Distributed zero-latency multi-product batch process production scheduling method

Abstract

The invention relates to a distributed zero-latency multi-product batch process production scheduling method. The method comprises the following steps: establishing a distributed zero-latency multi-product batch process production scheduling model taking minimization of maximum completion time as a target function; the model is solved by adopting a discrete coding whale optimization algorithm to obtain a scheduling scheme, and in the solving process, the calculation process of the target function is accelerated by utilizing a time interval matrix. Compared with the prior art, an effective method is provided for distributed zero-latency multi-product intermittent process production scheduling, and rapid positioning of an optimal scheduling scheme is ensured; the invention provides a new objective function calculation method, which can save the time required for calculating the objective function, can quickly find the most suitable scheduling scheme in more candidate schemes through more efficient objective calculation, and is beneficial to optimizing resource allocation and improving production efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and in particular to a distributed zero-wait multi-product intermittent process production scheduling method. Background Art

[0002] Batch production, also known as batch production, is a common manufacturing model that plays a vital role in industries such as chemical, pharmaceutical, and food processing. Due to the relatively low utilization of equipment and time in batch production processes, different products or different batches of the same product may simultaneously place processing requirements on certain equipment, resulting in conflicts. Therefore, it is crucial to schedule the production of various products on different units and rationally plan the production sequence to ensure the efficient operation of the production process and thus optimize performance indicators. Appropriate scheduling strategies can improve production efficiency, reduce resource waste, and ensure product quality. However, traditional centralized production scheduling methods have limitations when dealing with the complexity of distributed manufacturing environments. As distributed manufacturing models are increasingly widely used due to their flexibility and cost-effectiveness, research on this issue is particularly important.

[0003] To solve the production scheduling problem of distributed zero-wait intermittent processes with the manufacturing period as the goal, intelligent algorithms need to continuously search in the solution space to obtain the optimal scheduling plan. This process requires frequent calculation of the objective function value to judge the quality of the current scheduling plan. The existing methods for calculating the objective function are relatively cumbersome and consume a large amount of computing resources and time. In addition, how to search in the solution space to quickly approach the optimal solution depends on the algorithm's structure design. CN116011726A discloses a method and system for optimizing distributed no-wait job-shop scheduling with delivery, which includes: proposing a hybrid whale optimization algorithm to solve the distributed no-wait job-shop scheduling problem with delivery. The goal of the problem is to minimize the makespan and minimize the total energy consumption. Therefore, a mixed-integer linear programming model is proposed to describe the multi-objective distributed no-wait job-shop scheduling problem with delivery. First, four arrays are used to represent a solution. Second, to generate high-quality and diverse initial solutions, it is proposed to sort the jobs according to the maximum processing time first, and then use the NEH heuristic algorithm to assign the jobs to the factories. Finally, the hybrid whale optimization algorithm adds the insert inversion block operation, path linking strategy, and variable neighborhood descent algorithm to the original whale optimization algorithm. However, this method does not fully consider the impact of setup time on the scheduling process, and in actual production, setup time often affects the overall scheduling efficiency. In addition, although this method uses an acceleration method in the solution process, there is still a problem of repeated calculation in the calculation of the objective function. Each time the objective function is calculated, relevant formulas need to be called again for calculation, which is relatively complex and redundant, resulting in low calculation efficiency. And the efficiency of objective function calculation directly affects the iteration speed and search efficiency of the scheduling algorithm. Another problem is that this method does not consider the situation where there are multiple orders for one product in the product processing stage, and the customer's order demand is a key factor in scheduling. In addition, this method uses a single NEH heuristic algorithm to generate the initial solution, which results in poor diversity of the initial population. In the later stage of algorithm iteration, the solutions in the population will be highly similar and prone to falling into local optima. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies, and provide a production scheduling method for distributed zero-wait multi-product intermittent processes. A mathematical model is established with the goal of minimizing the makespan, and a new method for calculating the objective function and a discrete-coded whale optimization algorithm (Discrete Whale Optimization Algorithm, DWOA) are proposed to quickly obtain a better scheduling plan and reduce the time consumed for calculating the objective value.

[0005] The purpose of the present invention can be achieved through the following technical solutions:

[0006] A distributed zero-wait multi-product batch process production scheduling method, comprising the following steps:

[0007] Establish a distributed zero-wait multi-product batch process production scheduling model with minimizing the makespan as the objective function;

[0008] Use a discrete-coded whale optimization algorithm to solve the model to obtain a scheduling plan. During the solving process, a time interval matrix is used to accelerate the calculation process of the objective function.

[0009] The constraint conditions of the model include:

[0010] Zero-wait constraint: Any two orders in the same factory satisfy the zero-wait constraint, that is, the difference between the start processing times of any two orders falls within the set of feasible values of the difference between the start processing times of two adjacent orders;

[0011] Order allocation constraint: The same order is processed in only one factory;

[0012] Order allocation and processing time constraint: The factory allocation and processing time of the order do not conflict;

[0013] Order start processing time constraint: The start processing time of the order is a positive number.

[0014] The set of feasible values is expressed as:

[0015]

[0016] Where represents the set of feasible values; δ u , δ v respectively represent the product numbers corresponding to orders u and v; represents the cumulative processing time when the products corresponding to orders u and v are completed on equipment k; represents the processing time of the process of the product corresponding to order u on equipment k; represents the sequence-related setup time when the product corresponding to order u is processed in the same factory as the product corresponding to order v and the product corresponding to order u is processed before the product corresponding to order v. m is the number of equipment.

[0017] The order allocation and processing time constraint is expressed as:

[0018]

[0019] Where t v , t u respectively represent the start processing times of order v and order u; represents the set of feasible values The left endpoint; x u,v Represents a binary variable, which is 1 if order v is processed after order u, and 0 otherwise; y l,u , y l,v Are binary variables, which are 1 if the corresponding order u / v is processed in factory l, and 0 otherwise; M represents a preset value.

[0020] The construction of the time interval matrix includes the following steps:

[0021] Calculate the completion times of order u and order v respectively as Where, t v , t u Represent the start processing times of order v and order u respectively, Represents the cumulative processing time when the products corresponding to order u and v are completed on equipment k;

[0022] To make the processing times of order u and order v non - conflicting, the time relationship between order u and order v is obtained as: Where, Represents the processing time of the operation of the product corresponding to order u on equipment k; Represents the sequence - related setup time when the product corresponding to order u and the product corresponding to order v are processed in the same factory and the product corresponding to order u is processed before the product corresponding to order v;

[0023] Calculate the elements in the time interval matrix based on the time relationship Where, m is the number of equipment, and the element Is the set of feasible values The left endpoint;

[0024] Construct the time interval matrix RS=(rs i,j ) n×n ; Where, n is the number of products.

[0025] The objective function of the entire scheduling sequence is:

[0026]

[0027] Where, Π represents the order processing sequence of each factory, C max Represents the makespan, π l ={π l (1),π l (2),...,π l (B l )} represents the order processing sequence of factory l, B l Represents the number of orders in factory l, and f represents the number of factories;

[0028] The calculation expression of the objective function of Factory l is as follows:

[0029]

[0030] Among them, π l (i) represents the product number corresponding to the i-th order in the processing sequence of Factory l, and rs i,j represents the element in the time interval matrix.

[0031] The specific process of accelerating the calculation of the objective function by using the time interval matrix is as follows:

[0032] When inserting an order into the current processing sequence, the calculation expression of the objective function of Factory l is:

[0033]

[0034] Among them, π(*) represents the order inserted into the current processing sequence, g represents the position where the order π(*) is inserted into the current processing sequence, and C max (π l ) represents the value of the objective function before inserting this order, and C max ′(π l ) represents the new value of the objective function after inserting this order;

[0035] When taking an order out of the current processing sequence, the calculation expression of the objective function of Factory l is:

[0036]

[0037] Among them, g′ represents the position of taking out the order π l (g′) from the current processing sequence, and C max (π l ) represents the value of the objective function before taking out this order, and C max ″(π l ) represents the new value of the objective function after taking out this order.

[0038] The whale optimization algorithm includes the following steps:

[0039] Step 1) Set the parameters and termination conditions of the whale optimization algorithm;

[0040] Step 2) Initialize the population by using the heuristic rule based on random order allocation and the random allocation strategy;

[0041] Step 3) Update the individuals in the population by using the hybrid search strategy;

[0042] Step 4) Determine whether the individual meets the termination condition. If it meets the termination condition, output the optimal scheduling plan; if it does not meet the termination condition, return to Step 3).

[0043] The method for initializing the population is as follows:

[0044] Generate NP / 2 solutions based on the heuristic rule of random order allocation, where NP is the population size. Specifically: Arrange all products in ascending order of total processing time, take out one order for each product, and place the taken orders in the processing sequences of the corresponding factories in sequence from the first factory to the last factory; Insert the remaining orders into the processing sequence of a certain factory in turn to minimize the objective function value of the current processing sequence until a complete processing sequence is formed;

[0045] Generate the remaining NP / 2 solutions in the population based on the random allocation strategy. Specifically: Randomly assign each order to a factory in turn and insert it into a random position in the processing sequence until a complete processing sequence is formed.

[0046] The specific hybrid search strategy is as follows:

[0047] Divide the current population into two equal parts on average. The first half part executes the neighborhood operator based on insertion, and the second half part executes the neighborhood operator based on swapping. Compare the optimal solutions in the two parts, and select the solution with a smaller current makespan as the population optimal solution. Among them,

[0048] The neighborhood operator based on insertion is specifically as follows: In the first stage, randomly select two factories other than the key factory, and randomly take out one order from each of the selected factories to form the first external sequence with the two taken orders, and randomly take out two orders from the key factory to form the second external sequence. Among them, the key factory is the factory with the largest current objective function value; In the second stage, randomly take out one order from the first external sequence and pre-insert it into all possible positions in the key factory, find the position that makes the makespan the shortest and insert the order, and repeat this process until all orders in the first external sequence are taken out and inserted; In the third stage, take out the orders in the second external sequence in turn and pre-insert them into all possible positions in all factories, find the position that makes the makespan the shortest and insert the corresponding orders;

[0049] The neighborhood operator based on swapping is specifically as follows: Randomly select an order from the key factory and swap it with all other orders, including the order swapping within the key factory and the order swapping between the key factory and other factories, and perform the best swapping operation that makes the makespan the shortest.

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

[0051] 1. The present invention takes into account the problem that there are multiple orders for each product in the intermittent production process. Reasonable scheduling of all orders during the processing can reduce unnecessary adjustments and equipment switching, which helps to improve the coherence of the production process, thereby reducing the completion time. In addition, the scheduling scheme can be dynamically adjusted according to the requirements of the orders, making the scheduling process more flexible.

[0052] 2. By establishing a distributed zero-waiting multi-product intermittent process production scheduling model, the present invention can make more accurate predictions and controls on the production process, which helps to improve the reliability of the production system. In addition, the correctness and feasibility of the scheduling scheme can be verified through the established model, and the scheduling method can be further optimized.

[0053] 3. The present invention fully considers the impact of the setup time on the scheduling process, enabling the setup time in the production process to be reasonably allocated and minimized. This helps to improve the overall scheduling efficiency.

[0054] 4. By designing a new calculation method for minimizing the makespan, the present invention effectively reduces the time complexity of the objective calculation. By constructing the RS matrix, each time the objective function is calculated, the already calculated values can be directly called from the matrix, which helps to reduce the time consumed by the objective calculation, enabling the algorithm to evaluate more solutions in a shorter time, thereby having a greater chance of finding the optimal solution and helping to improve the search efficiency of the algorithm. Through a more efficient objective calculation method, the algorithm can quickly find the most suitable scheduling scheme among more candidate solutions, thereby optimizing the resource allocation and enhancing the search efficiency of the algorithm.

[0055] 5. By improving the search mechanism and evolution process of the whale optimization algorithm, the present invention discretizes the whale algorithm, aims to minimize the makespan, determines the optimal scheduling scheme, and reduces unnecessary processing waiting time, which helps to improve the production efficiency.

[0056] 6. The present invention initializes the population by using heuristic rules and random assignment strategies, which can improve the quality and diversity of the initial population. The hybrid search strategy enables the algorithm to cover as many solutions as possible during the global search process, locate the region where the potential optimal solution is located, and at the same time avoid the algorithm from falling into the local optimum prematurely. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 is the flowchart of the method of the present invention;

[0058] Figure 2 is the flowchart of the DWOA algorithm of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0059] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented on the premise of the technical solution of the present invention, and the detailed implementation manners and specific operation processes are given, but the protection scope of the present invention is not limited to the following embodiments.

[0060] Embodiment 1

[0061] This embodiment provides a distributed zero-waiting multi-product batch process production scheduling method, as Figure 1 shown, including the following steps:

[0062] S1. Establish a distributed zero-waiting multi-product batch process production scheduling model with minimizing the makespan as the objective function.

[0063] In this embodiment, the constraint conditions of the established model include:

[0064] 1. Zero-waiting constraint, that is, any two orders in the same factory satisfy the zero-waiting constraint, that is, the difference between the start processing times of any two orders falls within the feasible value set of the difference between the start processing times of two adjacent orders.

[0065] First, define the feasible value set of the difference between the start processing times of two adjacent orders:

[0066]

[0067] Among them, represents the feasible value set; δ u and δ v respectively represent the product numbers corresponding to orders u and v; represents the cumulative processing time when the products corresponding to orders u and v are completed on equipment k; represents the processing time of the operation of the product corresponding to order u on equipment k; represents the sequence-dependent setup time when the product corresponding to order u is processed in the same factory as the product corresponding to order v and the product corresponding to order u is processed before the product corresponding to order v, and m is the number of equipment.

[0068] Then, the zero-waiting constraint is expressed as:

[0069] Among them, t v and t u represent the start processing times of order v and order u.

[0070] 2. Order allocation constraint, that is, the same order is processed in only one factory:

[0071] Among them, y l,uDenote as a binary variable, which is 1 if order u is processed in factory l, and 0 otherwise.

[0072] 3. Order allocation and processing time constraints, that is, the factory allocation and processing time of orders do not conflict:

[0073]

[0074] Among them, Denote the left endpoint of the set of feasible values ; x u,v Denote as a binary variable, which is 1 if order v is processed after order u, and 0 otherwise; y l,v is a binary variable, which is 1 if order v is processed in factory l, and 0 otherwise; M represents a sufficiently large number.

[0075] 4. Order start processing time constraints, that is, the start processing time of orders is positive:

[0076] t u ≥ 0.

[0077] S2. Solve the model using the discrete coding whale optimization algorithm to obtain a scheduling plan. Among them, during the solving process, use the time interval matrix to accelerate the calculation process of the objective function.

[0078] S21. Construct a time interval matrix, which specifically includes the following steps:

[0079] S211. Calculate the completion times of order u and order v respectively as

[0080] S212. To ensure that the processing times of order u and order v do not conflict, obtain the time relationship between order u and order v as:

[0081] S213. Calculate the elements in the time interval matrix based on the time relationship Among them, m is the number of devices, and the element is the left endpoint of the set of feasible values ;

[0082] S214. Construct the time interval matrix RS = (rs i,j ) n×n ; where n is the number of products.

[0083] S22. Determine the objective function.

[0084] The objective function of the entire scheduling sequence is:

[0085]

[0086] Among them, Π represents the order processing sequence of each factory, and C max represents the makespan, and π l ={π l (1), π l (2),..., π l (B l )} represents the order processing sequence of factory l, B l represents the number of orders in factory l, and f represents the number of factories.

[0087] The calculation expression of the objective function of factory l is:

[0088]

[0089] Among them, π l (i) represents the product number corresponding to the i-th order in the processing sequence of factory l, and rs i,j represents the element in the time interval matrix.

[0090] S23, accelerating the calculation of the objective function using the time interval matrix.

[0091] When inserting an order into the current processing sequence, the calculation expression of the objective function of factory l is:

[0092]

[0093] Among them, π(*) represents the order inserted into the current processing sequence, g represents the position where the order π(*) is inserted into the current processing sequence, and C max (π l ) represents the value of the objective function before inserting this order, and C max ′(π l ) represents the new value of the objective function after inserting this order;

[0094] When taking out an order from the current processing sequence, the calculation expression of the objective function of factory l is:

[0095]

[0096] Among them, g′ represents the position where the order π l (g′) is taken out from the current processing sequence, C max (π l ) represents the value of the objective function before taking out this order, and C max ″(π l ) represents the new value of the objective function after taking out this order.

[0097] S24, solving using the discrete-coded whale optimization algorithm.

[0098] As Figure 2 shown, the whale optimization algorithm performs the following steps:

[0099] Step 1) Set the parameters and termination conditions of the whale optimization algorithm.

[0100] Step 2) Initialize the population using a heuristic rule based on random order allocation and a random allocation strategy.

[0101] First, generate NP / 2 solutions based on the heuristic rule of random order allocation, where NP is the population size. Specifically: Arrange all products in ascending order of total processing time, take out one order for each product, and place the taken orders in the processing sequences of the corresponding factories in order from the first factory to the last factory; Insert the remaining orders into the processing sequence of a certain factory in turn to minimize the objective function value of the current processing sequence until a complete processing sequence is formed;

[0102] Then, generate the remaining NP / 2 solutions in the population based on the random allocation strategy. Specifically: Randomly assign each order to a factory in turn and insert it into a random position in the processing sequence until a complete processing sequence is formed.

[0103] Step 3) Update the individuals in the population using a hybrid search strategy.

[0104] In this embodiment, the hybrid search strategy is specifically as follows:

[0105] Divide the current population into two equal parts on average. The first half performs a neighborhood operator based on insertion, and the second half performs a neighborhood operator based on swapping. Compare the optimal solutions in the two parts and select the solution with a smaller current makespan as the population optimal solution, where,

[0106] The neighborhood operator based on insertion is specifically as follows:

[0107] In the first stage, randomly select two factories other than the key factory, and randomly take out one order from each of the selected factories. Use the two taken orders to form the first external sequence ESa, and randomly take out two orders from the key factory to form the second external sequence ESb, where the key factory is the factory with the largest current objective function value;

[0108] In the second stage, randomly take out one order from the first external sequence ESa and pre-insert it into all possible positions in the key factory. Find the position that makes the makespan the shortest and insert the order. Repeat this process until all orders in the first external sequence ESa are taken out and inserted;

[0109] In the third stage, the orders in the second external sequence ESb are taken out one by one and pre-inserted into all possible positions in all factories, and the position that minimizes the completion time is found and the corresponding order is inserted.

[0110] The neighborhood operator based on swapping is specifically as follows: randomly select an order from the key factories and swap it with all other orders, including swapping orders within the key factories and swapping orders between the key factories and other factories, and perform the best swapping operation that minimizes the completion time.

[0111] Step 4) Determine whether the individual meets the termination condition. If it meets the termination condition, output the optimal scheduling plan; if it does not meet the termination condition, return to Step 3).

[0112] In this embodiment, the maximum number of iterations is used as the termination condition, and the maximum number of allowed iterations is 50. If the number of iterations reaches 50, output the optimal scheduling plan; if the number of iterations is less than 50, return to Step 3).

[0113] Embodiment 2

[0114] Based on Embodiment 1, this embodiment details the set of feasible values for the difference in start processing times between two adjacent orders.

[0115] This embodiment relates to a certain distributed zero-wait multi-product batch production process. This process has 5 products, 5 devices, 2 factories, and 10 orders. The processing times of each product on each device and the sequence-dependent setup times between different products are shown in Table 1 and Table 2 respectively. Assume a solution is Π = {{1, 4, 1, 5, 5}, {2, 4, 4, 1, 3}}, which means a total of 10 orders are assigned to 2 factories for processing. The two parts in Π correspond to the order processing sequences of the two factories respectively. Among them, {1, 4, 1, 5, 5} means that orders 1, 4, 1, 5, 5 are processed in Factory 1 in the current order, and {2, 4, 4, 1, 3} means that orders 2, 4, 4, 1, 3 are processed in Factory 2 in the current order.

[0116] In this embodiment, from Table 1, it can be obtained that the processing times of Product 3 on devices 1 - 5 are p 3,1 = 88, p 3,2 = 62, p 3,3 = 27, p 3,4 = 93, p 3,5 = 22. Therefore, the cumulative processing time of Product 3 on the five devices is Similarly, the cumulative processing time of Product 5 on the five devices is

[0117] The set of feasible values for the difference in start processing times between two adjacent orders is:

[0118]

[0119] Taking products 3 and 5 as examples, the set of feasible values that the difference in start times between products 3 and 5 satisfies is:

[0120] Among them, when k = 1, When k = 2, When k = 3, Similarly, when k = 4, When k = 5, Therefore, S 3,5 = [max{98, 88, 35, 112, 103}, +∞) = [112, +∞}.

[0121] This means that if in the same factory, product 5 is processed immediately after product 3, the difference in their processing times must satisfy the above set of feasible values. In order to meet the zero-waiting constraint and make the completion time of the scheduling sequence as early as possible, the difference in start times between products 3 and 5 can only take the left boundary value of 112.

[0122] Table 1 Processing times of products on each device

[0123] Device 1 Device 2 Device 3 Device 4 Device 5 Product 1 21 95 28 3 84 Product 2 7 34 40 11 47 Product 3 88 62 27 93 22 Product 4 64 83 56 89 50 Product 5 72 80 16 31 82

[0124] Table 2 Sequence-related setup times between different products

[0125] Product 1 Product 2 Product 3 Product 4 Product 5 Product 1 0 6 9 14 17 Product 2 2 0 3 3 2 Product 3 8 15 0 18 10 Product 4 18 16 3 0 3 Product 5 16 11 3 19 0

[0126] Example 3

[0127] Based on Example 2, this example details the construction of the time interval matrix and the process of accelerating the objective function calculation.

[0128] Calculate the elements in the time interval matrix:

[0129] At this time, the element in the 3rd row and 5th column of the time interval matrix is then 112.

[0130] In this way, the difference in start times for processing any two products can be calculated in advance and stored in the time interval matrix as Then when product 1 is processed before product 2, the value rs that the start processing times of product 2 and product 1 satisfy 1,2is the value of the first row and second column in the matrix, i.e., 145. If order u belongs to product 1 and order v belongs to product 2, then order u is processed before order v. Then the time between order u and order v satisfies Similarly, when product 2 is processed before product 3, the value rs that the start processing times of product 2 and product 3 satisfy 2,3 is the value of the second row and third column in the matrix. When product 3 is processed before product 2, the value rs that the start processing times of product 3 and product 2 satisfy 3,2 is the value of the third row and second column in the matrix, and so on.

[0131] According to the assumed processing sequence, the objective function of factory 1 is calculated as The objective function of factory 2 is calculated as Therefore, the minimum makespan of the entire scheduling sequence is C max (Π) = max{693, 641} = 693.

[0132] In this example, if the last order in factory 1 is inserted into the last position of the processing sequence in factory 2, the objective function value of the new factory 1 is The objective function value of the new factory 2 is

[0133] Example 4

[0134] Based on Example 3, to verify the performance of the algorithm in this example, experimental analysis is carried out using examples of different scales. However, since there is no standard example of the distributed zero-wait intermittent process production scheduling problem in the existing technology, in order to evaluate the performance of the DWOA algorithm proposed in the present invention, according to the characteristics of intermittent production and the industrial background in this example, the experimental design method is adopted to randomly generate test data within a certain range and conduct simulation tests to evaluate the algorithm performance.

[0135] The number of products is {5, 10, 20}, the number of devices is {5, 10, 20}, and the parameters are combined to obtain a total of 9 examples. Among them, the number of factories in each example is three cases of 2, 4, and 6, and the order quantity of each product is randomly generated between [1, 5]. The processing time of each process of the product is randomly generated between [1, 99], and the sequence-related setup time is randomly generated between [1, 19].

[0136] Since there is no existing algorithm for the same distributed zero-wait intermittent process production scheduling problem, in this embodiment, the HEDFOA algorithm (Hybrid enhanced discrete fruit fly optimization algorithm) and the DABC (A discrete artificial bee colony algorithm) algorithm are adapted and re-implemented for this problem, and compared with the algorithm of the present invention to verify the effectiveness of the algorithm.

[0137] To ensure the fairness of the experiment, the three algorithms use the same programming environment and equipment. All algorithms are programmed in C++. The running environment is a PC equipped with an Intel Core(TM)i7-6700 3.4-GHz processor. All algorithms use the same termination condition, and each algorithm runs independently 5 times on all test cases. The relative percentage deviation (RPD) is used as the evaluation criterion.

[0138] Table 3 Relative percentage deviation of three algorithms applied to 9 instances (number of factories is 2)

[0139] The present invention HEDFOA DABC Example 1 (5×5) 0.00 0.00 0.26 Example 2 (5×10) 0.00 6.15 0.00 Example 3 (5×20) 0.00 0.00 0.17 Example 4 (10×5) 0.00 0.70 0.91 Example 5 (10×10) 0.00 5.04 4.68 Example 6 (10×20) 0.00 2.70 1.27 Example 7 (20×5) 0.00 2.67 2.36 Example 8 (20×10) 0.00 2.55 2.65 Example 9 (20×20) 0.00 6.96 5.65 Average 0.00 2.98 1.99

[0140] Table 4 Relative percentage deviation of three algorithms applied to 9 instances (number of factories is 4)

[0141] The present invention HEDFOA DABC Example 1 (5×5) 0.00 0.33 0.00 Example 2 (5×10) 0.00 0.00 0.00 Example 3 (5×20) 0.00 0.00 0.27 Example 4 (10×5) 0.00 2.24 2.24 Example 5 (10×10) 0.00 3.79 5.29 Example 6 (10×20) 0.00 4.12 5.02 Example 7 (20×5) 0.00 2.24 4.18 Example 8 (20×10) 0.00 4.08 6.15 Example 9 (20×20) 0.00 7.06 9.00 Average 0.00 2.65 3.57

[0142] Table 5 Relative percentage deviation of three algorithms applied to 9 instances (number of factories is 6)

[0143]

[0144]

[0145] It can be seen from Table 3 - Table 5 that in the 9 test cases solved, regardless of the number of factories, the relative percentage deviation of the DWOA algorithm proposed by the present invention is the smallest, indicating that the scheduling solution obtained by the DWOA algorithm is the best and the performance of the algorithm is the best. Therefore, it can play an important role in the enterprise production process and help improve production efficiency.

[0146] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative labor. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field based on the concept of the present invention through logical analysis, reasoning, or limited experiments on the basis of the prior art should be within the protection scope determined by the claims.

Claims

1. A distributed zero-wait multi-product batch process production scheduling method, characterized in that, It includes the following steps: Establish a distributed zero-waiting multi-product batch process production scheduling model with minimizing the makespan as the objective function; Use a discrete-coded whale optimization algorithm to solve the model to obtain a scheduling plan. During the solution process, a time interval matrix is used to accelerate the calculation process of the objective function.

2. A distributed zero-wait multi-product batch process production scheduling method according to claim 1, characterized in that The constraint conditions of the model include: Zero-waiting constraint: Any two orders in the same factory satisfy the zero-waiting constraint, that is, the difference between the start processing times of any two orders falls within the set of feasible values of the difference between the start processing times of two adjacent orders; Order allocation constraint: The same order is processed in only one factory; Order allocation and processing time constraint: The factory allocation and processing time of the order do not conflict; Order start processing time constraint: The start processing time of the order is a positive number.

3. A distributed zero-wait multi-product batch process production scheduling method according to claim 2, characterized in that The set of feasible values is expressed as: Among them, represents the set of feasible values; δ u , δ v respectively represent the product numbers corresponding to orders u and v; represent the cumulative processing time when the products corresponding to orders u and v are completed on device k; represents the processing time of the process of the product corresponding to order u on device k; represents the sequence-related setup time when the product corresponding to order u and the product corresponding to order v are processed in the same factory and the product corresponding to order u is processed before the product corresponding to order v, where m is the number of devices.

4. A distributed zero-wait multi-product batch process production scheduling method according to claim 2, characterized in that The order allocation and processing time constraint is expressed as: where t v and t u respectively represent the start processing times of order v and order u; represents the left endpoint of the set of feasible values ; x u,v represents a binary variable, which is 1 if order v is processed after order u, and 0 otherwise; y l,u and y l,v are binary variables, which are 1 if the corresponding order u / v is processed in factory l, and 0 otherwise; M represents a preset value.

5. A distributed zero-wait multi-product batch process production scheduling method according to claim 1, characterized in that, The construction of the time interval matrix includes the following steps: The completion times of order u and order v are calculated as where t v , t u represent the start processing times of order v and order u respectively, represents the cumulative processing time when the products corresponding to order u and order v are completed on device k; To ensure that the processing times of order u and order v do not conflict, the time relationship between order u and order v is obtained as follows: wherein, represents the processing time of the operation of the product corresponding to order u on equipment k; represents the sequence-related setup time when the product corresponding to order u and the product corresponding to order v are processed in the same factory and the product corresponding to order u is processed before the product corresponding to order v; Calculate the elements in the time interval matrix based on the time relationship where m is the number of devices, and the element is the left endpoint of the set of feasible values ; Construct a time interval matrix RS = (rs i,j ) n×n based on the said elements; where n is the number of products.

6. A distributed zero-wait multi-product batch process production scheduling method according to claim 1, characterized in that The objective function of the entire scheduling sequence is: Among them, Π represents the order processing sequence of each factory, and C max represents the makespan, and π l ={π l (1), π l (2),..., π l (B l )} represents the order processing sequence of factory l, B l represents the number of orders in factory l, and f represents the number of factories; The calculation expression of the objective function of factory l is: Among them, π l (i) represents the product number corresponding to the i-th order in the processing sequence of factory l, rs i,j represents an element in the time interval matrix.

7. A distributed zero-wait multi-product batch process production scheduling method according to claim 6, characterized in that The specific process of using the time interval matrix to accelerate the calculation of the objective function is: When inserting an order into the current processing sequence, the calculation expression of the objective function of factory l is: Among them, π(*) represents the order inserted into the current processing sequence, g represents the position where the order π(*) is inserted into the current processing sequence, and C max (π l ) represents the objective function value before inserting this order, and C max ′(π l ) represents the new objective function value after inserting this order; When removing an order from the current processing sequence, the calculation expression of the objective function of factory l is: where, g′ represents the position of removing order π from the current processing sequence l (g′), C max (π l ) represents the objective function value before removing this order, C max ″(π l ) represents the new objective function value after removing this order.

8. A distributed zero-wait multi-product batch process production scheduling method according to claim 1, characterized in that The whale optimization algorithm includes the following steps: Step 1) Set the parameters and termination conditions of the whale optimization algorithm; Step 2) Initialize the population using a heuristic rule based on random order allocation and a random allocation strategy; Step 3) Update the individuals in the population using a hybrid search strategy; Step 4) Determine whether the individual meets the termination condition. If it meets the termination condition, output the optimal scheduling plan; if it does not meet the termination condition, return to Step 3).

9. A distributed zero-wait multi-product batch process production scheduling method according to claim 8, characterized in that The method for initializing the population is: Generate NP / 2 solutions using a heuristic rule based on random order allocation, where NP is the population size. Specifically: Arrange all products in ascending order of total processing time, take out one order for each product, and place the taken orders in the processing sequences of the corresponding factories in order from the first factory to the last factory; Insert the remaining orders into the processing sequence of a certain factory in turn to minimize the objective function value of the current processing sequence until a complete processing sequence is formed; Generate the remaining NP / 2 solutions in the population using a random allocation strategy. Specifically: Randomly assign each order to a factory and insert it into a random position in the processing sequence until a complete processing sequence is formed.

10. A distributed zero-wait multi-product batch process production scheduling method according to claim 8, characterized in that, The hybrid search strategy is specifically: Divide the current population into two equal parts. The first half executes a neighborhood operator based on insertion, and the second half executes a neighborhood operator based on swapping. Compare the optimal solutions in the two parts and select the solution with a smaller current makespan as the optimal solution of the population. Among them, The neighborhood operator based on insertion is specifically as follows: In the first stage, randomly select two factories other than the key factory, and randomly take out one order from each of the selected factories. Use the two taken-out orders to form the first external sequence, and randomly take out two orders from the key factory to form the second external sequence, where the key factory is the factory with the largest current objective function value; in the second stage, randomly take out an order from the first external sequence and pre-insert it into all possible positions in the key factory, find the position that minimizes the completion time and insert the order at that position. Repeat this process until all orders in the first external sequence are taken out and inserted; in the third stage, sequentially take out the orders in the second external sequence, and pre-insert each of them into all possible positions in all factories, find the position that minimizes the completion time and insert the corresponding order. The neighborhood operator based on swapping is specifically as follows: Randomly select an order from the key factory and swap it with all other orders, including swapping orders within the key factory and swapping orders between the key factory and other factories, and perform the best swapping operation that minimizes the completion time.

Images