. The transformation neighborhood structure refers to randomly generating two integers a and b between [1, N] and exchanging the workpiece serial numbers corresponding to a and b.

[0038] The left-right flip neighborhood structure refers to randomly selecting two integers a and b between [1, N] and flipping all workpieces with workpiece numbers between a and b left-right.

[0039] The present invention has the following beneficial effects:

[0040] (1) A population initialization method based on the improved NEH heuristic algorithm (INEH), random initialization and reverse learning is proposed. This method constructs a high-quality initial population, which enables the algorithm to search for the area with better solutions more quickly.

[0041] (2) According to the characteristics of the continuous position update formula of the red-billed blue magpie optimization algorithm, multiple discrete coding position update formulas of the red-billed blue magpie optimization algorithm were designed to better simulate the foraging behavior of the red-billed blue magpie and better solve the zero-wait flow shop scheduling problem.

[0042] (3) In the variable neighborhood search operation, an adaptive parameter q is designed so that the algorithm will execute the neighborhood structure transformation with a high probability in the early stage, improving the global search capability of the algorithm, and will execute the neighborhood structure flipping with a high probability in the later stage, improving the local search capability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Flowchart for solving the zero-wait flow shop scheduling problem using the discrete-coded red-billed blue magpie optimization algorithm;

[0044] Figure 2 An example diagram of searching for food locations updated for the present invention;

[0045] Figure 3 An example diagram of the attack prey position update of the present invention;

[0046] Figure 4 It is the iterative curve diagram of the adaptive parameter q;

[0047] Figure 5 Two examples of neighborhood structures of the present invention are shown;

[0048] Figure 6This is the Gantt chart of the optimal solution for Example 1 with 8 workpieces and 8 machines;

[0049] Figure 7 This is the Gantt chart of the optimal solution for Example 2 with 12 workpieces and 5 machines;

[0050] Figure 8 This is the Gantt chart of the optimal solution for Example 3 with 20 workpieces and 10 machines;

[0051] Fig. 9 This is the Gantt chart of the optimal solution for Example 4 with 20 workpieces and 15 machines; DETAILED DESCRIPTION

[0052] The specific technical solutions of the present invention are further described below to help those skilled in the art further understand the present invention without limiting the rights thereof.

[0053] Reference Figure 1-Figure 9 ,A zero-wait flow shop scheduling method based on discrete coding red-billed blue magpie optimization algorithm, including step 1: parameter initialization, MAXT is the maximum number of iterations, t is the current number of iterations, P is the population size, N is the number of workpieces, and M is the number of machines;

[0054] Step 2: Population initialization. By encoding based on discrete coding, a population initialization method based on improved NEH heuristic algorithm (INEH), random initialization and reverse learning is proposed; first, 0.3P individuals are generated by INEH method; second, 0.2P individuals are generated by random initialization method; finally, 0.5P individuals are generated by reverse learning method for the generated 0.5P individuals;

[0055] The discrete coding means that one individual is a scheduling scheme, and one red-billed blue magpie individual can be expressed as π={π1,π2,…,π N}(π1 is workpiece 1, π N is workpiece N), and the workpieces in individual π are processed in sequence;

[0056] The present invention proposes a population initialization method of an improved NEH heuristic algorithm (INEH), random initialization and reverse learning. The detailed steps of the INEH algorithm can be described as follows:

[0057] The first step is to calculate the total processing time T of all processes in workpiece i (i = 1, 2, ..., N) according to the processing time matrix i ;

[0058] The second step is to i Arrange the N artifacts in descending order according to the value;

[0059] The third step is to select the first two workpieces, assuming that the first two workpieces are workpiece i and workpiece j, calculate the workpiece waiting time of the two processing methods of workpiece i, workpiece j and workpiece j, workpiece i, and select the processing method with the smallest waiting time (assuming that it is workpiece i and workpiece j) as the optimal sequence ij;

[0060] Step 4: Select T from step 2 i The workpiece k with the third largest value is inserted into the optimal sequence ij in the third step, and the workpiece waiting time of the three processing methods ijk, ikj and kij is calculated. The processing method with the smallest waiting time (set as workpiece i, workpiece j, workpiece k) is selected as the optimal sequence ijk;

[0061] Step 5: Use the method in step 4 to insert the remaining workpieces in step 2 into the optimal sequence one by one in order until all workpieces are arranged;

[0062] The random initialization method refers to randomly arranging all integers between [1, N];

[0063] The initialization method based on reverse learning refers to the above-mentioned INEH-based and randomly generated 0.5P individuals according to X (0.5P+i) =fliplr(X i )(i=1,2,…,0.5P,fliplr is the i 0.5P individuals are generated by flipping the sequence in left and right) as individuals generated based on reverse learning.

[0064] Step 3: Divide the population, calculate the fitness values ​​of individuals in the population, and divide the individuals in the population into large groups and small groups according to the size of the fitness values. At the same time, the minimum fitness value in the population is recorded as gbest, and the individual corresponding to the minimum fitness value is recorded as

[0065] The division of the population comprises the following steps:

[0066] In the first step, let the size of the population be P, and P is an even number, and sort the individuals in P in ascending order according to the fitness value F (maximum completion time);

[0067] In the second step, the population before sorting is X = (X1, X2, ..., X n ), after sorting, X'=(X1',X'2,…,X' n ), and after sorting, F(X1')≤F(X'2)≤…≤F(X' n );

[0068] The third step is to divide the first 70% of individuals in the sorted population into large groups, and the last 30% of individuals into small groups.

[0069] Step 4: Update the position of the red-billed blue magpie. First, the red-billed blue magpie searches for food and updates its position; second, the red-billed blue magpie attacks the prey and updates its position; if the fitness value of the individual after position update is smaller than that before the update, then replace the individual before the update with the updated individual.

[0070] As Figure 2 shown, an operation example in the food search stage is given. The position update in the food search stage includes the following steps:

[0071] First step, randomly select an individual from the large population as Parent 1, randomly select an individual from the small group as Parent 2, randomly select two workpiece numbers from Parent 1, and record them as I1 in the processing order. Record the remaining workpieces in the processing order as I2. Find the processing order of the workpieces in I1 in Parent 2, and record it as I3.

[0072] Second step, determine whether the processing order of the workpieces in I1 and I3 is the same. If they are the same, randomly select another individual from the large population as Parent 1, and then randomly select two workpiece numbers I1 from Parent 1 until the processing order of the workpieces in I1 and I3 is different; if they are different, replace the corresponding workpiece positions in Parent 2 with the two workpiece orders in I1 to obtain the first offspring, denoted as off1, and replace the corresponding workpiece positions in Parent 2 with the workpiece order in I2 to obtain the second offspring, denoted as off2.

[0073] Third step, repeat the first step and the second step until P offspring individuals are generated, and replace the original population with the newly generated population.

[0074] As Figure 3 shown, an operation example in the prey attack stage is given. The position update in the prey attack stage includes the following steps:

[0075] First step, assume the number of workpieces is N, and randomly generate an integer a between [1, N].

[0076] Second step, randomly generate a distinct integers b, where b is the workpiece number. Copy the workpieces with workpiece number b in Parent 1 and Parent 2 to the first offspring and the second offspring respectively, while ensuring that their order and position in the offspring are the same as those in the parent.

[0077] Third step, copy the remaining workpiece numbers in Parent 1 and Parent 2 to the second offspring and the first offspring in order.

[0078] Step 5: Variable neighborhood search operation. Given an adaptive parameter q, generate a random number k in the range of 0 to 1. If k < q, search according to the transformed neighborhood structure; otherwise, search according to the left-right flip neighborhood structure.

[0079] The adaptive parameter where \(t\) is the current iteration number, \(MAXT\) is the maximum iteration number, and \(q\) is a parameter that varies from 1 to 0, such that the algorithm is likely to execute the transformation neighborhood structure in the early stage to improve the global search ability of the algorithm, and is likely to execute the left - right flipping neighborhood structure in the later stage to improve the local search ability of the algorithm;

[0080] The two neighborhood structures refer to the transformation neighborhood structure and the left - right flipping neighborhood structure; the transformation neighborhood structure means randomly generating two integers \(a\) and \(b\) between \([1, N]\), and swapping the workpiece numbers corresponding to \(a\) and \(b\);

[0081] The left - right flipping neighborhood structure means randomly selecting two integers \(a\) and \(b\) between \([1, N]\), and flipping all the workpieces between workpiece numbers \(a\) and \(b\) left - right.

[0082] Step 6: Substitution operation. Calculate the fitness values of the individuals in the population. If there are two or more identical individuals in the population, only keep one and remove the remaining duplicate individuals. Let the number of removed individuals be \(P1\). At this time, the population size becomes \(P - P1\). Finally, to keep the population size unchanged, replace the removed \(P1\) duplicate individuals with \(P1\) randomly generated individuals;

[0083] Step 7: Calculate the fitness values of the individuals in the population and sort them in ascending order of fitness values. Denote the minimum fitness value as \(pbest\), and the corresponding individual as \(X\) b p est ; if \(pbest < gbest\), then let \(gbest = pbest\),

[0084] Step 8: Judge whether the iteration termination condition is satisfied. If satisfied, stop the iteration and give the optimal scheduling scheme. Otherwise, return to Step 3.

[0085] The objective function of this method is where \(j\) represents the workpiece number, \(n\) represents the total number of workpieces, and \(c\) j represents the completion time of each workpiece;

[0086] Example: Refer to Figure 1 where \(N\) represents the total number of workpieces, \(M\) represents the total number of machines, \(T\) is the time processing matrix, \(P\) is the population size, and \(MAXT\) is the maximum iteration number;

[0087] Through the discrete coding red-billed blue magpie optimization algorithm, four examples are solved respectively: 8 workpieces, 8 machines; 12 workpieces, 5 machines; 20 workpieces, 10 machines; and 20 workpieces, 15 machines. In the solution process, the population size P = 100, the maximum number of iterations MAXT = 300 are set, and the maximum number of iterations is used as the termination condition. The optimal solutions corresponding to the four examples are obtained, including the workpiece processing sequence and completion time. Figures 6 to 9 The Gantt chart in Figure 1 shows the optimal scheduling scheme for these four examples. Scheduling production according to this scheme can effectively reduce the waiting time of workpieces and avoid unnecessary delays in the production process, thereby further shortening the production cycle and improving overall production efficiency.

[0088] The above description is only a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Any simple modification, equivalent change or improvement of the above embodiment based on the technical essence of the present invention shall be regarded as within the scope of the technical solution of the present invention.

Claims

1. A zero-wait flow shop scheduling method based on discrete coding red-billed blue magpie optimization algorithm, characterized by: It includes the following steps: Step 1: Parameter initialization. MAXT is the maximum number of iterations, t is the current iteration number, P is the population size, N is the number of jobs, and M is the number of machines; Step 2: Population initialization. Encoding is carried out by discrete encoding method, and a population initialization method based on improved NEH heuristic algorithm (INEH), random initialization and opposition-based learning is proposed. First, use the INEH method to generate 0.3P individuals; Secondly, use the random initialization method to generate 0.2P individuals; finally, use the opposition-based learning method to generate another 0.5P individuals for the generated 0.5P individuals; Step 3: Divide the population, calculate the fitness values ​​of individuals in the population, and divide the individuals in the population into large groups and small groups according to the size of the fitness values. At the same time, the minimum fitness value in the population is recorded as gbest, and the individual corresponding to the minimum fitness value is recorded as Step 4: Update the position of the red-billed blue magpie. First, the red-billed blue magpie searches for food and updates its position; secondly, the red-billed blue magpie attacks the prey and updates its position; if the fitness value of the individual after updating the position is smaller than that of the individual before updating, then replace the individual before updating with the updated individual; Step 5: Variable neighborhood search operation. Give an adaptive parameter q, generate a random number k within the range of 0 to 1. If k < q, search according to the transformed neighborhood structure, otherwise, search according to the left-right flip neighborhood structure; Step 6: Substitution operation. Calculate the fitness values of the individuals in the population. If there are two or more identical individuals in the population, only retain one and remove the remaining duplicate individuals. Let the number of removed individuals be P1. At this time, the population size becomes P - P1. Finally, in order to keep the population size unchanged, use randomly generated P1 individuals to replace the removed P1 duplicate individuals; Step 7: Calculate the fitness values of the individuals in the population, and sort them in ascending order of fitness values. Denote the minimum fitness value as pbest, and the corresponding individual as If pbest < gbest, then let gbest = pbest, Step 8: Judge whether the iteration termination condition is satisfied. If it is satisfied, stop the iteration and give the optimal scheduling scheme. Otherwise, return to Step 3.

2. A zero-wait flow shop scheduling method based on discrete coding red-billed blue magpie optimization algorithm according to claim 1, characterized in that: In step 2, the discrete coding means that one individual is a scheduling scheme, and one red-billed blue magpie individual can be represented by π={π1,π2,…,π N }(π1 is workpiece 1, π N is workpiece N), and the workpieces in individual π are processed in sequence; The proposed population initialization method based on improved NEH heuristic algorithm (INEH), random initialization and opposition-based learning. The detailed steps of the INEH algorithm can be described as follows: The first step is to calculate the total processing time T of all processes in workpiece i (i = 1, 2, ..., N) according to the processing time matrix i ; The second step is to use T i Arrange the N artifacts in descending order according to the value; The third step is to select the first two jobs. Let the first two jobs be job i and job j. Calculate the waiting time of the two processing methods of job i, job j and job j, job i, and select the processing method with the minimum waiting time (assumed to be job i and job j) as the optimal sequence ij; Step 4: Select T from step 2 i The workpiece k with the third largest value is inserted into the optimal sequence ij in the third step, and the workpiece waiting time of the three processing methods ij k, ikj and kij is calculated. The processing method with the smallest waiting time (set as workpiece i, workpiece j, workpiece k) is selected as the optimal sequence ij k; The fifth step is to use the method in the fourth step to insert the remaining jobs in the second step into the optimal sequence one by one until all jobs are arranged; The random initialization method refers to randomly arranging all integers between [1, N]; The initialization method based on reverse learning refers to the above-mentioned INEH-based and randomly generated 0.5P individuals according to X (0.5P+i) =fliplr(X i )(i=1,2,…,0.5P,fliplr is the i 0.5P individuals are generated by flipping the sequence in left and right) as individuals generated based on reverse learning.

3. The zero-wait flow shop scheduling method based on the discrete coding red-billed blue magpie optimization algorithm according to claim 1 is characterized in that: The position update in the food search stage in Step 4 includes the following steps: In the first step, randomly select an individual in the large group as parent 1, randomly select an individual in the small group as parent 2, and randomly select two workpiece numbers from parent 1, which are recorded as I1 in the processing order. The remaining workpieces are recorded as I2 in the processing order. Find the processing order of the workpiece in I1 in parent generation 2, recorded as I3; The second step is to judge whether the processing order of the jobs in I1 and I3 is the same. If it is the same, randomly select another individual from the large population as the first parent, and then randomly select two job numbers I1 from the first parent until the processing order of the jobs in I1 and I3 is different; if it is different, replace the corresponding job positions in the second parent with the job order in I1 to obtain the first offspring denoted as off1, and replace the corresponding job positions in the second parent with the job order in I2 to obtain the second offspring denoted as off2; The third step is to repeat the first and second steps until P offspring individuals are generated, and use the generated new population to replace the original population. The position update in the attack prey phase includes the following steps: In the first step, let the number of workpieces be N, and randomly generate an integer a between [1, N]; The second step is to randomly generate a different integers b, where b is the workpiece number, and copy the workpieces with workpiece number b in parent generation 1 and parent generation 2 to child generation 1 and child generation 2 respectively, while ensuring that their order and position in the child generation are the same as in the parent generation; The third step is to copy the remaining workpiece numbers in parent generation one and parent generation two to child generation two and child generation one in sequence.

4. The zero-wait flow shop scheduling method based on the discrete coding red-billed blue magpie optimization algorithm according to claim 1 is characterized in that: In step 5, the adaptive parameters t is the current iteration number, MAXT is the maximum iteration number, and q is a parameter that changes from 1 to 0, which makes the algorithm execute the transformation neighborhood structure with a high probability in the early stage to improve the global search ability of the algorithm, and execute the left-right flip neighborhood structure with a high probability in the later stage to improve the local search ability of the algorithm; The two neighborhood structures are a transformation neighborhood structure and a left-right flip neighborhood structure; the transformation neighborhood structure is to randomly generate two integers a and b between [1, N], and exchange the workpiece serial numbers corresponding to a and b; The left-right flip neighborhood structure refers to randomly selecting two integers a and b between [1, N] and flipping all workpieces with workpiece numbers between a and b left-right.

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