Multi-target scheduling method for ship plate processing workshop

Abstract

The invention discloses a multi-target scheduling method for a ship plate processing workshop, which comprises the following steps of: establishing a brand-new ship plate processing workshop scheduling model on the basis of processing cost and machine load on the basis of a traditional optimization target; secondly, for the problem that a traditional NSGA-II algorithm is prone to falling into a local optimal solution in the later period, self-adaptive crossover and mutation probability are introduced, and meanwhile a dynamic decline operator selection method fusing simulated annealing cooling thinking is put forward, so that population diversity is increased, and falling into local optimum is prevented; secondly, combining with an improved NSGA-II algorithm to design a dynamic scheduling optimization method considering two disturbance events of machine fault and emergency order insertion; and finally, verifying the effectiveness of the algorithm through a public example, and applying the optimization method to an engineering example. The method is helpful for improving the capability of coping with random disturbance in the ship plate processing process, and has important practical significance.

Description

Technical Field

[0001] The invention relates to the technical field of ship plate processing, and in particular to a multi-objective scheduling method for a ship plate processing workshop. Background Art

[0002] At present, plate processing is the first step in the construction of ship sections, but the processing efficiency of most plate processing workshops is low. The main reasons are that there are many types of products involved in plate cutting, complex processing contours, and process constraints and parallel processing operations. As a result, the information flow in the plate workshop construction process is not timely, and the coupling of construction resources and production processes is difficult. In addition, when disturbances occur, production scheduling adopts the original on-site scheduling method, and most production scheduling plans use manual scheduling, which easily leads to resource waste and untimely updates of scheduling plans. Therefore, an efficient method is needed to schedule ship plate processing.

[0003] The problem of scheduling the segmented processing of ship plate can be understood as a Flexible Job Shop Scheduling Problem (FJSP). FJSP is the most common production scheduling problem in the manufacturing industry. The basic idea is how to minimize the objective function when multiple machines process multiple workpieces. At present, most FJSP solutions are applied in ship plate processing workshops to ensure that the scheduling plan achieves the best effect, but a single goal is difficult to meet the actual production needs. A lot of manpower and computing power will be wasted in the process of multi-objective optimization. In addition, various disturbance events will be encountered in the actual production process of the plate, resulting in the failure of the existing scheduling plan and causing serious losses to the shipbuilding companies. The single-objective static scheduling plan is difficult to meet the actual production scheduling, so a more flexible dynamic scheduling method is needed to deal with disturbance events. Summary of the invention

[0004] Purpose of the invention: In view of the above problems, the purpose of the present invention is to provide a multi-objective scheduling method for a ship plate processing workshop, which can improve the scheduling efficiency and accuracy of ship plates.

[0005] Technical solution: A multi-objective scheduling method for a ship plate processing workshop includes the following steps:

[0006] Step 1: Define the ship plate processing workshop scheduling problem to be solved;

[0007] Step 2: Construct the objective function in the mathematical model of ship plate processing, which includes minimizing the completion time, minimizing the processing cost, and minimizing the machine load;

[0008] Step 3: Define the constraints in the mathematical model of the ship plate processing workshop, including process sequence constraints, machine selection constraints, and delivery time constraints;

[0009] Step 4: Use the improved NSGA-Ⅱ algorithm to solve the optimal scheduling plan for ship plate processing;

[0010] Step 5: Determine whether a disturbance event occurs. If so, return to step 4 and regenerate the scheduling plan; if not, continue production according to the current scheduling plan.

[0011] Furthermore, in step 1, the ship plate processing workshop scheduling problem refers to assuming that the ship plate to be processed process Z ij Assigned to processing machine M k , waiting for processing step Z ij In processing machine M k The processing sequence is followed, and the processing step Z ij In different processing machines M k With different processing times, all processing procedures of all plates are assigned to processing machines for marking, cutting and lifting, where i = 1, 2, 3, ..., n; j = 1, 2, 3, ..., m; k = 1, 2, 3, ..., s.

[0012] Furthermore, in step 2, the objective function for minimizing completion time is:

[0013]

[0014] in, Indicates the maximum completion time of ship plate processing;

[0015] The objective function of minimizing processing cost is:

[0016]

[0017] Among them, the first item is the energy consumption of the machine in operation, and the second item is the energy consumption of the machine in standby mode. ijke It is represented by the energy consumption generated by the j-th process of plate i on machine k. represents the energy consumption of machine k during standby;

[0018] The objective function for minimizing machine load is:

[0019]

[0020] in, It represents the end processing time of the jth process of plate i; It indicates the start time of the jth process of plate i; It represents the standby time of machine k during the production process.

[0021] Furthermore, in step 3, the machine selection constraints include:

[0022]

[0023] Indicates that the same process of the same plate can only be processed by one machine at the same time, where X ijk is a binary variable. If the jth process of plate i is assigned to machine k for processing, then X ijk =1, otherwise X ijk =0;

[0024]

[0025] It means that each machine can start processing at time 0;

[0026]

[0027] It means that the same machine can only process one plate at a time;

[0028] Process sequence constraints include:

[0029]

[0030] It means that the next process can be processed only after the previous process is completed. is a binary variable. When the jth process of sheet i is processed at station k before the j+1th process, otherwise

[0031]

[0032] It means that the next plate can be processed only after the previous plate is processed. represents the start processing time of the j-1th process of plate i; represents the start processing time of the jth process of plate i-1;

[0033] The delivery time constraints are:

[0034]

[0035] This means that the order processing time must not exceed the specified delivery time.

[0036] Furthermore, in step 4, the establishment of the improved NSGA-Ⅱ algorithm includes the following steps:

[0037] S1: Read the production information of the ship plate processing workshop, including processing tasks, machine information, and perform MSOS encoding, and initialize the algorithm parameters;

[0038] S2: Generate the first generation population by random initialization according to the production information read;

[0039] S3: Perform fast non-dominated sorting on the initial population and calculate the crowding degree of each individual;

[0040] S4: Generate a new offspring population through adaptive crossover and mutation operations, and merge the parent and offspring populations;

[0041] S5: Perform fast non-dominated sorting on the merged population and calculate the individual crowding degree;

[0042] S6: Individual selection is performed through a dynamic decreasing elite operator selection method to generate a new parent population;

[0043] S7: Determine whether the maximum number of iterations has been reached. If so, output the result. If not, return to S3 and loop again until the maximum number of iterations has been reached and the result is output.

[0044] Optimally, in step S1, the algorithm parameters are initialized, the algorithm population size and the number of iterations are set to 100 times, and the processing task information is input;

[0045] The MSOS coding adopts MS coding for machine chromosome and OS coding for process chromosome. Each integer of the machine coding represents the machine number selected for the current process. The first integer of the process coding represents the plate number, and the second integer represents the process number.

[0046] In the best case, in step S3, the generated initial population is subjected to fast non-dominated sorting, that is, the initial population is sorted by dominance level to realize individual stratification, all individuals in the Pareto front are taken out as the first non-dominated layer, and the taken out individuals are removed from the population, and all individuals in the newly generated Pareto front are taken out as the second non-dominated layer, and the operation is repeated until individuals that meet the quantity requirement are selected;

[0047] Crowding P a for:

[0048]

[0049] In the formula, r is the number of objective functions, f n (i+1), f n (i-1) is the Pareto frontier point at both ends of the objective function n, are the two extreme values ​​of the nth objective function.

[0050] Preferably, in step S4, the adaptive crossover and mutation operation uses POX crossover in the process stage, including the following steps:

[0051] S41: Randomly select two parent individuals and initialize two empty child individuals;

[0052] S42: When performing crossover, the first child retains the set position of P1 in the first parent, and the other positions of the first child are determined by P2 in the second parent;

[0053] S43: swap the positions of parent generation 1 and parent generation 2, and repeat steps S41 and S42 to generate child generation 2;

[0054] The machine code uses uniform crossover, which includes the following steps:

[0055] S401: Select two parent individuals and initialize two empty child individuals;

[0056] S402: Generate a binary chromosome with the same length as the parent individual, which can be represented as w1, w2, ..., w s ;

[0057] S403: According to w i = 1, the offspring 1 inherits the gene i from the parent 2, and the remaining positions are inherited by the gene w from the parent 1. i =0 to generate offspring 1; repeat this operation, and i = 1, the offspring 2 inherits the i gene from the parent 1, and the remaining positions are inherited by the w gene from the parent 2. i = The gene at 0 is supplemented to generate offspring 2;

[0058] Adaptive crossover rate P b and adaptive mutation rate P c They are:

[0059]

[0060] Among them, the crossover probability is [0.9, 1], the mutation probability is [0.01, 0.1], and N max and N avg Respectively represent the maximum and average fitness values ​​in the population, It represents the maximum fitness value of the parent population selected in the crossover operation, and Nc represents the fitness value of the current mutant individual;

[0061] The mutated crossover population after one iteration is merged with the parent population to obtain a combined population that is twice the size of the initial population.

[0062] Preferably, in step S6, the dynamic decreasing elite operator selection method comprises the following steps:

[0063] S61: Keep the population with low non-dominated level and select the number of individuals in the Pareto frontier according to the temperature coefficient;

[0064] S62: Add a hierarchical cooling strategy based on the temperature coefficient, and use it as a selection criterion to allocate to the remaining non-dominated layers. If the number of selected individuals after one calculation does not meet the standard, the unselected individuals will be re-sorted by fast non-dominated sorting, and individuals with lower non-dominated levels will be selected to join the solution set until the population number requirement is met;

[0065] S63: Add a cooling coefficient based on the temperature coefficient to reduce the number of individuals selected in each generation of Pareto frontier and ensure the diversity of the later population:

[0066]

[0067] Among them, α ij It is expressed as the number of individuals selected in the jth layer of the i-th iteration; n ij It is represented by the total number of individuals in the jth layer of the i-th iteration; β is the temperature coefficient; g i is the cooling coefficient of the algorithm iteration i; b j is the temperature reduction coefficient when the algorithm iterates to the jth layer.

[0068] Furthermore, in step 5, it is determined whether a disturbance event occurs in the current production, including machine failure and emergency insertion. When a machine failure occurs, the machine shall not process any process until the machine recovers its working capacity; when an emergency insertion occurs, the rework process shall be arranged immediately.

[0069] Beneficial effects: Compared with the prior art, the advantages of the present invention are: adding a processing cost function on the basis of the traditional scheduling objective, and proposing an improved NSGA-Ⅱ algorithm to address the problem that the traditional NSGA-Ⅱ algorithm is prone to premature convergence and falling into a local optimal solution. The algorithm introduces an elite operator selection method with adaptive crossover, mutation probability and dynamic decrease, that is, the algorithm converges prematurely and can also avoid the algorithm from falling into a local optimal solution; finally, a dynamic scheduling event considering machine failure and emergency insertion is designed based on the improved NSGA-Ⅱ algorithm to verify the effectiveness of this scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 is a flow chart of the present invention;

[0071] Figure 2 This is a schematic diagram of the MSOS encoding method;

[0072] Figure 3 This is a schematic diagram of POX crossover;

[0073] Figure 4 It is a schematic diagram of uniform crossover;

[0074] Figure 5 Graph of the method for selecting a dynamic decreasing elitist operator;

[0075] Figure 6 This is a box plot of the running results;

[0076] Figure 7 Gantt chart for initial scheduling;

[0077] Figure 8 Re-schedule the Gantt chart for the insertion order;

[0078] Fig. 9 Rescheduling Gantt chart for machine failure. DETAILED DESCRIPTION

[0079] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0080] A multi-objective scheduling method for ship plate processing workshop, such as Figures 1 to 9 As shown, the following steps are included:

[0081] Step 1: Define the ship plate processing workshop scheduling problem to be solved; ship plate processing process Z ij (i=1,2,3,……,n;j=1,2,3,……,m) are assigned to processing machine M k (k=1,2,3,……,s), waiting for processing step Z ij In processing machine M k The processing sequence must be followed and the processing step Z ij In different processing machines M k There are different processing times.

[0082] In step 1, the ship plate processing workshop scheduling model is conditionally assumed:

[0083] (1) Each plate must be processed according to a certain process production route, and there are process sequence constraints.

[0084] (2) All machines can start processing at time zero, and no complete process is allowed to be interrupted during the processing unless the processing equipment fails.

[0085] (3) Each machine can only process one process at a time.

[0086] (4) The same process of the same plate can only be processed by one machine at the same time.

[0087] (5) The flow time of the sheet between machines is not taken into account.

[0088] (6) The plate processing cycle cannot exceed the specified delivery time.

[0089] In step 1, the parameters of the ship plate processing workshop scheduling model are defined:

[0090] i is the plate number index; I is the plate set {1, 2, ..., n}; j is the processing step index; J is the processing step set {1, 2, ..., m}; k is the machine index; K is the machine set {1, 2, ..., s}; t is the time coefficient; e is the energy consumption coefficient; D is the delivery time of the plate processing task; is the maximum completion time of the plate production task; Z ij is the j-th process of plate i; M ijk The machine for the jth process of plate i is k; is the starting processing time of the jth process of plate i; is the end processing time of the jth process of plate i; is the standby time of machine k during the production process; P ijke is the energy consumption generated by the j-th process of plate i on machine k; is the energy consumption of machine k during standby; X ijk is a binary variable. If the jth process of plate i is assigned to machine k for processing, then X ijk =1, otherwise X ijk =0; is a binary variable. When the jth process of sheet i is processed at station k before the j+1th process, otherwise

[0091] Step 2: Define the objective function for the ship plate processing workshop:

[0092] (1) Minimize completion time

[0093]

[0094] (2) Minimize processing costs

[0095]

[0096] (3) Minimize machine load

[0097]

[0098] Step 3: Define the process sequence constraints, machine selection constraints, and delivery time constraints for the ship plate processing workshop:

[0099]

[0100] Formula (3-4) indicates that the same process of the same plate can only be processed by one machine at the same time;

[0101] Formula (3-5) indicates that each machine can start processing at time 0;

[0102] Formula (3-6) indicates that the same machine can only process one plate at a time;

[0103] Formula (3-7) indicates that there is a process sequence constraint in sheet metal processing, and the next process can only be processed after the previous process is completed;

[0104] Formula (3-8) indicates that there is a processing order constraint in plate processing, and the next plate can only be processed after the previous plate is processed;

[0105] Formula (3-9) indicates that there is a delivery time constraint for ship plate processing, that is, the order processing time must not exceed the delivery time limit;

[0106] Step 4: After the scheduling model for the ship plate processing workshop is built, the improved NSGA-Ⅱ algorithm is used for dynamic scheduling optimization. The improved algorithm flow is as follows: Figure 1 As shown, the specific steps are as follows:

[0107] S1: Read the processing tasks and machine information of the ship plate processing workshop and initialize the algorithm parameters;

[0108] S2: Generate the first generation population by random initialization according to the production information read;

[0109] S3: Perform fast non-dominated sorting on the initial population and calculate the crowding degree of each individual;

[0110] S4: Generate a new offspring population through adaptive crossover and mutation operations, and merge the parent and offspring populations;

[0111] S5: Perform fast non-dominated sorting on the merged population and calculate the individual crowding degree;

[0112] S6: Individual selection is performed through the proposed dynamic decreasing elite operator selection method to generate a new parent population;

[0113] S7: Determine whether the maximum number of iterations has been reached, and if so, output the result; if not, return to S3.

[0114] In S1, the algorithm parameters are initialized, the algorithm population size and the number of iterations are set to 100, and the processing task information is input.

[0115] In S1, Figure 2As shown, chromosomes use MSOS encoding, machine chromosomes use MS encoding, and process chromosomes use OS encoding. Each integer in the machine code represents the machine number selected for the current process, the first integer in the process code represents the plate number, and the second integer represents the process number. The initial population is generated by random initialization.

[0116] In S3, the generated initial population is quickly non-dominated sorted, that is, the initial population is sorted by dominance level to achieve individual stratification, all individuals in the Pareto front are taken out as the first non-dominated layer, and the taken out individuals are removed from the population, and all individuals in the newly generated Pareto front are taken out as the second non-dominated layer, and the operation is repeated until individuals that meet the quantity requirements are selected;

[0117] In S3, the original NSGA uses an artificially set shared radius function, and the subsequent NSGA-Ⅱ proposed crowding calculation to ensure the diversity of the population. The crowding degree Pa refers to the density of distribution points around a certain individual in the feasible solution space, which provides a calculation standard for the selection of individuals at the same non-dominated level. In order to meet the requirements of population diversity, the individual selection range needs to be as radiated as possible. Therefore, the greater the crowding degree, the greater the individual genetic probability. The specific calculation formula is shown in (3-10):

[0118]

[0119] Where: r is the number of objective functions, f n (i+1), f n (i-1) is the Pareto frontier point at both ends of the objective function n, The two extreme values ​​of the nth objective function.

[0120] In S4, since the initialization uses MSOS coding, POX crossover is used in the process stage, as shown in the following example: Figure 3 As shown. First, two parent individuals are randomly selected and two empty offspring individuals are initialized; then, when crossover is performed, offspring 1 retains the set position of P1 in parent 1, and the other positions of offspring 1 are determined by P2 in parent 2; finally, parent 1 and parent 2 are swapped, and the above operation is repeated to generate offspring 2.

[0121] In S4, the machine code uses uniform crossover, as shown in the following example: Figure 4As shown. First, two parent individuals are selected and two empty offspring individuals are initialized; then, a binary chromosome (w1, w2, ..., ws) of the same length as the parent individuals is generated; finally, according to the position where wi=1 is located, offspring 1 inherits the i gene of parent 2, and the remaining positions are supplemented by the gene at wi=0 in parent 1, generating offspring 1; repeat this operation, from the position where wi=1 is located, offspring 2 inherits the i gene of parent 1, and the remaining positions are supplemented by the gene at wi=0 in parent 2, generating offspring 2.

[0122] In S4, since the algorithm has low population diversity in the initial stage, a larger mutation and crossover probability should be set in the initial stage. As the iteration process proceeds, the high-quality population tends to be stable. At this time, a smaller crossover and mutation probability should be set. Therefore, the present invention introduces an adaptive crossover and mutation probability method here to cope with the crossover and mutation requirements at different stages. The specific adaptive crossover rate P b and adaptive mutation rate P c , as shown in formula (3-11) and (3-12):

[0123]

[0124] Among them, the crossover probability is [0.9, 1], the mutation probability is [0.01, 0.1], and N max and N avg Respectively represent the maximum and average fitness values ​​in the population, It represents the maximum fitness value of the parent population selected in the crossover operation, and Nc represents the fitness value of the current mutant individual.

[0125] In S4, the mutated crossover population after one iteration is merged with the parent population to obtain a combined population twice the size of the initial population.

[0126] In S5, the combined population is subjected to fast non-dominated sorting and crowding calculation, and individuals are selected in combination with their non-dominated levels and crowding until the selected individuals meet the quantity requirement.

[0127] In S6, the dynamic decreasing elite operator selection method is as follows: first, in the initial stage, the population with a low non-dominated level should be retained, and the number of individuals in the Pareto frontier is selected according to the temperature coefficient; then, a hierarchical cooling strategy is added on the basis of the temperature coefficient, and this is used as a selection criterion and allocated to the remaining non-dominated layers. If the number of selected populations after one calculation does not meet the standard, the unselected individuals will be re-sorted by fast non-dominated sorting, and individuals with lower non-dominated levels will be selected to join the solution set until the population number requirement is met; as the population iteratively evolves, the algorithm is prone to fall into a local optimum, so a cooling coefficient is added on the basis of the temperature coefficient to reduce the number of individuals selected in the Pareto frontier of each generation to ensure the diversity of the later population.

[0128]

[0129] Among them, α ij It is expressed as the number of individuals selected in the jth layer of the i-th iteration; n ij It is represented by the total number of individuals in the jth layer of the i-th iteration; β is the temperature coefficient; g i is the cooling coefficient of the algorithm iteration i; b j is the temperature reduction coefficient when the algorithm iterates to the jth layer.

[0130] In S7, it is determined whether the maximum number of iterations has been reached. If so, the result is output; if not, the process returns to S3.

[0131] Step 5, determining whether a disturbance event occurs in the current production. The present invention takes into consideration two disturbance events: machine failure and emergency insertion. When a machine failure occurs, the machine shall not process any process until the machine recovers its working capacity. When an emergency insertion occurs, the rework process shall be arranged immediately.

[0132] In order to evaluate the performance of the proposed improved NSGA-Ⅱ algorithm, the present invention uses public examples MK01 and MK02 for simulation verification. The evaluation indicators are HV and IGD. The larger the HV value, the better the distribution of the solution set in the target space. The smaller the IGD value, the better the convergence of the algorithm. The algorithms before and after the improvement are run independently 10 times for comparison. The test results are shown in Table 1.

[0133] Table 1 Experimental comparison between MK01 and MK02

[0134]

[0135] In Table 1, the HV and IGD values ​​are taken from the average of 10 running results (retain three decimal places), and the HV average and IGD average are also better than the original algorithm, indicating that the introduction of adaptive crossover and mutation probability and improved elite retention strategy on the basis of the original algorithm can increase the diversity of the algorithm and improve the convergence, proving that the improvement proposed in the present invention has certain practical value. The box plot is drawn with 10 running data, as shown in the following figure. Figure 6 shown.

[0136] The disturbance event problem is studied by taking the plate processing workshop of a shipbuilding company in Yangzhou as an example. Table 2 is the construction list of a batch of orders. The delivery time constraint is 180 minutes. It contains 16 processing tasks and 48 processes in total, of which 1#-4# are scribing and cutting machines, and 5#-7# are cranes. The specific processing information is shown in Table 2.

[0137] Table 2 Processing information of a batch of plates

[0138]

[0139] Initial scheduling: The squares represent the processing tasks and processing process numbers (e.g. 1-1 represents the first process of processing task No. 1). The calculation results are as follows: Figure 7 As shown, the delivery time constraint is met.

[0140] Emergency order insertion: After 7-1 is processed, 13-2 and 13-3 in the historical order need to be urgently inserted. The calculation results are as follows Figure 8 As shown, the delivery time constraint is met.

[0141] Machine failure: Machine 2# fails at 0 minutes, and maintenance lasts until 50 minutes to restore production capacity. The scheduling results are calculated as follows: Fig. 9 As shown, the delivery time constraint is met.

[0142] The present invention is a multi-objective scheduling method for a ship plate processing workshop based on an improved NSGA-Ⅱ algorithm, which has the following advantages: a processing cost function is added on the basis of the traditional scheduling objective, and an improved NSGA-Ⅱ algorithm is proposed to address the problem that the traditional NSGA-Ⅱ algorithm is prone to premature convergence and falling into a local optimal solution. The algorithm introduces an elite operator selection method of adaptive crossover, mutation probability and dynamic decrease, that is, the algorithm converges prematurely and can also avoid the algorithm from falling into a local optimal solution; finally, the effectiveness of the proposed method is verified by a public example, and a dynamic scheduling event considering machine failure and emergency insertion is designed based on the improved NSGA-Ⅱ algorithm, which proves the guiding role of the present invention in actual production.

Claims

1. A multi-objective scheduling method for a ship plate processing workshop, characterized in that The following steps are involved: Step 1: Define the ship plate processing workshop scheduling problem to be solved; Step 2: Construct the objective function in the mathematical model of ship plate processing, which includes minimizing the completion time, minimizing the processing cost, and minimizing the machine load; Step 3: Define the constraints in the mathematical model of the ship plate processing workshop, including process sequence constraints, machine selection constraints, and delivery time constraints; Step 4: Use the improved NSGA-Ⅱ algorithm to solve the optimal scheduling plan for ship plate processing; Step 5: Determine whether a disturbance event occurs. If so, return to step 4 and regenerate the scheduling plan; if not, continue production according to the current scheduling plan.

2. A multi-objective scheduling method for a ship plate processing workshop according to claim 1, characterized in that: In step 1, the ship plate processing workshop scheduling problem refers to assuming that the ship plate processing process Z ij Assigned to processing machine M k , waiting for processing step Z ij In processing machine M k The processing sequence is followed, and the processing step Z ij In different processing machines M k With different processing times, all processing procedures of all plates are assigned to processing machines for marking, cutting and lifting, where i = 1, 2, 3, ..., n; j = 1, 2, 3, ..., m; k = 1, 2, 3, ..., s.

3. A multi-objective scheduling method for a ship plate processing workshop according to claim 1, characterized in that: In step 2, the objective function for minimizing completion time is: in, Indicates the maximum completion time of ship plate processing; The objective function of minimizing processing cost is: Among them, the first item is the energy consumption of the machine in operation, and the second item is the energy consumption of the machine in standby mode. ijke It is represented by the energy consumption generated by the j-th process of plate i on machine k. represents the energy consumption of machine k during standby; The objective function for minimizing machine load is: in, It represents the end processing time of the jth process of plate i; It indicates the start time of the jth process of plate i; It represents the standby time of machine k during the production process.

4. A multi-objective scheduling method for a ship plate processing workshop according to claim 1, characterized in that: In step 3, the machine selection constraints include: Indicates that the same process of the same plate can only be processed by one machine at the same time, where X ijk is a binary variable. If the jth process of plate i is assigned to machine k for processing, then X ijk =1, otherwise X ijk =0; It means that each machine can start processing at time 0; It means that the same machine can only process one plate at a time; Process sequence constraints include: It means that the next process can be processed only after the previous process is completed. is a binary variable. When the jth process of sheet i is processed at station k before the j+1th process, otherwise It means that the next plate can be processed only after the previous plate is processed. represents the start processing time of the j-1th process of plate i; represents the start processing time of the jth process of plate i-1; The delivery time constraints are: This means that the order processing time must not exceed the specified delivery time.

5. The multi-objective scheduling method for a ship plate processing workshop according to claim 1 is characterized in that: In step 4, the establishment of the improved NSGA-Ⅱ algorithm includes the following steps: S1: Read the production information of the ship plate processing workshop, including processing tasks, machine information, and perform MSOS encoding, and initialize the algorithm parameters; S2: Generate the first generation population by random initialization according to the production information read; S3: Perform fast non-dominated sorting on the initial population and calculate the crowding degree of each individual; S4: Generate a new offspring population through adaptive crossover and mutation operations, and merge the parent and offspring populations; S5: Perform fast non-dominated sorting on the merged population and calculate the individual crowding degree; S6: Individual selection is performed through a dynamic decreasing elite operator selection method to generate a new parent population; S7: Determine whether the maximum number of iterations has been reached. If so, output the result. If not, return to S3 and loop again until the maximum number of iterations has been reached and the result is output.

6. A multi-objective scheduling method for a ship plate processing workshop according to claim 5, characterized in that: In step S1, the algorithm parameters are initialized, the algorithm population size and the number of iterations are set to 100 times, and the processing task information is input; In the MSOS coding, the machine chromosome adopts the MS coding method, and the process chromosome adopts the OS coding method. Each integer of the machine code represents the machine number selected for the current process, the first integer of the process code represents the plate number, and the second integer represents the process number.

7. A multi-objective scheduling method for a ship plate processing workshop according to claim 5, characterized in that: In step S3, the generated initial population is subjected to fast non-dominated sorting, that is, the initial population is sorted by dominance level to realize individual stratification processing, all individuals in the Pareto front are taken out as the first non-dominated layer, and the taken out individuals are removed from the population, and all individuals in the newly generated Pareto front are taken out as the second non-dominated layer, and the operation is repeated until individuals that meet the quantity requirements are selected; Crowding P a for: In the formula, r is the number of objective functions, f n (i+1), f n (i-1) is the Pareto frontier point at both ends of the objective function n, are the two extreme values ​​of the nth objective function.

8. The multi-objective scheduling method for a ship plate processing workshop according to claim 5 is characterized in that: In step S4, the adaptive crossover and mutation operation adopts POX crossover in the process stage, including the following steps: S41: Randomly select two parent individuals and initialize two empty child individuals; S42: When performing crossover, the first child retains the set position of P1 in the first parent, and the other positions of the first child are determined by P2 in the second parent; S43: swap the positions of parent generation 1 and parent generation 2, and repeat steps S41 and S42 to generate child generation 2; The machine code uses uniform crossover, which includes the following steps: S401: Select two parent individuals and initialize two empty child individuals; S402: Generate a binary chromosome with the same length as the parent individual, which can be represented as w1, w2, ..., w s ; S403: According to w i = 1, the offspring 1 inherits the gene i from the parent 2, and the remaining positions are inherited by the gene w from the parent 1. i =0 to generate offspring 1; repeat this operation, and i = 1, the offspring 2 inherits the i gene from the parent 1, and the remaining positions are inherited by the w gene from the parent 2. i = The gene at 0 is supplemented to generate offspring 2; Adaptive crossover rate P b and adaptive mutation rate P c They are: Among them, the crossover probability is [0.9, 1], the mutation probability is [0.01, 0.1], and N max and N avg Respectively represent the maximum and average fitness values ​​in the population, It represents the maximum fitness value of the parent population selected in the crossover operation, and Nc represents the fitness value of the current mutant individual; The mutated crossover population after one iteration is merged with the parent population to obtain a combined population that is twice the size of the initial population.

9. A multi-objective scheduling method for a ship plate processing workshop according to claim 5, characterized in that: In step S6, the dynamic decreasing elite operator selection method includes the following steps: S61: Keep the population with low non-dominated level and select the number of individuals in the Pareto frontier according to the temperature coefficient; S62: Add a hierarchical cooling strategy based on the temperature coefficient, and use it as a selection criterion to allocate to the remaining non-dominated layers. If the number of selected individuals after one calculation does not meet the standard, the unselected individuals will be re-sorted by fast non-dominated sorting, and individuals with lower non-dominated levels will be selected to join the solution set until the population number requirement is met; S63: Add a cooling coefficient based on the temperature coefficient to reduce the number of individuals selected in each generation of Pareto frontier and ensure the diversity of the later population: Among them, α ij It is expressed as the number of individuals selected in the jth layer of the i-th iteration; n ij It is represented by the total number of individuals in the jth layer of the i-th iteration; β is the temperature coefficient; g i is the cooling coefficient of the algorithm iteration i; b j is the temperature reduction coefficient when the algorithm iterates to the jth layer.

10. The multi-objective scheduling method for a ship plate processing workshop according to claim 1, characterized in that: In step 5, determine whether a disturbance event occurs in the current production, including machine failure and emergency insertion. When a machine failure occurs, the machine shall not process any process until the machine recovers its working capacity; when an emergency insertion occurs, the rework process shall be arranged immediately.

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