Multi-team collaborative job scheduling method and system based on improved whale optimization algorithm

Abstract

The invention discloses a multi-team collaborative operation scheduling method and system based on an improved whale optimization algorithm, and the method comprises the steps: taking the minimization of the maximum completion time and the minimization of the maximum team task load as a dual-objective function for the condition that a plurality of teams need to cooperatively process the same workpiece; a scheduling model oriented to multi-team continuous collaborative operation is constructed, a whale optimization algorithm including task sequence and team collaborative double-layer discrete coding is adopted for solving, and improved operators such as multi-strategy whale group initialization, multi-strategy whale search, multi-strategy whale predation and multi-dimensional similarity calculation are designed for multi-team continuous processing features. According to the method, the shift continuity and the rest time constraint are directly mapped through a task and team double-layer coding mechanism, the target function is constructed based on the shift index, the optimization efficiency of multi-team collaborative scheduling is remarkably improved, and the method is widely applied to long-period multi-team collaborative manufacturing scenes of large spacecraft cabin structural members, high-speed rail carriages, ships, heavy machinery and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of production workshop scheduling, and in particular to a multi-shift collaborative operation scheduling method and system based on an improved whale optimization algorithm. Background Art

[0002] With the increasing adoption of Industrial Internet technologies, modern manufacturing enterprises are continuously moving towards automation and intelligence, with many manufacturing processes now fully automated by equipment. However, in workshops producing workpieces for large, complex equipment (such as spacecraft, high-speed rail, and ships), the high complexity and technical difficulty of the product processes make fully automated production impossible, requiring manual processing by teams of workers. Furthermore, the processing cycles for large, complex workpieces are long, making it difficult for a single team to complete them in a single shift. Multiple teams must collaborate on the same workpiece over consecutive shifts. Therefore, when scheduling such production tasks, manufacturing workshops must not only consider multi-team collaboration but also take into account team rest periods to ensure that all tasks are completed as quickly as possible and that the task load is balanced across teams.

[0003] Current research on production shop scheduling primarily focuses on flow or flexible shop floor operations, where task equipment is arranged. Less research has been devoted to scheduling task teams and the complexities of multiple teams collaborating on the same workpiece. Furthermore, traditional precise solution methods for large-scale task scheduling suffer from high computational complexity, making it difficult to generate high-quality solutions within an acceptable timeframe. While evolutionary algorithms, such as genetic algorithms, can handle large-scale problems, they face bottlenecks in improving their ability to search for globally optimal solutions and avoid falling into local optima.

[0004] CN118068785A discloses the use of an improved whale optimization algorithm for job shop scheduling, taking into account the two objectives of completion time and machine energy consumption, and designing the code based on the constraint of mandatory same-machine operation. However, this solution only takes into account the processing machine and does not involve the situation where multiple teams need to collaborate to process the same workpiece. The workshop scheduling method disclosed in CN118551977A takes into account the proficiency of the skills possessed by the assembly workers, but each assembly stage can still only be handled by one team, which makes it difficult to adapt to the situation where large and complex equipment requires collaborative processing by multiple teams. Therefore, there is an urgent need to build a dedicated model for the problem of continuous collaborative scheduling of multiple teams in large and complex task manufacturing, and to design an efficient evolutionary algorithm framework to improve the search capability of high-quality scheduling solutions. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a multi-shift collaborative work scheduling method and system based on the improved whale optimization algorithm. A scheduling model based on shift index is constructed to address the technical difficulties of continuous collaborative processing of multiple shifts. The whale optimization algorithm improves the technical problems that whale initialization, searching, predation and other operations cannot adapt to task discretization and multi-shift collaboration, and solves the technical dilemma of low scheduling efficiency and easy to fall into local optimality due to complex shift constraints in continuous collaborative work of multiple shifts.

[0006] Technical solution: The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm described in the present invention includes the following steps:

[0007] Step 1: Obtain the task and team information of the production workshop, including dividing the day into several shifts, the processing time of each workpiece into one or more shifts, each workpiece is processed by at least one team, each team cannot work two or more shifts consecutively, and the interval between two work shifts is no less than several shifts;

[0008] Step 2: Establish a shop scheduling model for continuous collaborative work among multiple teams, with the objective function being to minimize the maximum completion time and the maximum team task load;

[0009] Step 3: Using the improved whale optimization algorithm to solve the shop scheduling model to obtain candidate scheduling solutions, wherein the improved whale optimization algorithm uses a two-layer encoding, namely a task layer representing the order of task workpiece numbers and a team layer representing the order of task workpiece processing team numbers;

[0010] Step 4: Select the best scheduling plan from the candidate scheduling plans, including the workpiece processing sequence and team scheduling results.

[0011] Furthermore, the production workshop Arrange processing within days Each workpiece The processing time is hours, i.e. workpiece exist The processing is completed within a shift, and each day is divided into The production workshop has Teams, each team If the team Unable to complete the workpiece within 1 shift The workpiece can be processed by other teams. It can be completed by multiple teams working together. At the same time, the interval between two working times of each team should not be less than shifts.

[0012] In step 2, the constraints of the workshop scheduling model include:

[0013] Each workpiece must be scheduled to start processing in one shift, that is:

[0014] ;

[0015] Once each workpiece begins processing, it must be processed continuously for several shifts until it is completed without interruption, that is:

[0016] ;

[0017] Each team can only process one job at a time, that is:

[0018] ;

[0019] The interval between two working hours of each team shall not be less than the preset threshold, namely:

[0020] ;

[0021] The end time of each workpiece is no greater than the maximum completion time, that is:

[0022] ;

[0023] The task load of each team is no greater than the maximum team task load, that is:

[0024] ;

[0025] The value range of the variable is defined as follows:

[0026] ;

[0027] ;

[0028] ;

[0029] ;

[0030] Where, It is a 0-1 decision variable. If it is 1, it means the task In shift By team Otherwise, it will not be processed. It is a 0-1 decision variable. If it is 1, it means the task In shift Otherwise, no processing will occur. is a continuous variable representing the maximum completion time. It is a continuous variable, indicating the maximum team task load.

[0031] Furthermore, in step 3, the improved whale optimization algorithm includes the following steps:

[0032] Step 3.1: Initialize the whale group according to the whale individual code and generate The initial group of whales performs whale repair operations and decodes individual whales;

[0033] Step 3.2: Sort the whales to get the leading whale group and the following whale group;

[0034] Step 3.3: Randomly select an individual from the leading whale group and use a binary tournament to select an individual from the following whale group to form a pair of parents. Repeat this step to obtain To the parent whale;

[0035] Step 3.4: Calculate the individual similarity of each pair of parent whales. If it is less than the similarity threshold, perform the whale search operation; otherwise, perform the whale predation operation; thus, two child whales are obtained, and the whale repair operation is performed and the whale individual decoding is performed;

[0036] Step 3.5: If the offspring is better than the parent, replace the parent; otherwise, retain it to obtain a new generation of whales.

[0037] Step 3.6: Repeat steps 3.2 to 3.5 until the preset number of iterations is reached, and the Pareto optimal whale group, i.e., the candidate scheduling solution, is output.

[0038] Furthermore, in the improved whale optimization algorithm, the whale group initialization operation is: randomly selecting a strategy from the three initialization strategies of random allocation strategy, uniform allocation strategy and proportional allocation strategy according to a preset probability to generate whale individuals.

[0039] Furthermore, in the improved whale optimization algorithm, the whale repair operation is: to perform a validity check on the whale code. For a processing team sequence, if a team in the sequence does not meet the constraint that the interval between two works is not less than its preset threshold, then a team is randomly selected from other teams that meet the constraint to replace it until the processing team sequence meets the constraint.

[0040] Furthermore, in the improved whale optimization algorithm, the individual similarity of two whales is ,in is the coding similarity, i.e., the mean of the processing sequence similarity and the task team allocation similarity. The processing sequence similarity is calculated based on the Kendall tau correlation coefficient of the two individual task-level codings and normalized to 0–1. The task team allocation similarity is the ratio of the sum of the number of teams with the same sequence and the same task in all processing teams for the same workpiece to the total number of teams required for all workpieces. To decode the similarity, the ratio of the total number of shifts that the same team can schedule for the same task at the same time in the two individual scheduling plans to the total number of shifts that can be scheduled by all teams is calculated. The total number of shifts that can be scheduled by all teams is the product of the number of shifts that can be scheduled by a single team and the number of teams. .

[0041] Furthermore, in the improved whale optimization algorithm, the whale search operation is: for two parent whale individual codes, the task exchange operation and the team exchange operation are sequentially performed to obtain two offspring; the whale predation operation is: for any one of the two parent whale individuals, the task replacement operation and the team replacement operation are sequentially performed to finally obtain two offspring respectively;

[0042] Among them, the task exchange operation randomly selects a strategy from the task position strategy and the task sequence strategy. The task position strategy is: randomly select 40%-60% of the task coding layer positions to be retained, and fill the other positions of the task coding layer of parent A in order with the task codes of parent B that are not retained in parent A. The team sequence corresponding to the task code remains unchanged, and parent B performs the same operation; the task sequence strategy is: randomly select a task coding layer segment to be retained; for the task codes outside the parent A segment, select the tasks in the task coding layer of parent B that are not in the parent A segment in turn, and the team sequence corresponding to the task code remains unchanged; parent B performs the same operation;

[0043] Among them, the team exchange operation randomly selects a strategy from the team segment strategy and the random selection strategy. The team segment strategy is: randomly select a task coding layer segment; if there are tasks with the same coding but different team arrangements in the segment, the corresponding team arrangements are exchanged; the random selection strategy is: from 1 to Traverse the task artifact encoding; for task artifacts , randomly generate a value from 0 to 1, if the value is less than 0.5, the task artifacts in the two parents are exchanged Corresponding team sequence;

[0044] The task replacement operation is as follows: randomly select two positions in the code and exchange the task codes and team sequences corresponding to the two positions;

[0045] The team replacement operation is as follows: randomly select a position in the code, and for the workpiece corresponding to the position , randomly selected from the processing team A team, if , the team can be sampled repeatedly, otherwise the team cannot be sampled repeatedly, and the order of the newly selected teams is randomly disrupted; is the number of teams required for workpiece i, and m is the total number of teams in the workshop.

[0046] Furthermore, in the improved whale optimization algorithm, the whales are sorted according to the two target values ​​of the maximum completion time of the individual whales and the maximum team task load, and the fast non-dominated sorting method in the NSGA-II algorithm is used for sorting. The first several whales are selected as the leading whale group according to the set number and the rest are selected as the following whale groups.

[0047] Furthermore, the method of selecting the best scheduling solution from the candidate scheduling solutions in step 4 includes:

[0048] Obtain the two target values ​​of maximum completion time and maximum team task load corresponding to all candidate scheduling schemes;

[0049] The ideal point is formed by calculating the minimum value of the maximum completion time and the minimum value of the maximum team task load, and the worst point is formed by calculating the maximum value of the maximum completion time and the maximum value of the maximum team task load;

[0050] Perform minimum and maximum normalization on the two target values ​​corresponding to all candidate scheduling schemes according to the ideal point and the worst point;

[0051] The average of the normalized target values ​​is taken to obtain the index of the minimum value, and the candidate scheduling scheme corresponding to the index is the optimal scheduling scheme.

[0052] The multi-shift collaborative operation scheduling system based on the improved whale optimization algorithm of the present invention includes:

[0053] An information acquisition unit is used to obtain task and team information of the production workshop, including dividing a day into several shifts, the processing time of each workpiece into one or more shifts, each workpiece is processed by at least one team, each team cannot work two or more shifts consecutively, and the interval between two working shifts is no less than several shifts;

[0054] The workshop scheduling model modeling unit is used to establish a workshop scheduling model for continuous collaborative work among multiple teams. The objective function is to minimize the maximum completion time and minimize the maximum team task load.

[0055] a candidate scheduling scheme generating unit, configured to solve the shop scheduling model using an improved whale optimization algorithm to obtain a candidate scheduling scheme, wherein the improved whale optimization algorithm uses a two-layer encoding, namely a task layer representing the order of task workpiece numbers and a team layer representing the order of task workpiece processing team numbers;

[0056] The optimal scheduling scheme generation unit is used to select the optimal scheduling scheme from the candidate scheduling schemes, including the workpiece processing sequence and team scheduling results.

[0057] Beneficial effects: Compared with the existing technology, the advantages of the present invention are: (1) The present invention considers the problem of continuous collaborative production scheduling of multiple teams and constructs a mathematical model based on the shift index. The model takes into account the constraints of the actual workshop scenario, such as the continuous shift processing limit of the workpiece, the interval limit of the team's work shift, and the limit of the workpiece processing of a single shift of the team. (2) The present invention adopts the improved whale optimization algorithm framework to solve the production scheduling problem considering the continuous collaborative operation of multiple teams. The algorithm adds whale encoding and decoding based on dual encoding of tasks and teams, multi-strategy whale group initialization operation, multi-strategy whale search operation, multi-strategy whale predation operation, multi-dimensional similarity calculation operation and other operators, so that the algorithm can effectively find the Pareto optimal solution set and avoid falling into the local optimal dilemma, thereby improving the algorithm's search ability for the optimal scheduling solution. (3) The present invention normalizes the dual objective values ​​of the excellent scheduling solution obtained by the algorithm by introducing ideal points and worst points, thereby obtaining the optimal scheduling solution and a visual Gantt chart. The selection of the optimal scheduling solution eliminates the dimensional influence of the maximum completion time and the maximum team task load, selects the best scheduling solution from the Pareto optimal solution set, and avoids the problem of difficulty in selecting multiple results obtained by the multi-objective algorithm. (4) This invention not only improves the efficiency of multi-team scheduling for complex workpiece manufacturing, but also has good generalizability and can be applied to other similar flexible job shop scheduling environments where multiple production resources (such as equipment, workers, teams, etc.) are continuously and collaboratively processed. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flow chart of a multi-shift collaborative work scheduling method according to an embodiment of the present invention.

[0059] Figure 2 This is a schematic diagram of a multi-shift collaborative production workshop according to an embodiment of the present invention.

[0060] Figure 3 Flowchart of the improved whale optimization algorithm according to an embodiment of the present invention.

[0061] Figure 4 Schematic diagram of whale encoding and decoding of the improved whale optimization algorithm according to an embodiment of the present invention.

[0062] Figure 5 This is a Gantt chart of multi-shift scheduling results according to an embodiment of the present invention. DETAILED DESCRIPTION

[0063] First, the meaning of the data involved in the present invention is introduced.

[0064] Team: A team in a production workshop is a production group consisting of one or more workers, and the workshop arranges production in teams.

[0065] Shift: The shift of a production workshop is the work arrangement divided by time periods within the workshop, generally a two-shift or three-shift system, that is, 2 or 3 shifts per day.

[0066] Task: The production workshop needs to complete the processing of several workpieces within a certain period of time. In the task workpiece production workshop of large and complex equipment (such as spacecraft, high-speed railways, ships, etc.), the total processing time of each workpiece is different and there is no restriction on the processing order.

[0067] Task load: The total number of shifts that a team needs to perform processing tasks within the planned schedule.

[0068] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0069] like Figure 1 As shown, the multi-shift collaborative work scheduling method based on the improved whale optimization algorithm includes the following steps.

[0070] S1, obtains task information and team information of the production workshop. In this example, the workshop is a large spacecraft cabin structure production workshop, which mainly involves information such as the number of tasks, task processing time, and the number of teams.

[0071] The specific description of the mission information is: The large spacecraft cabin structure production workshop is in Arrange processing within days artifacts, this example The number of workpieces is 20. This embodiment takes the three-shift working mode as an example, with three shifts per day, namely , where each shift is 8 hours and each workpiece The processing time is Hours, this embodiment also sets , that is, the corresponding workpiece exist The specific task information is shown in Table 1.

[0072] Table 1 Task information table

[0073]

[0074] The specific description of the team information is: The cabin structure production workshop has teams, each of which You can only work in one shift at a time, and the interval between two working hours should not be less than two shifts, that is, , If the team Unable to complete the workpiece within 1 shift The workpiece can be processed by other teams. It can be completed by multiple teams working together. Specifically, in this example, the number of teams is 5, and the schematic diagram of the multi-team collaborative production workshop is as follows: Figure 2 shown. Figure 2 This is the workshop production status for a particular shift. Currently, only tasks 20, 7, and 11 are being processed. Teams 2, 3, and 5 are processing tasks 20, 7, and 11 in their respective workspaces. Teams 1 and 5 are idle and resting.

[0075] S2, based on task information and team information, builds a shop scheduling model for continuous collaborative work among multiple teams. Traditional mathematical models often use sequential indexing and start and end time variables for modeling, but fail to fully integrate the shift index-based optimization of completion time and team load balancing. The shop scheduling model proposed in this invention includes an objective function and constraints. The model is specifically:

[0076] ; (1)

[0077] ; (2)

[0078] ; (3)

[0079] ; (4)

[0080] ; (5)

[0081] ; (6)

[0082] ; (7)

[0083] ; (8)

[0084] ; (9)

[0085] ; (10)

[0086] ; (11)

[0087] ; (12)

[0088] Among them, formula (1) means that the maximum completion time of the target task is minimized; formula (2) means that the target maximum team task load is minimized; formula (3) means that each workpiece must be scheduled to start processing in one shift; formula (4) means that once each workpiece starts processing, it must be processed continuously. shifts, without interruption; Formula (5) indicates that each team can only process one workpiece at a time; Formula (6) indicates that the interval between two workpieces of each team must be greater than or equal to shifts; Formula (7) indicates that the end time of each workpiece is less than or equal to the maximum completion time; Formula (8) indicates that the task load of each team is less than or equal to the maximum team task load; Formula (9)-Formula (12) indicate the value range of the variables, It is a 0-1 decision variable. If it is 1, it means the task In shift By team Otherwise, it will not be processed. It is a 0-1 decision variable. If it is 1, it means the task In shift Otherwise, no processing will occur. is a continuous variable representing the maximum completion time. It is a continuous variable, indicating the maximum team task load. Assign a time frame to the task, Used to enumerate the times of each shift. In this example, For 15 days.

[0089] S3 uses the improved whale optimization algorithm to solve the workshop scheduling model for continuous collaborative operations of multiple shifts to obtain candidate scheduling solutions.

[0090] The classic whale optimization algorithm is mainly aimed at continuous optimization problems, using continuous mathematical formula search. The whale group initialization strategy is simple, and the crossover mutation strategy is single. It cannot directly handle the scheduling problem of discrete coding of process-shift teams. At the same time, it lacks a sequence constraint coding mechanism for multiple teams to continuously process the same workpiece, as well as corresponding search, predation, similarity calculation and other operations, resulting in low efficiency in solution space search. Therefore, the present invention mainly improves the whale optimization algorithm. The algorithm enhances the algorithm's excellent solution exploration performance by introducing operators such as multi-strategy whale group initialization operations, multi-strategy whale search operations, multi-strategy whale predation operations, and multi-dimensional similarity calculation operations for multi-shift collaboration problems. This improves the global excellent solution search capability while avoiding the algorithm from falling into the local optimal problem.

[0091] like Figure 3 As shown in Figure 2, the specific steps to improve the whale optimization algorithm are:

[0092] Step 3.1: Perform whale group initialization operation according to the whale individual code to generate The initial group of whales performs whale repair operations and decodes individual whales;

[0093] Step 3.2: Perform the whale group sorting operation to sort the whales and obtain the leading whale group and the following whale group;

[0094] Step 3.3: Randomly select an individual from the leading whale group and use a binary tournament to select an individual from the following whale group to form a parent pair, and repeat to obtain To the parent whale;

[0095] Step 3.4: Calculate the similarity of each pair of parent whale individuals based on the similarity calculation operation , if it is less than the similarity threshold , perform the whale search operation, otherwise perform the whale predation operation, thereby obtaining two offspring whales, perform the whale repair operation and perform whale individual decoding;

[0096] Step 3.5: If the offspring is better than the parent, replace the parent; otherwise, retain it to obtain a new generation of whales.

[0097] Step 3.6: Repeat steps 3.2 to 3.5 until the execution generations and output the Pareto optimal whale group.

[0098] Specifically, the key operations in the above steps are:

[0099] Whale individual coding: For the production scheduling problem of large spacecraft cabin structure parts considering multi-shift collaboration, the length of The first layer is the task layer, which indicates the order of task workpiece numbers; the second layer is the team layer, which indicates the order of task workpiece processing team numbers. Figure 3 The example of 5 tasks and 3 teams shown: the task layer coding is , indicating that the priority order of task artifacts is 3, 2, 5, 1, 4; the team level code is , represents the team combination that performs the most corresponding task. It means that team 2 and team 1 work together to process workpiece 3 in sequence; It means that teams 1, 3, and 2 will work together to process workpiece 2 in sequence; This means that teams 2, 3, 1, and 2 will work together to process workpiece 5 in sequence, and the working interval of team 2 is not less than 2 shifts; It means that teams 1 and 2 work together to process workpiece 1 in sequence; It means that team 3 processes workpiece 4 alone.

[0100] Whale individual decoding: Arrange the task artifacts and corresponding team combinations in the order of whale individual coding. of When there are three shifts, we check whether the task can be arranged starting from shift 1. If the corresponding shifts can be arranged in sequence starting from this shift, that is, the shift is idle at this shift time and no other tasks are arranged within the interval of less than two shifts before and after, then the task can be arranged. Otherwise, we check the next shift until the task can be arranged. When all the task artifacts encoded by the whale individual are arranged, we get the processing shift time and the corresponding processing shift of all the task artifacts, and calculate the corresponding target value, that is, the maximum completion time and the maximum task load of the shift. Figure 4 The decoding results shown show that Task 3 is processed sequentially by Teams 2 and 1, ensuring continuous and uninterrupted production. After Team 2 completes Task 5 on Shift 7, it cannot immediately process Task 5 due to the shift interval constraint of at least 2. Therefore, it is scheduled for processing on Shift 10. When Team 3 schedules Task 4, it can be pre-assigned to Shift 1 because it is available on Shift 1 and meets the shift scheduling constraints. The Gantt chart, obtained by decoding individual whales using individual whale encoding, shows that this scheduling scheme has a maximum completion time of 16 (the completion time required for Team 2 to complete Task 1) and a maximum team load of 5 (the total task load for Team 2).

[0101] Whale group initialization operation: by probability 、 、 Randomly select one of the three initialization strategies: random allocation strategy, uniform allocation strategy, and proportional allocation strategy to generate whale individual codes, and repeat the selection operation until the generation whales. , the three initialization strategies are:

[0102] (1) Random assignment strategy: 1) Randomly shuffle the task artifact numbers to obtain the task layer code; 2) For each task number , randomly selected from the processing team A team, if , the team can be sampled repeatedly, otherwise the team cannot be sampled repeatedly; 3) Randomly disrupt the order of the teams.

[0103] (2) Uniform distribution strategy: 1) Randomly generate a length of The team number sequence is as uniform as possible; 2) randomly shuffle the task workpiece numbers to obtain the task layer code; 3) traverse the task layer code, for each task number , select teams from the team number sequence in order until the team is assigned A team.

[0104] (3) Load distribution strategy: 1) Sort tasks in descending order of processing time, and randomly sort tasks with the same processing time to obtain task layer codes; 2) Traverse the task layer codes and for each task workpiece , find the team list with the smallest current load, randomly select a team from it, and update the team load; 3) Repeat 2) until the task artifact arrange A team.

[0105] Whale Repair: This operation verifies the validity of the whale code, specifically the processing team sequence for each task artifact. For a processing team sequence, the team is traversed sequentially. If a team does not meet the constraint that the interval between two work shifts is at least two shifts in the sequence, a team is randomly selected from other teams that meet this constraint to replace it, until the processing team sequence meets the constraint.

[0106] Whale group sorting operation: According to the dual objective values ​​of individual whales, a fast non-dominated sorting is performed based on the NSGA-II algorithm, and the corresponding congestion degree is calculated. The first whale was marked as the leader, and the second Mark whales as follow whales.

[0107] Similarity calculation operation: similarity between two whale individuals ,in is the coding similarity, specifically the mean of the processing sequence similarity and the task team allocation similarity. The processing sequence similarity is calculated based on the two individual task layer coding Kendall tau correlation coefficient and normalized to 0-1. The task team allocation similarity is the sum of the number of teams with the same sequence and the number of teams with the same task workpiece. ratio. To decode the similarity, the total number of shifts that schedule the same task for the same team at the same time in the two individual scheduling plans is calculated as ratio.

[0108] Whale search operation: For two parent whale individual codes, the task exchange operation and the team exchange operation are performed in sequence to obtain two offspring. The task exchange operation and the team exchange operation are specifically as follows:

[0109] (1) The task exchange operation randomly selects a strategy from the task position strategy and the task sequence strategy. The specific task position strategy is as follows: 1) Randomly select 40%-60% of the task coding layer positions to be retained; 2) The other positions of the task coding layer of parent 1 are sequentially filled with the task codes in parent 2 that are not retained in parent 1, and the team sequence corresponding to the task codes remains unchanged. 3) Parent 2 performs the same operation. The specific task sequence strategy is as follows: 1) Randomly select a task coding layer segment to be retained; 2) For task codes outside the parent 1 segment, select tasks in the task coding layer of parent 2 that are not in the parent 1 segment in sequence, and the team sequence corresponding to the task codes remains unchanged. 3) Parent 2 performs the same operation.

[0110] (2) The team exchange operation randomly selects a strategy from the team segment strategy and the random selection strategy. The team segment strategy is as follows: 1) Randomly select a task coding layer segment; 2) If there are tasks with the same coding but different team arrangements in the segment, the corresponding team arrangements are exchanged. The random selection strategy is as follows: 1) Randomly select a task coding layer segment; 2) If there are tasks with the same coding but different team arrangements in the segment, the corresponding team arrangements are exchanged. Traverse the task artifact encoding; 2) For the task artifact , randomly generate a value from 0 to 1, if the value is less than 0.5, the task artifacts in the two parents are exchanged The corresponding team sequence.

[0111] Whale predation operation: For any individual of the two parent whales, perform the task replacement operation and the team replacement operation in sequence, and finally obtain two offspring. The task replacement operation is specifically as follows: 1) randomly select two positions in the code; 2) swap the task codes and team sequences corresponding to the two positions. The team replacement operation is specifically as follows: 1) randomly select a position in the code; 2) for the workpiece corresponding to the position , randomly selected from the processing team A team, if , the team can be sampled repeatedly, otherwise the team cannot be sampled repeatedly. 3) Randomly disrupt the order of the newly selected teams.

[0112] The relevant parameter settings of the whale optimization algorithm in this example are shown in Table 2:

[0113] Table 2 Whale optimization algorithm parameters

[0114]

[0115] S4 selects the optimal scheduling solution from the candidate solutions and outputs the team scheduling results. The specific process is as follows: First, obtain the two target values ​​corresponding to all candidate solutions: maximum completion time and maximum team task load. Then, among all target values, calculate the minimum maximum completion time and the minimum maximum team task load to form the ideal point, and calculate the maximum maximum completion time and the maximum maximum team task load to form the worst point. Second, perform minimum-maximum normalization on the two target values ​​corresponding to all candidate solutions based on the ideal point and the worst point. Again, average the normalized targets to obtain the index of the minimum value and the corresponding optimal scheduling solution. Finally, generate the scheduling solution based on the solution decoding and draw a Gantt chart for visualization. Table 3 shows the final scheduling solution results for this example. The "Processing Team and Order" column in Table 3 indicates the teams required to process the corresponding task and the order in which they are processed. For example, processing task 2 requires four teams: teams 1, 5, 2, and 4. The first team has a processing shift of 9, and the last team has a processing shift of 12. Figure 5This is the Gantt chart result for scheduling. The horizontal axis represents the shift number, and the vertical axis represents the team number. The rectangles in the figure represent the tasks processed by the corresponding shift and team. The rectangle number represents the task number, and rectangles for the same task have the same color. For example, processing task 2 is a light blue rectangle. Starting from shift 9, teams 1, 5, 2, and 4 will process it in order, for a total of four shifts. The scheduling results show that the maximum completion time in this example is 27 shifts, and the maximum team task load is 9 shifts.

[0116] Table 3 Scheduling results

[0117]

[0118] In summary, the multi-shift collaborative work scheduling method based on the improved whale optimization algorithm described in the present invention takes minimizing the maximum completion time and minimizing the maximum team task load as the dual objectives, and constructs a targeted workshop scheduling model for continuous collaborative work of multiple teams. The core of the present invention is to design a whale optimization algorithm framework based on double-layer discrete coding of task sequence and team collaboration, and integrate a variety of improved operators into it, including multi-strategy whale group initialization, multi-strategy whale search, multi-strategy whale predation, and multi-dimensional similarity calculation. It can be specifically explained from the following aspects:

[0119] 1) The mathematical model of the present invention adopts shift index modeling: the constraints and objective functions are constructed based on the team shift, rather than the traditional start and end time and task sequence, which reduces the complexity of the model;

[0120] 2) The whale algorithm of the present invention adopts multiple strategies to improve the operator adaptation to the multi-shift collaborative work scheduling problem:

[0121] a) Process-shift dual-layer discrete coding mechanism: The second layer of coding defines the processing sequence of the shifts (e.g., shifts 1→2→3 continuously process workpieces), directly mapping the continuous shift constraint;

[0122] b) During the whale initialization phase, random allocation, uniform allocation, and proportional allocation strategies are used to balance tasks and team load.

[0123] c) The whale repair operator is based on a two-layer discrete coding structure to repair the work interval constraints in the processing team sequence and avoid illegal solutions;

[0124] d) Both the search and predation operators integrate multiple strategies for dual-objective and multi-team collaborative task scheduling problems, including task exchange, team exchange, task replacement, and team replacement;

[0125] e) Since the second-level coding involves multiple teams, the traditional coding matrix-based similarity calculation method cannot be applied. Therefore, a dual-dimensional "coding + decoding" and dual-level "task + team" similarity calculation method is adopted.

[0126] These improved operators fully meet the characteristics and actual needs of continuous collaborative work scheduling of multiple teams in complex task production workshops. They can effectively improve the search efficiency of the optimal scheduling plan and significantly improve the scheduling efficiency of multiple teams. At the same time, they have good versatility and applicability, and can be expanded to long-cycle multi-team collaborative manufacturing scenarios such as large spacecraft cabin structures, high-speed rail carriages, ships, and heavy machinery.

Claims

1. A multi-shift collaborative work scheduling method based on an improved whale optimization algorithm, characterized in that: The steps include: Step 1: Obtain the task and team information of the production workshop, including dividing the day into several shifts, the processing time of each workpiece into one or more shifts, each workpiece is processed by at least one team, each team cannot work two or more shifts consecutively, and the interval between two work shifts is no less than several shifts; Step 2: Establish a shop scheduling model for continuous collaborative work among multiple teams, with the objective function being to minimize the maximum completion time and the maximum team task load; Step 3: Using the improved whale optimization algorithm to solve the shop scheduling model to obtain candidate scheduling solutions, wherein the improved whale optimization algorithm uses a two-layer encoding, namely a task layer representing the order of task workpiece numbers and a team layer representing the order of task workpiece processing team numbers; Step 4: Select the best scheduling plan from the candidate scheduling plans, including the workpiece processing sequence and team scheduling results.

2. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 1 is characterized in that: In step 2, the constraints of the workshop scheduling model include: Each workpiece must be scheduled to start processing in one shift; Once each workpiece begins processing, it must be processed continuously for several shifts until it is completed without interruption; Each team can only process one workpiece at a time; The interval between two working hours of each team shall not be less than the preset threshold; The end time of each workpiece is no greater than the maximum completion time; The task load of each team shall not exceed the maximum team task load.

3. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 1 is characterized in that: In step 3, the improved whale optimization algorithm includes the following steps: Step 3.1: Initialize the whale group according to the whale individual code and generate The initial group of whales performs whale repair operations and decodes individual whales; Step 3.2: Sort the whales to get the leading whale group and the following whale group; Step 3.3: Randomly select an individual from the leading whale group and use a binary tournament to select an individual from the following whale group to form a pair of parents. Repeat this step to obtain To the parent whale; Step 3.4: Calculate the individual similarity of each pair of parent whales. If it is less than the similarity threshold, perform the whale search operation; otherwise, perform the whale predation operation; thus, two child whales are obtained, and the whale repair operation is performed and the whale individual decoding is performed; Step 3.5: If the offspring is better than the parent, replace the parent; otherwise, retain it to obtain a new generation of whales. Step 3.6: Repeat steps 3.2 to 3.5 until the preset number of iterations is reached, and the Pareto optimal whale group, i.e., the candidate scheduling solution, is output.

4. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 3 is characterized in that: In the improved whale optimization algorithm, the whale group initialization operation is: randomly selecting a strategy from the three initialization strategies of random allocation strategy, uniform allocation strategy and proportional allocation strategy according to a preset probability to generate whale individuals.

5. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 3 is characterized in that: In the improved whale optimization algorithm, the whale repair operation is as follows: the whale code is checked for legitimacy. For a processing team sequence, if a team in the sequence does not meet the constraint that the interval between two working operations is not less than its preset threshold, a team is randomly selected from other teams that meet the constraint to replace it until the processing team sequence meets the constraint.

6. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 3 is characterized in that: In the improved whale optimization algorithm, the individual similarity of two whales ,in is the coding similarity, i.e., the mean of the processing sequence similarity and the task team allocation similarity. The processing sequence similarity is calculated based on the Kendall tau correlation coefficient of the two individual task-level codings and normalized to 0–1. The task team allocation similarity is the ratio of the sum of the number of teams with the same sequence and the same task in all processing teams for the same workpiece to the total number of teams required for all workpieces. To decode the similarity, the ratio of the total number of shifts with the same task scheduled by the same team at the same time in the two individual scheduling plans to the total number of shifts that can be scheduled by all teams is calculated.

7. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 3 is characterized in that: In the improved whale optimization algorithm, the whale search operation is: for two parent whale individual codes, the task exchange operation and the team exchange operation are performed in sequence to obtain two offspring; the whale predation operation is: for any individual of the two parent whales, the task replacement operation and the team replacement operation are performed in sequence to finally obtain two offspring respectively; Among them, the task exchange operation randomly selects a strategy from the task position strategy and the task sequence strategy. The task position strategy is: randomly select 40%-60% of the task coding layer positions to be retained, and fill the other positions of the task coding layer of parent A in order with the task codes of parent B that are not retained in parent A. The team sequence corresponding to the task code remains unchanged, and parent B performs the same operation; the task sequence strategy is: randomly select a task coding layer segment to be retained; for the task codes outside the parent A segment, select the tasks in the task coding layer of parent B that are not in the parent A segment in turn, and the team sequence corresponding to the task code remains unchanged; parent B performs the same operation; Among them, the team exchange operation randomly selects a strategy from the team segment strategy and the random selection strategy. The team segment strategy is: randomly select a task coding layer segment; if there are tasks with the same coding but different team arrangements in the segment, the corresponding team arrangements are exchanged; the random selection strategy is: from 1 to Traverse the task artifact encoding; for task artifacts , randomly generate a value from 0 to 1, if the value is less than 0.5, the task artifacts in the two parents are exchanged Corresponding team sequence; The task replacement operation is as follows: randomly select two positions in the code and exchange the task codes and team sequences corresponding to the two positions; The team replacement operation is as follows: randomly select a position in the code, and for the workpiece corresponding to the position , randomly selected from the processing team A team, if , the team can be sampled repeatedly, otherwise the team cannot be sampled repeatedly, and the order of the newly selected teams is randomly disrupted; is the number of teams required for workpiece i, and m is the total number of teams in the workshop.

8. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 3 is characterized in that: In the improved whale optimization algorithm, the whales are sorted according to the two target values ​​of the maximum completion time of the individual whales and the maximum team task load. The fast non-dominated sorting method in the NSGA-II algorithm is used for sorting, and the first several whales are selected in order according to the set number as the leading whale group, and the rest are selected as the following whale groups.

9. The multi-shift collaborative work scheduling method based on the improved whale optimization algorithm according to claim 1 is characterized in that: The method of selecting the best scheduling solution from the candidate scheduling solutions in step 4 includes: Obtain the two target values ​​of maximum completion time and maximum team task load corresponding to all candidate scheduling schemes; The ideal point is formed by calculating the minimum value of the maximum completion time and the minimum value of the maximum team task load, and the worst point is formed by calculating the maximum value of the maximum completion time and the maximum value of the maximum team task load; Perform minimum and maximum normalization on the two target values ​​corresponding to all candidate scheduling schemes according to the ideal point and the worst point; The average of the normalized target values ​​is taken to obtain the index of the minimum value, and the candidate scheduling scheme corresponding to the index is the optimal scheduling scheme.

10. A multi-shift collaborative work scheduling system based on an improved whale optimization algorithm, characterized in that: include: An information acquisition unit is used to obtain task and team information of the production workshop, including dividing a day into several shifts, the processing time of each workpiece into one or more shifts, each workpiece is processed by at least one team, each team cannot work two or more shifts consecutively, and the interval between two working shifts is no less than several shifts; The workshop scheduling model modeling unit is used to establish a workshop scheduling model for continuous collaborative work among multiple teams. The objective function is to minimize the maximum completion time and minimize the maximum team task load. a candidate scheduling scheme generating unit, configured to solve the shop scheduling model using an improved whale optimization algorithm to obtain a candidate scheduling scheme, wherein the improved whale optimization algorithm uses a two-layer encoding, namely a task layer representing the order of task workpiece numbers and a team layer representing the order of task workpiece processing team numbers; The optimal scheduling scheme generation unit is used to select the optimal scheduling scheme from the candidate scheduling schemes, including the workpiece processing sequence and team scheduling results.

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