A method for solving multi-objective distributed flexible job shop scheduling optimization based on grey wolf algorithm

Abstract

The application discloses a method for solving multi-objective distributed flexible workshop scheduling optimization based on a grey wolf algorithm, first, parameters are initialized, an initial population is generated, and the initial population is updated to have higher quality through plug-in coding; then, non-dominated sorting and congestion calculation are performed according to processing time, machine load and energy consumption, three kinds of wolves, namely alpha, beta and delta, are determined, and the population is updated by using the grey wolf algorithm; the population is uniformly crossed to obtain a new population, non-dominated sorting is performed again, and a pareto solution set is obtained; whether the algorithm reaches the iteration number is judged, if yes, the pareto solution set is output. The grey wolf algorithm is applied to the multi-objective distributed flexible workshop scheduling problem through the above scheme, the quality of the solution is greatly improved, the actual production efficiency is improved, and the actual production environment is closer, so that the application has high use value and popularization value.

Description

Technical Field

[0001] The present invention belongs to the technical field of workshop scheduling, and specifically designs a method for solving multi-objective distributed flexible workshop scheduling optimization based on a grey wolf algorithm. Background Art

[0002] Production scheduling is a crucial component in manufacturing systems, and the distributed flexible job-shop scheduling problem (DFJSP) is an extension of this problem. With the development of economic globalization, multi-shop collaborative production is becoming increasingly accepted and put into practical use. Consequently, the distributed flexible job-shop scheduling problem has gradually gained attention. According to relevant statistics, less than 5% of the time spent on a workshop's production process is spent on processing and assembly, while over 95% is spent on workpiece transportation. This means that the proper transportation scheduling of workpieces directly impacts workshop production costs and energy consumption. Therefore, to better meet actual production needs and satisfy user demands, it is essential to consider workpiece transportation time. Furthermore, as productivity increases, energy consumption also increases. Therefore, optimizing processing tasks and resources through production scheduling, while minimizing energy consumption while considering production efficiency and transportation time, is crucial for achieving green manufacturing.

[0003] Current research on shop scheduling problems typically focuses solely on minimizing the completion time. Studies that consider multiple objectives often employ a decision-first optimization approach. This approach first obtains the decision maker's preferences, then applies a linear weighted summation to the multiple objectives, transforming the multi-objective problem into a single-objective problem. This approach yields only a single optimal solution. However, due to the complexity of scheduling problems, accurate preference information is often difficult to obtain, and the resulting solution is likely to be inconsistent with the decision maker's preferences. The optimization-first approach, which introduces an intelligent optimization algorithm to obtain a Pareto-optimal set of solutions, then has the decision maker select the most appropriate solution from these solutions according to a specific decision-making method, is more accurate in obtaining the desired solution than the weighted summation approach. Currently, most researchers studying DFJSP employ intelligent optimization algorithms, which are highly effective. The Gray Wolf Algorithm (GWA) has a relatively small number of parameters, is easy to implement, and exhibits good convergence. Furthermore, it is parallelizable. Compared to other intelligent optimization algorithms, the GWA exhibits stronger global convergence and robustness, making it well-suited for studying complex problems. Therefore, it is imperative to design a GWA-based approach for solving multi-objective distributed flexible shop scheduling problems that consider transportation. Summary of the Invention

[0004] This invention aims to provide an optimization method for solving the multi-objective distributed flexible shop scheduling problem based on the Gray Wolf Algorithm. Most distributed shop scheduling problems fail to consider the possibility of processing a single workpiece at multiple plants, and most multi-objective studies simply weight different objectives. Based on the Gray Wolf Algorithm and the Pareto frontier, this invention proposes a method for solving the multi-objective distributed flexible shop scheduling problem (targeting processing time, machine load, and energy consumption) with transportation considerations. This method improves the quality of the solution, thereby increasing production efficiency and enhancing feasibility in actual production.

[0005] In order to achieve the above purpose, the technical solution adopted by this method is as follows:

[0006] A multi-objective distributed flexible workshop scheduling optimization method based on the grey wolf algorithm is characterized by comprising the following steps:

[0007] (1) Initialize parameters, generate an initial population, and update it to a higher quality initial population through plug-in coding;

[0008] (2) According to the processing time, machine load and energy consumption, non-dominated sorting and congestion calculation are performed to determine the three wolves α, β and δ and update the population using the gray wolf algorithm;

[0009] (3) Perform uniform crossover on the population to obtain a new population, and then perform non-dominated sorting to obtain the Pareto solution set;

[0010] (4) Determine whether the algorithm has reached the number of iterations. If so, output the Pareto solution set. If not, go to (2).

[0011] Update to a higher quality initial population. The population initialization rule is as follows: the encoding mechanism of the initial population uses three-segment encoding of the same length, each segment representing process sorting information, machine selection information, and transportation time information, where the transportation time information is the transportation time required for adjacent processes to be processed in different factories. The process sorting is random, and in the machine selection, some individuals select the machine with the shortest processing time for the process according to a preset probability, and the remaining individuals are randomly selected. The transportation time sorting changes with the process sorting and machine sorting. After the initial three-layer encoding is generated, it is subjected to an insert operation;

[0012] Furthermore, the plug-in encoding specifically includes the following rules:

[0013] Process O i,j is the jth process of workpiece i processed on machine l in factory f, process O i,j-1 is the j-1th process of processing workpiece i on machine k in factory u, O i,j-1 For process O i,jThe previous process of the same workpiece; on machine l in factory f, process O i,j The preceding process is O q,z , the subsequent process is O g,h ; When process O i,j The first process of non-workpiece i and process O i,j If the machine k used for processing is not used for the first time, if one of the following conditions is met, the process O can be i,j Perform an insert operation.

[0014] Specifically, the following conditions are included:

[0015]

[0016]

[0017]

[0018] For each machine's last processing operation, if one of the following conditions is met, the operation can be moved forward.

[0019] Specifically, the following conditions are included:

[0020]

[0021]

[0022] c i,j-1,k,u For process O i,j-1 The time to complete the process on machine k in factory u, c q,z,l,f For process O q,z The time to complete the process on machine l in factory f; T u,f is the transportation time of the process from factory u to factory f; p i,j,l,f For process O i,j Processing time on machine l in factory f; s g,h,l,f For process O g,h The time when processing begins on machine l in factory f.

[0023] In step (2), the initial population is subjected to non-dominated sorting and crowding calculation, and the three best individuals are selected as the three wolves α, β, and δ according to the crowding sorting;

[0024] Furthermore, the rules for non-dominated sorting are as follows:

[0025] Non-dominated sorting is to reclassify each individual according to their dominance and non-domination relationship, and proposes crowding degree and crowding degree comparison operator to replace the fitness sharing strategy that needs to specify the sharing radius. The weight of the same level comparison after quick sorting is used as the winning criterion, so that individuals in the quasi-pareto domain can be expanded to the entire pareto domain and evenly distributed. After non-dominated sorting, X non-inferior frontiers (denoted by P1, P2, ..., P X Each non-inferior frontier satisfies the following properties:

[0026] (1) and After non-dominated sorting, the individuals in the population are independent of each other;

[0027] (2) The population size remains unchanged before and after non-dominated sorting;

[0028] (3)P1>P2>…>P X , after non-dominated sorting, the population is divided into X non-inferior frontiers.

[0029] The non-dominated sorting steps are:

[0030] Step 1: Find all individuals in the population with n(x) = 0 and store them in the current set P(1);

[0031] Step 2: For each individual y in the current set P(1), examine the set of individuals S(y) it dominates, and reduce n(k) by 1 for each individual k in S(y);

[0032] Step 3: If n(k)-1=0, store individual k in another set H. Finally, take P(1) as the first-level non-dominated individual set and assign the same non-dominated rank to the individuals in the set. Then continue to perform the above-mentioned grading operation on H and assign the corresponding non-dominated rank until all individuals are graded. The computational complexity is O(mN ∧ {2}).

[0033] n(x) is the number of solution individuals that dominate individual x in the population, S(y) is the set of solution individuals dominated by individual y, m is the number of objective functions, and N is the population size;

[0034] Furthermore, the calculation formula of congestion is as follows:

[0035]

[0036] I (ST1).d and I (S-1).d are the function values ​​of the next solution and the previous solution of solution s on the d function, and are the maximum and minimum values ​​on the d function, respectively, and the d function is a different objective function;

[0037] Furthermore, the rules for sorting individual crowding are as follows:

[0038] (1) The more outstanding individuals in the non-dominated layer are at the front, that is, the individuals with smaller rank values ​​are at the front;

[0039] (2) If two individuals have the same dominant layer, the one with greater crowding is in front.

[0040] After sorting by crowding degree, the three best individuals are selected as α, β, and δ wolves, and then the population is updated according to the gray wolf algorithm (for detailed gray wolf algorithm, refer to [1]).

[0041] In step (3), a new population is obtained by uniformly crossing the machine codes of the population, and after performing non-dominated sorting again, P(1) is the first-level non-dominated individual set, that is, the current Pareto solution set;

[0042] Furthermore, the specific steps of uniformly crossing the machine layer are as follows:

[0043] Step 1: Randomly select parent individuals F1, F2, F3 from the population;

[0044] Step 2: Randomly generate a set R with the same length as the total number of processes, which consists of 0 and 1;

[0045] Step 3: Randomly select the code corresponding to the position 1 in the set R from the parent individuals F2 and F3, and copy it to the corresponding position in the offspring T1;

[0046] Step 4: Randomly select the code corresponding to the position 1 in the set R on the parent individuals F1 and F3, and copy it to the corresponding position in the offspring T2;

[0047] Step 5: Select the other coding parts in F1 and F2 and keep them in the offspring T1 and T2 respectively;

[0048] Step 6: Update the transportation time layer based on the process layer and the crossed machine selection layer.

[0049] After completing the machine uniform cross coding, if the solution of the new code is better than the original code, it will replace the original code F1, F2, otherwise the original code will be maintained.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] (1) Based on the Grey Wolf Algorithm, combined with plug-in coding, uniform crossover, and the Pareto frontier, this paper obtains an excellent and effective optimization method for solving the multi-objective distributed flexible shop scheduling problem. Compared with the existing technology, the quality of the obtained solution is greatly improved, more in line with actual needs, and has increased use value, reduced production costs, and is suitable for practical applications;

[0052] (2) The present invention has strong practical value and can be used to solve the multi-objective distributed flexible workshop problem. It is suitable for obtaining the optimal scheduling solution in a multi-workshop environment. Compared with the existing technology, it is more in line with actual needs and has strong scalability and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is the workflow diagram of the present invention.

[0054] References

[0055] [1] Seyedali Mirjalili, Seyed Mohammad Mirjalili, and Andrew Lewis. 2014. Gray Wolf Optimizer. Adv. Eng. Softw. 69 (March, 2014), 46–61. DETAILED DESCRIPTION

[0056] The present invention will be further described below with reference to the accompanying drawings and examples. The embodiments of the present invention include but are not limited to the following examples.

[0057] Example 1

[0058] like Figure 1 As shown, the method for solving multi-objective distributed flexible workshop scheduling optimization based on the gray wolf algorithm provided in this embodiment includes the following specific steps:

[0059] Step (1): Initialize the parameters, generate the initial population, and update it to a higher quality initial population through plug-in coding. The task attributes and rules are as follows:

[0060] The encoding mechanism for the initial population uses three segments of the same length, each representing process ordering, machine selection, and transportation time. Transportation time refers to the time required to transport adjacent processes from different factories. The process ordering is random. During machine selection, some individuals select the machine with the shortest processing time for that process according to a preset probability, while the remaining individuals are randomly selected. The transportation time order varies with the process and machine ordering. After the initial three-layer code is generated, it is then subjected to an insertion operation.

[0061] The plug-in encoding rules are as follows:

[0062] Process O i,j is the jth process of workpiece i processed on machine l in factory f, process O i,j-1 is the j-1th process of processing workpiece i on machine k in factory u, O i,j-1 For process O i,j The previous process of the same workpiece; on machine l in factory f, process O i,j The preceding process is O q,z , the subsequent process is O g,h ; When process O i,j The first process of non-workpiece i and process O i,j If the machine k used for processing is not used for the first time, if one of the following conditions is met, the process O can be i,j Perform an insert operation.

[0063] Specifically, the following conditions are included:

[0064]

[0065]

[0066]

[0067] For each machine's last processing operation, if one of the following conditions is met, the operation can be moved forward.

[0068] Specifically, the following conditions are included:

[0069]

[0070]

[0071] c i,j-1,k,u For process O i,j-1 The time to complete the process on machine k in factory u, c q,z,l,f For process O q,z The time to complete the process on machine l in factory f; T u,f is the transportation time of the process from factory u to factory f; p i,j,l,f For process O i,j Processing time on machine l in factory f; s g,h,l,f For process O g,h The time when processing begins on machine l in factory f.

[0072] Step (2): Based on the processing time, machine load and energy consumption, non-dominated sorting and congestion calculation are performed to determine the three wolves α, β and δ and update the population using the gray wolf algorithm. The task attributes and rules are as follows:

[0073] Non-dominated sorting reclassifies each individual according to their dominance and non-domination relationship, proposes crowding and crowding comparison operators, replaces the fitness sharing strategy that requires specifying the sharing radius, and uses the weight of the same-level comparison after quick sorting as the winning criterion, so that individuals in the quasi-pareto domain can be expanded to the entire pareto domain and evenly distributed. After non-dominated sorting, X non-inferior frontiers (denoted by P1, P2, ..., P X Each non-inferior frontier satisfies the following properties:

[0074] (1) and After non-dominated sorting, the individuals in the population are independent of each other;

[0075] (2) The population size remains unchanged before and after non-dominated sorting;

[0076] (3)P1>P2>…>P X , after non-dominated sorting, the population is divided into X non-inferior frontiers.

[0077] The non-dominated sorting steps are:

[0078] Step 1: Find all individuals in the population with n(x) = 0 and store them in the current set P(1);

[0079] Step 2: For each individual y in the current set P(1), examine the set of individuals S(y) it dominates, and reduce n(k) by 1 for each individual k in S(y);

[0080] Step 3: If n(k)-1=0, store individual k in another set H. Finally, take P(1) as the first-level non-dominated individual set and assign the same non-dominated rank to the individuals in this set. Continue to perform the above grading operation on H and assign the corresponding non-dominated rank until all individuals are graded and obtain the non-dominated rankings P(1), P(2)…P(X). The computational complexity is O(mN ∧ {2}).

[0081] n(x) is the number of solution individuals that dominate individual x in the population, S(y) is the set of solution individuals dominated by individual y, m is the number of objective functions, and N is the population size;

[0082] The calculation formula for congestion is as follows:

[0083]

[0084] I (S+1).d and I (S-1).d are the function values ​​of the next solution and the previous solution of solution s on the d function, and are the maximum and minimum values ​​on the d function, respectively, and the d function is a different objective function;

[0085] The rules for sorting individual crowding degrees are as follows:

[0086] (1) The more outstanding individuals in the non-dominated layer are at the front, that is, the individuals with smaller rank values ​​are at the front;

[0087] (2) If two individuals have the same dominant layer, the one with greater crowding is in front.

[0088] After sorting by crowding degree, the three best individuals are selected as α, β, and δ wolves, and then the population is updated according to the gray wolf algorithm (for detailed gray wolf algorithm reference [1])

[0089] Step (3): Perform uniform crossover on the population to obtain a new population, and then perform non-dominated sorting to obtain the Pareto solution set. The task attributes and rules are as follows:

[0090] Perform uniform crossover on the machine codes of the population to obtain a new population. After performing non-dominated sorting again, P(1) is the first-level non-dominated individual set, that is, the current Pareto solution set.

[0091] The specific steps of uniformly crossing the machine layer are as follows:

[0092] (1) Randomly select parent individuals F1, F2, and F3 from the population;

[0093] (2) Randomly generate a set R whose length is the same as the total number of processes, which consists of 0 and 1;

[0094] (3) Randomly select the code corresponding to the position 1 in the set R from the parent individuals F2 and F3, and copy it to the corresponding position in the offspring T1;

[0095] (4) Randomly select the code corresponding to the position 1 in the set R from the parent individuals F1 and F3, and copy it to the corresponding position in the offspring T2;

[0096] (5) Select the other coding parts in F1 and F2 and retain them in the offspring T1 and T2 respectively;

[0097] (6) Update the transportation time layer based on the process layer and the crossed machine selection layer.

[0098] After completing the machine uniform cross coding, if the solution of the new code is better than the original code, it will replace the original code F1, F2, otherwise the original code will be maintained.

[0099] Step (4): Determine whether the algorithm has reached the number of iterations. If so, output the Pareto solution set. If not, go to step (2).

[0100] The above embodiments are only preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes that adopt the design principles of the present invention and any changes made through non-creative work on this basis should fall within the scope of protection of the present invention.

Claims

1. A multi-objective distributed flexible workshop scheduling optimization method based on the Grey Wolf Algorithm, characterized in that: The steps include: (1) Initializing parameters to generate an initial population, and then updating it to a higher-quality initial population through plug-in coding. The population initialization rule is as follows: the coding mechanism of the initial population adopts a three-segment coding with the same length, where each segment represents process sorting information, machine selection information, and transportation time information, where the transportation time information is the transportation time required for adjacent processes to be processed in different factories. After the initial three-layer code is generated, an insert operation is performed on it; the insert coding specifically includes the following rules: Process O i,j is the jth process of workpiece i processed on machine l in factory f, process O i,j-1 is the j-1th process of processing workpiece i on machine k in factory u, O i,j-1 For process O i,j The previous process of the same workpiece; on machine l in factory f, process O i,j The preceding process is O q,z , the subsequent process is O g,h ; When process O i,j The first process of non-workpiece i and process O i,j When the machine k used for processing is not used for the first time, if one of the following conditions is met, the process O i,j Perform an insert operation: Specifically, the following conditions are included: For each machine's last processing step, if one of the following conditions is met, the step can be moved forward; Specifically, the following conditions are included: c i,j-1,k,u For process O i,j-1 The time to complete the process on machine k in factory u, c q,z,l,f For process O q,z The time to complete the process on machine l in factory f; T u,f is the transportation time of the process from factory u to factory f; p i,j,l,f For process O i,j Processing time on machine l in factory f; s g,h,l,f For process O g,h The time when processing begins on machine l in factory f; (2) According to the processing time, machine load and energy consumption, non-dominated sorting and congestion calculation are performed to determine the three wolves α, β and δ and update the population using the gray wolf algorithm; (3) Perform uniform crossover on the population to obtain a new population, and then perform non-dominated sorting to obtain the Pareto solution set; (4) Determine whether the algorithm has reached the number of iterations. If so, output the Pareto solution set. If not, go to (2).

2. The method for solving multi-objective distributed flexible workshop scheduling optimization based on the Grey Wolf Algorithm according to claim 1 is characterized in that: In step (2), the initial population is sorted non-dominated and the crowding degree is calculated, and the three best individuals are selected according to the crowding degree sorting as the three wolves α, β, and δ.

3. The multi-objective distributed flexible workshop scheduling optimization method based on the grey wolf algorithm according to claim 2 is characterized in that: The non-dominated sorting steps are: Step 1: Find all individuals in the population with n(x) = 0 and store them in the current set P(1); Step 2: For each individual y in the current set P(1), examine the set of individuals S(y) it dominates, and reduce n(k) by 1 for each individual k in S(y); Step 3: If n(k)-1=0, store individual k in another set H. Finally, take P(1) as the first-level non-dominated individual set and assign the same non-dominated rank to the individuals in this set. Then continue to perform the above grading operation on H and assign the corresponding non-dominated rank until all individuals are graded. n(x) is the number of solution individuals that dominate individual X in the population, and S(y) is the set of solution individuals dominated by individual y.

4. The method for solving multi-objective distributed flexible workshop scheduling optimization based on the grey wolf algorithm according to claim 2 is characterized in that: In step (2), the calculation formula of the congestion degree is as follows: I (s+1).d and I (s-1).d are the function values ​​of the next solution and the previous solution of S on the d function, and are the maximum and minimum values ​​on the d function respectively, and the d function is a different objective function.

5. The method for solving multi-objective distributed flexible workshop scheduling optimization based on the grey wolf algorithm according to claim 2 is characterized in that: In step (2), the rules for sorting individual crowding degrees are as follows: (1) The more outstanding individuals in the non-dominated layer are at the front, that is, the individuals with smaller rank values ​​are at the front; (2) If two individuals have the same dominant layer, the one with greater crowding is in front; After sorting according to the size of crowding, the three best individuals are selected as α, β, and δ wolves, and then the population is updated according to the gray wolf algorithm.

6. The method for solving multi-objective distributed flexible workshop scheduling optimization based on the grey wolf algorithm according to claim 1 is characterized in that: In step (3), a new population is obtained by uniformly crossing the machine codes of the population, and after non-dominated sorting is performed again, P(1) is the first-level non-dominated individual set, that is, the current Pareto solution set.

7. The method for solving multi-objective distributed flexible workshop scheduling optimization based on the Grey Wolf Algorithm according to claim 6 is characterized in that: In step (3), the uniform crossover specifically includes the following steps: Step 1: Randomly select parent individuals F1, F2, F3 from the population; Step 2: Randomly generate a set R with the same length as the total number of processes, which consists of 0 and 1; Step 3: Randomly select the code corresponding to the position 1 in the set R from the parent individuals F2 and F3, and copy it to the corresponding position in the offspring T1; Step 4: Randomly select the code corresponding to the position 1 in the set R on the parent individuals F1 and F3, and copy it to the corresponding position in the offspring T2; Step 5: Select the other coding parts in F1 and F2 and keep them in the offspring T1 and T2 respectively; Step 6: Update the transportation time layer based on the process layer and the crossed machine selection layer; After completing the machine uniform cross coding, if the solution of the new code is better than the original code, it will replace the original code F1, F2, otherwise the original code will be maintained.

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