A Virtual Unit Air-Time-Person Integrated Scheduling Method and System for Shipbuilding

Abstract

The present invention discloses a virtual unit space-time-human integrated scheduling method and system for shipbuilding, including the following steps: constructing a processing workshop model; constructing a worker fatigue and recovery model; constructing a transportation model; constructing an objective function: comprehensively considering the overall task completion time, transportation time, and worker load, and taking minimizing the maximum completion time, the shortest total transportation distance, the balance of worker workload, and the minimum total worker load as the optimization objectives to construct the objective function; designing a hybrid algorithm based on NSGA-II and the grey wolf optimization algorithm, and solving the model. The integrated scheduling system of the present invention comprehensively considers factors such as the round-trip of transportation equipment, the capacity of the workpiece temporary storage area, and worker fatigue and recovery, and studies the virtual unit integrated scheduling system; the combination of NSGA-II and GWO realizes the balance between local search and global search; the algorithm of the present invention is more effective and has stronger robustness in solving the multi-objective optimization problem for shipbuilding.

Description

Technical Field

[0001] The present invention relates to a virtual unit integrated scheduling method and system, and particularly to a space-time-person integrated scheduling method and system for virtual units in shipbuilding. Background Art

[0002] In existing shipbuilding workshop operation scheduling planning systems, constraints such as process, processing machines, and delivery date are mostly considered, and the shortest construction time is taken as the goal. The obtained scheduling scheme is out of touch with the actual production, and the executability is poor. The adaptability between personnel and tasks is not high, the production logistics is disordered, and the production efficiency is low. At the same time, the influence of the workpiece buffer capacity on production continuity is not considered. Summary of the Invention

[0003] Object of the Invention: The object of the present invention is to propose a space-time-person integrated scheduling method and system for virtual units in shipbuilding, considering the real-time fatigue of workers and the capacity of the workpiece temporary storage area, to make up for the deficiencies in existing shipbuilding workshop scheduling technologies.

[0004] Technical Solution: The present invention includes the following steps: constructing a processing workshop model; constructing a worker fatigue and recovery model; constructing a transportation model; constructing an objective function: comprehensively considering the overall task completion time, transportation time, and worker load, and taking minimizing the maximum completion time, the shortest total transportation distance, the balance of worker workload, and the minimum total worker load as the optimization objectives to construct the objective function; designing a hybrid algorithm based on NSGA-II and the grey wolf optimization algorithm, and solving the model.

[0005] The construction of the processing workshop model is specifically as follows: The processing workshop contains a total of K virtual units, n workpieces to be processed, M processing devices, and W workers; each virtual unit contains multiple processing devices and undertakes the workpiece processing tasks of a specific workpiece family.

[0006] The construction of the worker fatigue and recovery model is specifically as follows: Analyzing and testing workers to obtain the work efficiency r′ of worker w at the end of the fth task fw , and the actual completion time P′ of worker w in the fth task fw :

[0007]

[0008]

[0009] where λ w represents the fatigue parameter of worker w, q fw is the fatigue decline time, α fw is the work efficiency steady state time, P fw is the standard completion time of each task of worker w, r fwThe work efficiency of worker w at the start of the f-th task and assume the work efficiency r of the initial worker 1w = 1

[0010] The constraint conditions for constructing the objective function include:

[0011] Each process of each workpiece can only be processed on one processing device:

[0012]

[0013] A worker needs to be arranged to complete the processing on each processing device where each process is arranged:

[0014]

[0015] A worker needs to be arranged for each process:

[0016]

[0017] Process O ij The actual completion time:

[0018]

[0019] The work efficiency of worker w at the start of the f-th task arranged:

[0020]

[0021] The work efficiency of worker w at the end of the f-th task arranged:

[0022]

[0023] The fatigue decline time when worker w completes the f-th task O ij :

[0024]

[0025] The rest time of the worker from the completion of the (f - 1)-th task to the start of the f-th task:

[0026] θ fw = h ijfw S ij - h i′j′(f-1)w C i′j′ f > 1 (18)

[0027] Process O ij The start and completion time relationship:

[0028]

[0029] The sequence relationship between processes:

[0030]

[0031] The completion time constraint of the workpiece:

[0032] C ij ≤d j (21)

[0033] Process O ij The start transportation time and O (i-1 ) j 's completion time constraint:

[0034] ST ijkt ≥C (i-1)j When i = 2, 3,... i (j) (22)

[0035] Process O ij The relationship between the start processing time and the transportation time of:

[0036] S ij ≥ET ijkt (23)

[0037] The relationship between the no-load transportation end time and the actual transportation start time:

[0038]

[0039] The relationship between the actual transportation start time and the end time:

[0040] ET ijkt =ST ijkt +B ijm B (i-1)jm′ t mm′ (25)

[0041] The relationship between the return no-load start time and the actual transportation end time:

[0042]

[0043] Each workpiece can only be transported by one transportation device:

[0044]

[0045] The relationship between the return no-load start time and the end time:

[0046]

[0047] The relationship between the no-load start time and the end time when driving to the workplace:

[0048]

[0049] The hybrid algorithm based on NSGA-II and Grey Wolf Optimization algorithm is specifically as follows: A four-layer coding method is adopted. The first layer of the chromosome is the operation coding layer; the second layer of the chromosome is the processing equipment segment coding; the third layer of the chromosome is the unit coding layer to which the processing equipment belongs; the fourth layer of the chromosome is the coding layer to which the worker belongs.

[0050] The specific steps for solving the model include:

[0051] Preset the number of iterations, crossover probability P c , mutation probability P m , population size N, coding method, decoding method, and fitness function;

[0052] Generate an initial population based on the opposition-based learning strategy;

[0053] Randomly select a parent and the global optimal individual for crossover and mutation to form a generation of offspring;

[0054] Number of iterations + 1;

[0055] Perform the selection operation using the binary tournament algorithm to obtain the first-generation parents; Obtain the decision-making layer individuals using the method based on non-dominated rank and crowding distance.

[0056] Perform crossover and mutation on the parents and the prey to obtain the offspring;

[0057] Merge the parents and the offspring, and perform non-dominated sorting and crowding degree calculation;

[0058] Adopt the elitist retention strategy to obtain a new population and update the global optimal individual;

[0059] Check whether the maximum number of iterations is reached. If so, output the result; otherwise, return Number of iterations + 1.

[0060] The decoding method is as follows:

[0061] (1) Starting from time τ = 0, select the operation of the workpiece to be processed according to the chromosome coding. If the processing equipment and worker selected for this operation are occupied, suspend this processing task until the occupied processing equipment and worker are released; Calculate the completion time of the current operation according to formulas (14) and (19), and calculate the work efficiency of the worker when completing the current task according to formula (16); When all workpieces to be processed are suspended, the time τ = 0 ends, and let τ = τ + 1;

[0062] (2) The first operation of each workpiece does not need to be transported, and the transportation time is 0; At each subsequent moment, traverse the operations of the workpieces to be processed in all workpiece families;

[0063] (3) At τ = 1, if the worker is arranged again, calculate the task start working efficiency of the worker according to formula (15).

[0064] (4) At the τ moment, after the i-th process of workpiece j is processed, if the (i + 1)-th process of workpiece j is processed on the current processing equipment, the transportation time is 0.

[0065] (5) If the (i + 1)-th process of this workpiece is processed on other equipment, judge whether the transportation equipment in this unit is available: if the transportation equipment is not available, suspend the transportation task until there is a transportation equipment that can execute this processing task.

[0066] (6) If the transportation equipment is available, judge whether there is space in the workpiece temporary storage area in front of the arranged processing equipment, that is

[0067] π mτ +Ω mτ <B m (30)

[0068] In the formula: π mτ represents the number of workpieces waiting to be processed in front of processing equipment m at the τ moment; Ω mτ represents the number of workpieces waiting to be transported in front of processing equipment m at the τ moment; B m represents the buffer capacity size in front of processing equipment m.

[0069] (7) If formula (30) is satisfied, calculate the no-load time of the transportation equipment according to formulas (28) and (29), and insert it forward to ensure that the transportation equipment just arrives in front of the processing equipment of the i-th process of workpiece j after the i-th process of workpiece j is processed, and calculate the actual transportation time of the current process according to formula (25). If not satisfied, suspend the transportation task.

[0070] (8) If multiple transportation equipment in the unit are all available, randomly select one transportation equipment to complete the current transportation task, and so on until all processes of all workpieces are processed.

[0071] The generation of the initial population based on the reverse learning strategy is specifically as follows: Generate a random initial population; According to the following formula: R i =A i +B i -r i , generate the reverse population of the initial population; In the formula: A and B respectively represent the upper and lower boundaries of the value range of the individual vector elements; r is the initial individual; R is the reverse individual; i is the dimension of the individual vector; Calculate the individual fitness values of the initial population and the reverse population; Perform non-dominated sorting on the individuals in the randomly generated population and the reverse population, and arrange them in ascending order, and take the first N populations as the initial population.

[0072] The crossover adopts IPOX crossover, and the specific operation steps are as follows: randomly divide the workpiece set {1, 2, 3, K, n} into two non-empty subsets and Copy Parent 1 contained in Artifacts in to Children 1, Parent 2 is contained in to Children 2, preserving their location; copy the artifacts contained in Parent 2 to Children 2 Artifacts in to Children l, Parent1 is contained in to Children 2, preserving their order.

[0073] A virtual unit space-time-personnel integrated scheduling system for shipbuilding includes: a processing workshop module, a worker fatigue and recovery module, a transportation module, an objective function module, and a solution module based on a hybrid algorithm of NSGA-II and the Grey Wolf Optimization Algorithm.

[0074] Beneficial effects: The integrated scheduling system of the present invention comprehensively considers factors such as the round-trip transportation equipment, the capacity of the workpiece temporary storage area, and the fatigue and recovery of workers, and studies the virtual unit integrated scheduling system; a hybrid algorithm based on NSGA-II and GWO is designed. The algorithm adopts a reverse learning strategy in the initialization stage to increase the quality of the initial population. At the same time, the combination of NSGA-II and GWO achieves a balance between local search and global search; in order to verify the effectiveness of the proposed algorithm, the proposed algorithm is compared with the NSGA-II algorithm and the GWO algorithm, which has been used more recently. It is found that the solution set obtained by the hybrid algorithm based on NSGA-II and GWO has better convergence and distribution, more uniform distribution of the solution set, and better optimization ability. Therefore, the algorithm of the present invention is more effective and robust in solving multi-objective optimization problems for shipbuilding. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 This is a flow chart of the space-time-personnel integrated scheduling method for virtual units for shipbuilding according to the present invention;

[0076] Figure 2 This is a schematic diagram of the four-layer chromosome encoding of the improved algorithm of the present invention;

[0077] Figure 3 This is a schematic diagram of the specific process of the improved IPOX crossover algorithm of the present invention;

[0078] Figure 4 This is a schematic diagram of the device layer crossover process of the improved algorithm of the present invention;

[0079] Figure 5Schematic diagram of two-point mutation for the processing equipment layer and the worker layer of the improved algorithm of the present invention. Detailed implementation manners

[0080] The present invention will be further described below with reference to the accompanying drawings.

[0081] As Figure 1 shown, the virtual unit space-time-human integrated scheduling method for shipbuilding of the present invention includes the following steps:

[0082] S1. Construct a processing workshop model: The processing workshop contains a total of K virtual units, n workpieces to be processed, M processing devices, and W workers. Each virtual unit contains multiple processing devices and undertakes the processing tasks of workpieces in a specific workpiece family. And the following assumptions are made:

[0083] (1) The workpieces in each workpiece family randomly enter the virtual unit manufacturing system;

[0084] (2) Each workpiece has the same priority;

[0085] (3) All the processing devices in the workshop are available at time 0;

[0086] (4) At the same time, each device can only process one workpiece;

[0087] (5) At the same time, each worker can only operate one device;

[0088] (6) After each process starts processing on the processing device, it cannot be interrupted;

[0089] (7) After each worker starts to execute the processing task on a processing device, it cannot be interrupted;

[0090] (8) The units to which the processing devices, workers, and workpieces belong are known;

[0091] (9) The processes of each workpiece have strict sequence constraints;

[0092] (10) The initial work efficiency of each worker is relatively stable;

[0093] (11) As time accumulates, the fatigue of the worker decreases exponentially;

[0094] (12) There is a linear relationship between the fatigue recovery of the worker and the work efficiency;

[0095] (13) The capacity of the semi-finished workpiece temporary storage area in front of each processing device is known;

[0096] (14) The setup time is included in the processing time;

[0097] (15) Equipment failures are ignored.

[0098] S2. Construct a worker fatigue and recovery model: To study the impact of fatigue and recovery on worker performance, a worker fatigue and recovery model is constructed. By using an fNIRS device and a movement stability tester to analyze and test workers, the work efficiency r' of worker w at the end of the f-th task is obtained fw , and the actual completion time P' of worker w in the f-th task fw :

[0099]

[0100] where λ w represents the fatigue parameter of worker w, q fw is the fatigue decline time, α fw is the work efficiency steady state time, P fw is the standard completion time of each task for worker w, r fw is the work efficiency of worker w at the start of the f-th task and it is assumed that the work efficiency r of the initial worker 1w = 1.

[0101] S3. Construct a transportation model: There are σ k transportation devices in each virtual unit. Besides completing the transportation tasks within the unit, the transportation devices in the virtual unit can also, as needed, complete the cross-unit transportation tasks of the workpieces within the unit. And the following assumptions are made:

[0102] (1) All transportation devices are available at time 0;

[0103] (2) Each transportation device has the same priority;

[0104] (3) Each transportation device can only transport one workpiece at the same time;

[0105] (4) If a transportation device is in the middle of a transportation operation, the transportation operation cannot be interrupted;

[0106] (5) After a transportation device in the virtual unit completes a cross-unit transportation, it immediately returns to the transportation device centralized parking area closer to the unit it belongs to, unless the transportation completion time of the current task is the same as the no-load start time of the next task of this transportation device;

[0107] (6) Only one transportation device can be parked in the transportation device parking area near the processing equipment each time;

[0108] (7) When the time from the completion of the current transportation task of a transportation device to the start time of the next scheduled transportation exceeds twice the time to return to the centralized parking area, the transportation device needs to return to the centralized parking area. Otherwise, it waits in the transportation device parking area near the current processing equipment;

[0109] (8) When the parking area for transportation equipment near the processing equipment is occupied, resulting in the inability of subsequent transportation equipment running to this processing equipment to park, the transportation equipment parked in this area needs to return to the centralized parking area;

[0110] (9) The distance from each unit to the nearest centralized parking area for transportation equipment is known;

[0111] (10) When the workpiece temporary storage area in the next working area of the workpiece to be transported is completely occupied, the transportation task cannot be executed.

[0112] S4. Construct the objective function: Considering the overall task completion time, transportation time, and worker load comprehensively, with the goal of minimizing the makespan, shortest total transportation distance, balanced worker workload, and minimum total worker load, construct the objective function.

[0113] Minimize the makespan: minf1 = maxC ij , where C ij is the processing completion time of O ij ; O ij is the i-th process of workpiece j;

[0114] Shortest total transportation distance:

[0115]

[0116] Among them, when h jk = 1, it means that workpiece j belongs to virtual unit k, otherwise it is 0; when g ijkt = 1, it means that O ij is transported by the transportation equipment t within the virtual unit, otherwise it is 0; ET ijkt represents the actual transportation end time when O ij is transported by the transportation equipment t within the virtual unit k to the next working place for processing; represents the no-load end time when the transportation of O ij is completed by the transportation equipment t within the unit and returns to the centralized parking area α of the equipment within the unit; represents the no-load start time when the transportation of O ij is completed by the transportation equipment t within the unit and returns to the centralized parking area α of the equipment within the unit; ST ijkt represents O ij is transported to the next working place for processing by the transportation equipment t within the virtual unit k, and the actual transportation start time; represents the no-load start time when the transportation equipment t within the virtual unit k is no-loaded to the transportation equipment parking area near the processing equipment where O (i-1)j is arranged, and is ready to complete the transportation of O ij ; Indicates transporting equipment t within virtual unit k, empty to O (i-1)j The transport equipment parking area near the arranged processing equipment is ready to complete O ij The empty end time of the transport.

[0117] Worker workload balancing:

[0118]

[0119] Among them, β ijmw =1 represents O ij The processing is completed by worker w on processing equipment m; otherwise 0;

[0120] Minimum total worker load:

[0121]

[0122] Constraints include:

[0123] Each process of each workpiece can only be completed on one processing equipment:

[0124]

[0125] Each process is assigned to a processing device that requires a worker to complete the processing:

[0126]

[0127] Each process requires a worker:

[0128]

[0129] Process O ij Actual completion time:

[0130]

[0131] The efficiency of worker w at the start of the fth task assigned to it:

[0132]

[0133] The work efficiency of worker w at the end of the fth task assigned to him is:

[0134]

[0135] Worker w completes the fth task O ij Fatigue reduction time:

[0136]

[0137] The rest time between the worker completing the f-1th task and the start of the fth task:

[0138] θ fw =h ijfw S ij -h i′j′(f-1)w C i′j′ f>1 (18)

[0139] Process O ij The relationship between the start and completion time:

[0140]

[0141] The relationship between processes:

[0142]

[0143] The completion time constraint of the workpiece:

[0144] C ij ≤d j (twenty one)

[0145] Process O ij Start shipping time and O (i-1)j The completion time constraint is:

[0146] ST ijkt ≥C (i-1)j When i=2,3,…i (j) (twenty two)

[0147] Process O ij The relationship between the start processing time and transportation time:

[0148] S ij ≥ET ijkt (twenty three)

[0149] The relationship between the end time of empty transport and the start time of actual transport:

[0150]

[0151] The relationship between the actual transportation start time and end time:

[0152] ET ijkt =ST ijkt +B ijm B (i-1)jm′ t mm′ (25)

[0153] Returns the relationship between the empty load start time and the actual transport end time:

[0154]

[0155] Each workpiece can only be transported by one transportation device:

[0156]

[0157] Return the relationship between the no-load start time and the end time:

[0158]

[0159] The relationship between the no-load start time and the end time when traveling to the workplace:

[0160]

[0161] S5. Design a hybrid algorithm based on NSGA-II and the Grey Wolf Optimization Algorithm, and solve the model: Due to the consideration of factors such as the real-time fatigue and recovery of workers and the capacity of the workpiece temporary storage area in the present invention, the model has more constraints and the iterative process is more complex. Therefore, aiming at the shortcomings of the NSGA-II algorithm, combined with the constructed model, and relying on the search ability of the Grey Wolf Optimization Algorithm, a hybrid algorithm based on NSGA-II and the Grey Wolf Optimization Algorithm is designed to solve the model. Specifically:

[0162] Adopt a four-layer coding method. The first layer of the chromosome is the process coding layer, which represents the processing process sequence of all workpieces to be processed in the workshop; the second layer of the chromosome is the processing equipment segment coding. Each value in the processing equipment coding layer chromosome represents the processing equipment selected for the corresponding process; the third layer of the chromosome is the unit coding layer to which the processing equipment belongs, which represents the unit where the processing equipment is located. Each value in the unit coding layer chromosome of the processing machine represents the unit number to which the equipment at the corresponding position belongs; the fourth layer of the chromosome is the coding layer to which the worker belongs, which represents the operator who operates the processing equipment for the processing process. Each value in the worker coding layer chromosome represents the worker arranged on the corresponding equipment.

[0163] As Figure 2 shown, based on the process coding layer, the first 1 represents O 11 , the second 1 represents O 12 , based on the processing equipment coding layer, the first 3 represents O 11 being processed on processing equipment M3, the first 4 represents O 12 being processed on processing equipment M4. Based on the unit coding layer to which the processing equipment belongs, the first 1 represents that processing equipment M3 belongs to unit 1, and 2 represents that processing equipment M4 belongs to the second unit. Based on the worker coding layer, the first 5 represents being processed by worker 5, and the second 4 represents O 32 being processed by worker 4.

[0164] The specific steps for solving the model include:

[0165] Step 1: Preset the number of iterations, crossover probability P c , mutation probability P m , population size N, coding method, decoding method, and fitness function; among them, the specific decoding method is:

[0166] (1) Starting from τ = 0, select the operation of the workpiece to be processed according to the chromosome coding. If the processing equipment and worker selected for this operation are occupied, suspend the processing task until the arranged processing equipment and worker are released. Calculate the completion time of the current operation according to formulas (14) and (19), and calculate the working efficiency of the worker when completing the current task according to formula (16). When all workpieces to be processed are suspended, the τ = 0 moment ends, and let τ = τ + 1.

[0167] (2) The first operation of each workpiece does not need to be transported, and the transportation time is 0. At each subsequent moment, traverse the operations of the workpieces to be processed in all workpiece families.

[0168] (3) At τ = 1, if the worker is arranged again, calculate the starting working efficiency of the worker's task according to formula (15).

[0169] (4) When at the τ moment, after the i-th operation of workpiece j is processed, if the (i + 1)-th operation of workpiece j is processed on the current processing equipment, the transportation time is 0;

[0170] (5) If the (i + 1)-th operation of this workpiece is processed on other equipment, judge whether the transportation equipment in this unit is available. If the transportation equipment is not available, suspend the transportation task until there is a transportation equipment that can execute this processing task.

[0171] (6) If the transportation equipment is available, judge whether there is space in the workpiece temporary storage area in front of the arranged processing equipment. That is

[0172] π mτ +Ω mτ <B m (30)

[0173] In the formula: π mτ represents the number of workpieces waiting to be processed in front of processing equipment m at the τ moment; Ω mτ represents the number of workpieces waiting to be transported in front of processing equipment m at the τ moment; B m represents the buffer capacity size in front of processing equipment m.

[0174] (7) If the formula (30) is satisfied, calculate the no-load time of the transportation equipment according to formulas (28) and (29), and insert it forward. As much as possible, ensure that after the i-th process of workpiece j is processed, the transportation equipment just arrives in front of the processing equipment of the i-th process of workpiece j, and calculate the actual transportation time of the current process according to formula (25). If not satisfied, suspend the transportation task.

[0175] (8) If multiple transportation equipment in the unit are available, randomly select one transportation equipment to complete the current transportation task. And so on until all processes of all workpieces are processed.

[0176] Step 2: Generate the initial population based on the reverse learning strategy

[0177] The quality of the initial population will directly affect the global search efficiency and solution quality of the proposed algorithm. Therefore, the reverse learning strategy is applied to the generation of the initial population to improve the optimization ability of the algorithm. This method first generates the reverse individuals according to each initial individual, and the specific expression is as follows:

[0178] R i =A i +B i -r i (31)

[0179] In the formula: A and B respectively represent the upper and lower boundaries of the value range of the individual vector elements; r is the initial individual; R is the reverse individual; i is the dimension of the individual vector.

[0180] Therefore, the specific method for generating the initial population based on the reverse learning strategy is as follows: generate a random initial population; generate the reverse population of the initial population according to formula (31); calculate the individual fitness values of the initial population and the reverse population; perform non-dominated sorting on the individuals in the randomly generated population and the reverse population, and arrange them in ascending order, and take the first N populations as the initial population.

[0181] Step 3: Randomly select a parent and cross and mutate with the global optimal individual to form a generation of offspring population.

[0182] Step 4: Iteration times +1.

[0183] Step 5: Perform the selection operation using the binary tournament algorithm to obtain the first-generation parents. Use the method based on non-dominated rank and crowding distance to obtain the decision-making layer individuals, that is, sort the individuals according to the non-dominated rank and crowding distance of the individuals in the population, and the first 3 individuals in the ranking have the opportunity to become the decision-making layer individuals, that is, α, β, γ of the grey wolf optimization algorithm. These 3 individuals are used to obtain the second-generation parents (prey) through formula (34).

[0184]

[0185]

[0186] In the formula: is the distance between the prey and the grey wolf; is the grey wolf position vector; is the prey position vector; and are coefficient vectors, r1 and r2 are random numbers within the range of [0, 1], The control parameter takes values within the range of [0, 2] and increases linearly with the increase of the algorithm iteration times.

[0187] Step Six: Cross and mutate the parent generation with the prey to obtain the offspring. Among them, the adaptive individual crossover and mutation probabilities are as follows:

[0188]

[0189] In the formula: P c : represents the crossover probability; P m represents the mutation probability; f max represents the maximum fitness value in the population; f avg represents the average fitness value in the offspring population; f′ represents the larger fitness value of the two individuals to be crossed; f represents the fitness value of the individual to be mutated.

[0190] The crossover method adopts IPOX crossover and crossover based on the device position. The IPOX operation is formed by improving on the basis of the POX operation. It only crosses the processing sequences of the parent chromosome processes, and at the same time retains the machines assigned to the processes in the workpiece to the offspring.

[0191] The specific operation steps of IPOX are as follows: Randomly divide the workpiece set {1, 2, 3, K, n} into two non-empty subsets and Copy the workpieces contained in Parent 1 in to Children l, and copy the workpieces contained in Parent 2 in to Children 2, and retain their positions; copy the workpieces contained in Parent 2 in to Children l, and copy the workpieces contained in Parent 1 in to Children 2, and retain their order. As Figure 3 shown is the specific crossover process of the two chromosomes.

[0192] The steps of the device-based crossover method are as follows: randomly select a group of positions; find the corresponding process numbers of Parent 1 and the corresponding positions of the processes in Parent 2; replace the entire encoding of the processes. The specific crossover process is as Figure 4 shown.

[0193] Two-point mutation based on the processing equipment layer and the worker layer is used to perform the mutation operation. The specific steps are as follows: randomly select two mutation positions, and respectively select the processing equipment and workers at the corresponding positions; randomly select a processing equipment and a worker from the alternative processing equipment and workers respectively; replace the selected processing equipment and workers on the chromosome, keep the order of the processing processes unchanged, and change the unit number to which the processing equipment belongs together with the processing equipment. The specific mutation process is as Figure 5 shown.

[0194] Step 7: Combine the parent generation and the offspring generation, and perform non-dominated sorting and crowding degree calculation.

[0195] Step 8: Adopt the elitist retention strategy to obtain a new population and update the global optimal individual.

[0196] Step 9: Check whether the maximum number of iterations is reached. If so, output the result; otherwise, return to Step 4.

[0197] Embodiment

[0198] This embodiment is adapted based on the Gong et al. example, and 13 benchmark instances are constructed. The method for generating the distance between devices adopts the moving distance generation method, and the transportation distance belongs to [1-1]. λ w = a random number between 1 / 280 - 1 / 400, 1 / 400 - 1 / 270, 1 / 10 - 1 / 130, a w = 0.005, 0.01, 0, α = a random number between 2 - 4. The capacity of the workpiece temporary storage area is a random number between [3-6]. Programming is carried out using MATLAB R2017a software, and the operating environment memory is 16G.

[0199] Taguchi experiments are used to test the parameter settings hou1, and the obtained parameter combination is: the population size is set to 100, the crossover probability is selected as 0.8, the mutation probability is selected as 0.15, and the number of iterations is selected as 150.

[0200] To verify the effectiveness of the proposed algorithm, the NSGA-II-GWO algorithm proposed in the present invention is compared with the NSGA-II and GWO algorithms in terms of performance. The parameter settings of these two algorithms are the same as those of the proposed algorithm. The population size of the GWO algorithm is 100, and the maximum number of iterations is 150. The workpiece arrival rate follows a U[0,10] distribution, and the IPOX crossover and the crossover based on processing equipment each account for 50%. These three algorithms are each run 30 times, and branch-and-bound sorting is performed. The obtained solution sets are used as the Pareto solution set.

[0201] The IGD, GD, and distribution metrics are used to analyze the algorithm performance.

[0202]

[0203] Among them, P is the solution set of the algorithm, P * is the reference set, and dis(x,y) represents the Euclidean distance between the solution set P and the reference set P * .

[0204]

[0205] In the formula: d f and d l are the Euclidean distances between the extreme solutions and the boundary solutions of the obtained non-dominated set; d i refers to the Euclidean distance between the consecutive solutions in the obtained non-dominated solution set; is the average value of d i . N represents the number of solutions, N = 1, 2, K, N. Δ represents the extent of the solution set.

[0206] After each algorithm is independently run 30 times, the Wilcoxon signed-rank test is used to compare whether there are significant differences between pairwise algorithms. The specific results are shown in Table 1.

[0207] Table 1 Results of Wilcoxon signed-rank test

[0208]

[0209] It can be seen from the table that the inverse generational distance index of the proposed algorithm has significant differences compared with the other two algorithms. The three evaluation indexes of the proposed algorithm are all better than NSGA-II. There is a weak correlation between its generational distance index and GWO, and the difference in its distribution index is not obvious.

[0210] The virtual unit space-time-human integrated scheduling system for shipbuilding of the present invention includes:

[0211] Workshop Module: The workshop consists of K virtual cells, n workpieces to be processed, M processing equipment, and W workers. Each virtual cell contains multiple processing equipment and is responsible for processing workpieces of a specific workpiece family.

[0212] Worker Fatigue and Recovery Module: To study the impact of fatigue and recovery on worker performance, a worker fatigue and recovery model is constructed. By using fNIRS equipment and a motion stability tester to analyze and test workers, the work efficiency r′ of worker w at the end of the fth task is obtained. fw , and the actual completion time P′ of worker w in task f fw .

[0213] Transport module: Each virtual unit has σ k In addition to completing the transportation tasks within the unit, the transportation equipment within the virtual unit can also complete the cross-unit transportation tasks of the workpieces within the unit as needed.

[0214] Objective function module: Taking into account the overall task completion time, transportation time and worker load, the objective function is constructed with minimizing the maximum completion time, shortest total transportation distance, balanced worker workload and minimum total worker load as the optimization goals.

[0215] Solving module based on the hybrid algorithm of NSGA-II and Gray Wolf Optimization Algorithm: Aiming at the shortcomings of the NSGA-II algorithm, combined with the constructed model, and with the help of the search capability of the Gray Wolf Optimization Algorithm, a hybrid algorithm based on NSGA-II and Gray Wolf Optimization Algorithm was designed to solve the model.

Claims

1. A virtual unit space-time-human integrated scheduling method for shipbuilding, characterized in that The steps include: Construct a processing workshop model, specifically: the processing workshop contains K virtual units, n workpieces to be processed, M processing equipments and W workers; each virtual unit contains multiple processing equipments and undertakes the processing tasks of workpieces in a specific workpiece family; Construct a worker fatigue and recovery model, specifically: Analyze and test workers to obtain the work efficiency r' of worker w at the end of the f-th task fw , and the actual completion time P' of worker w in the f-th task fw : where λ w represents the fatigue parameter of worker w, q fw is the fatigue decline time, α fw is the steady-state time of work efficiency, P fw is the standard completion time for each task of worker w, r fw is the work efficiency of worker w at the start of the f-th task, 0 < r fw ≤ 1, and it is assumed that the work efficiency r of the initial worker 1w = 1; Construct a transportation model: There are σ k transportation devices in each virtual unit, and the transportation devices in the virtual unit complete the transportation tasks within the unit and the cross-unit transportation tasks of the workpieces within the unit; Construct an objective function: comprehensively considering the overall task completion time, transportation time and worker load, and taking minimizing the makespan, the shortest total transportation distance, the balanced worker workload and the minimum total worker load as the optimization objectives to construct the objective function; The constraints for constructing the objective function include: The work efficiency of worker w at the start of the fth task assigned; where r' (f-1)w is the work efficiency of worker w at the end of the (f - 1)-th task; θ fw is the rest time of the worker from the end of the (f - 1)-th task to the start of the f-th task; Worker w completes the f-th task O ij Fatigue decline time when: Among them, P ijwm is the standard processing time for process O ij completed by worker w on equipment m; Design a hybrid algorithm based on NSGA-II and Grey Wolf Optimization Algorithm and solve the model. Among them, the hybrid algorithm based on NSGA-II and Grey Wolf Optimization Algorithm is specifically: adopt a four-layer coding method. The first layer of the chromosome is the operation coding layer, which represents the processing operation sequence of all workpieces to be processed in the workshop; the second layer of the chromosome is the processing equipment segment coding. Each value in the processing equipment coding layer chromosome represents the processing equipment selected for the corresponding operation; the third layer of the chromosome is the unit coding layer to which the processing equipment belongs, which represents the unit where the processing equipment is located. Each value in the unit coding layer chromosome of the processing machine represents the unit number to which the equipment at the corresponding position belongs; the fourth layer of the chromosome is the coding layer to which the worker belongs, which represents the operator who operates the processing equipment for the processing operation. Each value in the worker belonging coding layer chromosome represents the worker arranged on the corresponding equipment.

2. The virtual unit air-time-person integrated scheduling method for shipbuilding according to claim 1, characterized in that The specific steps for solving the model include: Set the iteration number, crossover probability P c , mutation probability P m , population size N, encoding method, decoding method, and fitness function in advance; Generate an initial population based on the opposition-based learning strategy; Randomly select a parent and cross and mutate it with the global optimal individual to form a generation of offspring; Iteration number +1; Perform a selection operation using the binary tournament algorithm to obtain the first generation of parents; obtain decision-making layer individuals using the method based on non-dominated rank and crowding distance; Cross and mutate the parent and the prey to obtain offspring; Merge the parent and the offspring, and perform non-dominated sorting and crowding degree calculation; Adopt the elitist retention strategy to obtain a new population and update the global optimal individual; Check whether the maximum number of iterations is reached. If yes, output the result; otherwise, return iteration number +1.

3. The virtual unit air-time-person integrated scheduling method for shipbuilding according to claim 2, wherein The generation of the initial population based on the reverse learning strategy is specifically as follows: Generate a random initial population; According to the following formula: R i = A i + B i - r i , generate the reverse population of the initial population; In the formula: A and B respectively represent the upper and lower boundaries of the value range of the individual vector elements; r is the initial individual; R is the reverse individual; i is the dimension of the individual vector; Calculate the individual fitness values of the initial population and the reverse population; Perform non-dominated sorting on the individuals in the randomly generated population and the reverse population, and arrange them in ascending order, and take the first N populations as the initial population.

4. A virtual unit air-time-person integrated scheduling method for shipbuilding according to claim 2, characterized in that The crossover adopts IPOX crossover, and the specific operation steps are as follows: randomly divide the workpiece set {1,2,3,...,n} into two non-empty subsets and Copy Parent 1 contained in Artifacts in to Children 1, Parent 2 is contained in to Children 2, preserving their location; copy the artifacts contained in Parent 2 to Children 2 Artifacts in to Children 1, Parent 1 is contained in to Children 2, preserving their order.

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