A method for co-ordination and rescheduling of multi-model coordinators based on improved NSGA-II algorithm

Abstract

The present invention discloses a method for rescheduling the collinear assembly and adjustment of multiple types of calibrators based on an improved NSGA‑II algorithm, which belongs to the technical problem of production scheduling in a job shop; it adopts a multi-objective evolutionary algorithm to solve the scheduling problem of assembling multiple types of calibrators on the same production line with three priorities of normal production, self-inspection and military inspection. The present invention first establishes a flexible job scheduling model with two goals of minimum total delay and minimum plan deviation, and then improves the non-dominated sorting genetic algorithm, which not only eliminates the characteristics of a large number of individual repetitions but also maintains the diversity of individuals, and then uses the improved non-dominated sorting genetic algorithm to solve the production scheduling problem of collinear assembly and adjustment of multiple types of calibrators, and uses the hierarchical analysis method to select the most satisfactory solution from the Pareto optimal solution set.

Description

Technical Field

[0001] The invention relates to the technical problem of production scheduling in a job shop, and more specifically, to a method for co-ordination and re-scheduling of multi-model position markers based on an improved NSGA-II algorithm. Background Art

[0002] The production scheduling of the installation and adjustment of the position marker belongs to the flexible job-shop scheduling problem (Flexible job-shop scheduling problem, FJSP). Its characteristic is that each process can be carried out on several parallel workstations. It mainly considers the installation and adjustment sequence between processes of different types of position markers and the selection of workstations for the processes. Its research has important theoretical value and application significance.

[0003] At present, many scholars mainly study the job shop scheduling problem with a single objective. Even if there are multiple objectives, they will convert each objective into a single objective by weighted summation. However, in actual production, each objective generally affects each other, and the weight of each objective is difficult to determine. A single objective is difficult to reflect the actual production scheduling problem. In addition, most of the literature studies the job shop scheduling problem where there is no priority or only one high priority, such as an emergency order. However, in the production process of the calibration device, there are two high priorities, self-inspection and military inspection. That is, the priority of self-inspection products is higher than that of normal assembly and production products, and the priority of military inspection products is higher than that of self-inspection products.

[0004] In multi-objective scheduling problems, conflicts may occur between various objectives, i.e., the improvement of one objective will lead to the deterioration of another objective. Therefore, the optimization result is generally not an optimal solution, but a solution set consisting of several solutions, called the Pareto optimal solution set or non-dominated solution set. A variety of solution algorithms have been proposed in the prior art. Among them, the non-dominated sorting genetic algorithm NSGA-II proposed by DEB et al. has the advantages of fast running speed and good convergence of solution set, and is widely used by scholars at home and abroad. Summary of the invention

[0005] The present invention aims at the technical problems existing in the prior art and provides a method for rescheduling the co-linear assembly of multiple types of calibrators based on an improved NSGA-II algorithm. The method firstly establishes a flexible job scheduling model with two goals, namely, minimizing the total delay and minimizing the deviation of the scheme, according to the characteristics that multiple types of products are co-produced in the actual process of calibrator assembly and adjustment and have two high priorities of self-inspection and military inspection; secondly, the non-dominated sorting genetic algorithm is improved, which not only eliminates the characteristics of a large number of individual repetitions but also maintains the diversity of individuals; then the improved non-dominated sorting genetic algorithm is used to solve the production scheduling problem of the co-linear assembly of multiple types of calibrators, and the most satisfactory solution is selected from the Pareto optimal solution set using the hierarchical analysis method.

[0006] The technical solution of the present invention:

[0007] The multi-model coordinator collinear installation and rescheduling method based on the improved NSGA-II algorithm includes the following steps:

[0008] Step 1. Read the scheduling-related information from the production system, establish constraints according to the product process, batch number, workstation and priority, set model parameters, establish objective function and constraint function, and then establish a dual-objective rescheduling model;

[0009] Step 2. Use the NSGA-II algorithm to obtain the initial population of the coordinator collinear installation and rescheduling problem, then set the encoding method and the corresponding decoding method, classify and group the individuals in the population through encoding, and mark the categories, and obtain new individuals through crossover operations on the selected individuals through decoding, expand the search space through mutation operations and enhance the local search ability of the algorithm;

[0010] Step 3. By setting a neighborhood radius in each non-dominated layer and deleting other neighbor individuals in the neighborhood of the individual in the layer, an improved NSGA-II algorithm is obtained, and the improved NSGA-II algorithm is applied to solve the rescheduling problem to obtain the Pareto solution set;

[0011] Step 4. Use the hierarchical analysis method to select the optimal solution from the Pareto solution set. First, build a hierarchical model, then construct a judgment matrix based on the hierarchical model, and calculate the eigenvector of the judgment matrix.

[0012] Preferably, in step 1, the heavy rescheduling needs to meet the following constraints:

[0013] The assembly and production sequence of each product is determined by the process, and its procedures are known and cannot be changed;

[0014] At the time of rescheduling, the ongoing process is still carried out at this workstation;

[0015] Only one workstation can be selected for assembly or testing at the same time in the same process;

[0016] Only one process can be processed at the same workstation at the same time;

[0017] The processing of the same process cannot be interrupted;

[0018] The specifications and functions of the parallel workstations are the same;

[0019] There are sequence constraints between the processes of the same type and the same batch of products;

[0020] There is no order constraint between different types or batches of products;

[0021] When products of different priorities are being assembled at the same workstation, products with higher priority will be arranged first.

[0022] Preferably, in step 1, the two objectives considered in the dual-objective rescheduling model include:

[0023] The first optimization goal is to minimize the total delay;

[0024] The second optimization goal is to minimize the deviation of the rescheduling plan from the original plan.

[0025] Preferably, the objective function is set as follows:

[0026] The total delay time function is

[0027]

[0028] The solution deviation function is

[0029]

[0030] The constraint function is:

[0031]

[0032]

[0033]

[0034] ST iw(j+1) ≥CT iwj ,j=1,2,…,J i -1 (6)

[0035] ST iwj ≥CT i'w'j' -ξ×z iwji′w′j′k (7)

[0036] ST i'w'j' ≥CT iwj -ξ×(1-z iwji′w′j′k ) (8)

[0037]

[0038] Among them, formula (3) and formula (4) represent 0 and 1 variables; formula (5) indicates that the start processing time and the overall completion time of a process should not be greater than the completion time of the process; formula (6) is used to restrict the subsequent process to start work only after the previous process is completed; formula (7) and formula (8) are used to restrict each workstation to process only one process of a batch of products at the same time; formula (9) is used to restrict each process to be processed at only one workstation, and the workstation cannot be changed in the middle.

[0039] Preferably, in step 2, the coding adopts a four-layer coding method, the first layer represents the priority corresponding to each product, the second layer represents the process information of each model of product, the third layer represents the batch number information of the workpiece, and the fourth layer represents the work station information corresponding to each process;

[0040] The decoding method adopts a hierarchical decoding strategy, that is, the chromosome is divided into at most three parts according to the priority, and then the chromosomes with lower priority are decoded by insert greedy decoding.

[0041] Preferably, in step 2, the specific steps of the crossover operation include:

[0042] Step 2.1.1. Randomly select several positions in the second layer of the two chromosomes of the parents;

[0043] Step 2.1.2. Copy the genes at these positions on the second layer of the parent chromosome to the same positions in the offspring;

[0044] Step 2.1.3. Fill in the genes missing from the second layer of the maternal chromosome in order;

[0045] Step 2.1.4. Adjust the genes of the first and third layers of chromosomes of the offspring. Adjust the third layer genes of the offspring individuals according to the third layer genes corresponding to the order of the genes encoding each process in the second layer of the paternal or maternal individuals. The adjustment method of the first layer chromosomes is the same as that of the third layer;

[0046] Step 2.1.5. Adjust the fourth-layer genes of the offspring by adjusting the fourth-layer genes in the offspring individuals according to the correspondence between the second-layer and third-layer genes and the fourth-layer genes in the paternal or maternal individuals.

[0047] Preferably, in step 2, the specific steps of the mutation operation include:

[0048] Step 2.2.1. First, mutate the process, randomly select two positions in the individual process sequence, and exchange the genes at these two positions;

[0049] Step 2.2.2. Adjust the first, third, and fourth layer genes of the mutant individuals in the same way as the crossover operation;

[0050] Step 2.2.3. Randomly select a position in the process sequence and mutate the gene at this position to a position in the optional position set.

[0051] Preferably, the specific steps of step 3 are as follows:

[0052] Assume the neighborhood radius is r, N(x) is the r-neighborhood of x, then:

[0053] N(x)={y∈X:d(x,y),,r}

[0054] Since each non-dominated layer under each objective function has a different neighborhood radius, let r ij is the objective function f i The neighborhood radius of the jth non-dominated layer is:

[0055]

[0056] In the formula, is the maximum value of all individuals in the j-th non-dominated layer under the i-th objective function, is the minimum value of all individuals in the jth non-dominated layer under the i-th objective function, n is the number of individuals in the jth non-dominated layer, and k is the neighborhood radius coefficient (k ≥ 1);

[0057] The solution for d(x,y) is:

[0058] N j (x) = {x, y∈X j :|f1(x)-f1(y)|r 1j ,|f2(x)-f2(y)|r 2j}

[0059] In the formula, X j are all individuals in the jth non-dominated layer;

[0060] Finally, after the fast non-dominated sorting stratification, we start from the 0th layer to the last layer, starting from the first individual in each layer. If there are other individuals in the layer within the neighborhood of this individual, they will be deleted until the last individual in the layer.

[0061] Preferably, in step 4, the constructed hierarchical structure model is a three-layer structure model, which includes an overall goal layer, a sub-goal layer, and a solution layer;

[0062] The overall goal layer is to solve the problem of multi-model position marker co-ordination and rescheduling decision-making;

[0063] The sub-goal layer is the various sub-goals considered when evaluating various options against the goal;

[0064] The solution layer is a set of Pareto solutions generated in the rescheduling optimization phase based on the multi-objective evolutionary algorithm.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] According to the characteristics that some products may be delayed in delivery due to self-inspection and military inspection in the actual assembly process, and the changes in the production schedule have an impact on the original plan, the present invention establishes a scheduling model with two objectives of minimizing the total delay and minimizing the plan deviation. Then, in view of the characteristics that the position marker has multiple models, each model has a number of batches, the same process has a number of parallel workstations, and there are three priorities, a four-layer encoding method and its decoding mechanism, as well as effective crossover and mutation operations are designed; in view of the phenomenon that there are a large number of individual repetitions in the actual application of the non-dominated sorting genetic algorithm, a neighborhood radius is set in each non-dominated layer and other neighbor individuals in the neighborhood of the individual in the layer are deleted; finally, the improved algorithm is applied to solve the assembly scheduling problem to obtain a set of Pareto solution sets, and the hierarchical analysis method is used to select the optimal solution. The simulation experiment is verified, and the results show that the improved algorithm is feasible and effective and can meet the actual production needs. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0068] Figure 1 This is a schematic diagram of the four-layer coding of the present invention;

[0069] Figure 2 This is a schematic diagram of the plug-in greedy decoding of the present invention;

[0070] Figure 3 This is a schematic diagram of the parental chromosomes of the present invention;

[0071] Figure 4 A schematic diagram of chromosome crossover of the present invention;

[0072] Figure 5 It is a schematic diagram of the third-layer chromosome adjustment in the crossover operation of the present invention;

[0073] Figure 6 Schematic diagram of the adjustment of the fourth layer chromosomes in the crossover operation of the present invention;

[0074] Figure 7 This is a schematic diagram of the variation operation of the present invention;

[0075] Figure 8 A schematic diagram of deleting individuals in each layer in the improved algorithm of the present invention;

[0076] Fig. 9 The overall flow chart of the improved NSGA-II algorithm of the present invention;

[0077] Fig.10 The three-layer structure model diagram of the rescheduling based on AHP of the present invention;

[0078] Fig.11 A Gantt chart of the initial production scheduling scheme for the test of the present invention;

[0079] Fig.12 is the Pareto frontier distribution diagram of the conventional NSGA-II of the present invention;

[0080] Fig.13 The Pareto frontier distribution diagram of the improved NSGA-II of the present invention is provided;

[0081] Fig.14 This is a graph showing the mutual coverage variation of the solution set of Experiment 2 of the present invention;

[0082] Fig.15 This is the Gantt chart for the 5.5h time of the third test of the present invention;

[0083] Fig.16 This is the Gantt chart that is rescheduled at 7.8h for Test 3 of the present invention. DETAILED DESCRIPTION

[0084] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0085] Example:

[0086] The present invention provides a method for co-ordination and rescheduling of multi-model position coordinators based on an improved NSGA-II algorithm, comprising the following steps:

[0087] Step 1. Build a rescheduling model

[0088] Step 1.1. Read scheduling related information from the production system and collect relevant data from the production line;

[0089] Specifically, multiple models of position markers share one production line for assembly and adjustment. Each model of product has one or several batches for assembly and adjustment. The products have multiple processes. The processes of different products may be the same or different. Each process corresponds to several workstations with the same functions. Therefore, each product on the production line can choose the parallel workstations on the corresponding process for assembly and testing.

[0090] When the position marker is normally assembled and adjusted, it will perform self-inspection, that is, select the products that have been normally assembled and adjusted to re-inspect certain processes. After the self-inspection, it will perform military inspection, and the product can be delivered only after passing the military inspection. The priority of normal assembly, self-inspection, and military inspection increases in sequence, that is, when products of these three priorities need to be carried out at the same workstation at a certain moment, the products for military inspection should be arranged first, followed by the products for self-inspection, and finally the products for normal assembly and adjustment.

[0091] Step 1.2. Design the constraints that the rescheduling process satisfies

[0092] 1) The assembly and production sequence of each product is determined by the process, and its process is known and cannot be changed;

[0093] 2) At the time of rescheduling, the ongoing process is still carried out at this workstation;

[0094] 3) Only one workstation can be selected for assembly or testing at the same time in the same process;

[0095] 4) Only one process can be processed at the same workstation at the same time;

[0096] 5) The processing of the same process cannot be interrupted;

[0097] 6) The specifications and functions of the parallel workstations are the same;

[0098] 7) There are sequence constraints between the processes of the same type and the same batch of products;

[0099] 8) There is no order restriction between products of different types or batches;

[0100] 9) When products of different priorities are being assembled at the same workstation, products with higher priority shall be arranged first.

[0101] Step 1.3. Set the rescheduling model parameters

[0102] The details are shown in Table 1.

[0103] Table 1 Parameter definition table

[0104]

[0105]

[0106] Step 1.4. Dual target establishment

[0107] Since the time of self-inspection and military inspection is uncertain, the insertion of products undergoing self-inspection and military inspection may cause delays in the completion of some products. Therefore, the first optimization goal set is to minimize the total delay. Also, when rescheduling is carried out, the production schedule of the products after the rescheduling time will change, which may cause the material preparation at some workstations to be advanced or delayed, which will have an impact on the original production schedule. Therefore, the second optimization goal set is to minimize the deviation of the rescheduling plan from the original plan.

[0108] The objective function is set up as follows:

[0109] The total delay time function is:

[0110]

[0111] The solution deviation function is:

[0112]

[0113] The constraint function is:

[0114]

[0115]

[0116]

[0117] ST iw(j+1) ≥CT iwj ,j=1,2,…,J i -1 (6)

[0118] ST iwj ≥CT i'w'j' -ξ×z iwji′w′j′k (7)

[0119] ST i'w'j' ≥CT iwj -ξ×(1-z iwji′w′j′k ) (8)

[0120]

[0121] Among them, formula (3) and formula (4) represent 0 and 1 variables; formula (5) indicates that the start processing time and the overall completion time of a process should not be greater than the completion time of the process; formula (6) is used to restrict the subsequent process to start work only after the previous process is completed; formula (7) and formula (8) are used to restrict each workstation to process only one process of a batch of products at the same time; formula (9) is used to restrict each process to be processed at only one workstation, and the workstation cannot be changed in the middle.

[0122] Step 2. Determine the rescheduling algorithm

[0123] The NSGA-II algorithm is used to obtain the initial population of the coordinator collinear installation and rescheduling problem, and then the encoding method and the corresponding decoding method are set.

[0124] Step 2.1. Coding

[0125] like Figure 1 As shown, the coding adopts a four-layer coding method. The first layer represents the priority corresponding to each product, the second layer represents the process information of each model of product, the third layer represents the batch number information of the workpiece, and the fourth layer represents the work station information corresponding to each process.

[0126] Specifically, in the priority sequence, 0 represents conventional assembly and adjustment production, 1 represents self-inspection (denoted as S), and 2 represents military inspection (denoted as J). The larger the number, the higher the priority. In the process sequence, the number represents the product model. When the numbers in the process sequence from left to right are the same (denoted as number i), and the corresponding batch numbers and numbers in the priority are the same (denoted as numbers v and w, respectively), the number of times number i appears in the process sequence represents the process of the wth batch of product number i. For example, if number 2 appears 4 times in the process sequence, that is, (2, 2, 2, 2), the corresponding batch number sequence and priority numbers are (1, 2, 1, 2) and (1, 1, 1, 1), respectively, which are denoted as O. 211 S.O. 221 S.O. 212 S.O. 222 S(If using O iwj represents the jth process of the wth batch of product i, O iwj S indicates the product is self-tested, O iwj J indicates products undergoing military inspection); in the station sequence, the numbers indicate the station numbers.

[0127] therefore, Figure 1 The process and batch number sequence is represented by {O 211 S, O 111 J, O 112 J, O 311 , O 221 S, O 312 , O 212 S, O 113 J, O 222 S, O 114 J}, and the corresponding workstation numbers are {2, 1, 3, 1, 4, 3, 7, 5, 7, 6}.

[0128] Suppose the completion time of the jth process of the wth batch of product No. i with priority v is t viwj , P viwjk is the process O with priority v iwj At the processing time of station number k, process O with priority viwj The completion time calculation formula is:

[0129] t viwj =max{max(t viw(j-1) ,T)+ct viw(j-1) ,t hp}+P viwjk (10)

[0130] In formula (10), T represents the time when rescheduling occurs, ct viw(j-1) Represents process O with priority v iw(j-1) The transfer time, t hp Indicates workstation k (process O with priority v) iwj The completion time of the previous process at the workstation to be processed (if there is no previous process, then t hp =0).

[0131] Step 2.2. Decoding

[0132] In order to ensure that higher priority products are installed first, a hierarchical decoding strategy is adopted.

[0133] That is, the chromosome is divided into three parts at most according to the priority, and then the completion time of the process is calculated for the chromosome with the highest priority using formula (10); secondly, the insertion greedy decoding method is used to decode the chromosomes with lower priority, such as Figure 2 shown.

[0134] Figure 2 In the process, starting from the completion time of the previous process of the secondary priority process, find the idle time period at the workstation that processes the process, select the time period that is greater than or equal to the process to be processed, and insert the process into the idle time period.

[0135] Step 2.3. Crossover operation

[0136] By decoding, the selected individuals are crossover operated to obtain new individuals to achieve the evolution of the population.

[0137] The present invention adopts a position-based method to perform crossover operation. The two chromosomes of the parents are as follows: Figure 3 As shown, the specific steps are as follows:

[0138] Step 2.3.1. Randomly select several positions in the second layer of the two chromosomes of the parents. The positions do not need to be consecutive.

[0139] Step 2.3.2. Copy the genes at these positions on the second layer of the parent chromosome to the same positions in the offspring;

[0140] Step 2.3.3. Fill in the genes missing from the second layer of the maternal chromosomes in order, such as Figure 4 As shown;

[0141] Step 2.3.4. Adjust the genes of the first and third layers of chromosomes of the offspring. Adjust the third layer genes of the offspring individuals according to the third layer genes corresponding to the order of the genes of each process in the second layer of the paternal or maternal individuals. For example, if the order of the third layer genes corresponding to product No. 2 in the paternal chromosome is 1, 2, 1, 2, then the order of the third layer genes corresponding to product No. 2 in the offspring chromosome is the same. Figure 5 As shown;

[0142] The chromosome adjustment method for the first layer is the same as that for the third layer;

[0143] Step 2.3.5. Adjust the fourth-layer genes of the offspring. Adjust the fourth-layer genes in the offspring individuals according to the corresponding relationship between the second-layer and third-layer genes and the fourth-layer genes in the father or mother individuals. For example, the fourth-layer genes corresponding to the first batch of product No. 2 in the mother's chromosome are 4 and 2, and the corresponding fourth-layer genes for the second batch of product No. 2 are 7 and 6. Therefore, the order of the fourth-layer genes corresponding to the first and second batches of product No. 2 in the offspring chromosome is the same, such as Figure 6 shown.

[0144] Step 2.4. Mutation operation

[0145] The mutation operation can not only maintain the diversity of the population to expand the search space and prevent premature convergence, but also enhance the local search capability of the algorithm, thus facilitating the evolution of the population. The present invention adopts two mutation operations, one is the mutation of the process, and the other is the mutation of the station selection. The mutation diagram is shown in Figure 7 As shown, the specific mutation operation steps are as follows:

[0146] Step 2.4.1. First, mutate the process, randomly select two positions in the individual process sequence, and exchange the genes at these two positions;

[0147] Step 2.4.2. Adjust the first, third, and fourth layer genes of the mutant individuals in the same way as the crossover operation;

[0148] Step 2.4.3. Randomly select a position in the process sequence and mutate the gene at this position to a position in the optional position set.

[0149] Step 3. Improved NSGA-II algorithm

[0150] When using the traditional NSGA-II algorithm to solve the co-linear installation and rescheduling problem of multiple models of coordinators, it is found that a large number of duplicate individuals will appear after a certain number of iterations, which greatly affects the quality and quantity of solutions in the Pareto solution set. Therefore, the present invention improves it by setting a neighborhood radius in each non-dominated layer and deleting other neighbor individuals in the neighborhood of the individual in the layer, thereby obtaining an improved NSGA-II algorithm, which can not only eliminate the phenomenon of duplicate individuals but also fully retain the search range of the solution.

[0151] Assume the neighborhood radius is r, N(x) is the r-neighborhood of x, then:

[0152] N(x)={y∈X:d(x,y),,r} (11)

[0153] Since there are two objective functions, each non-dominated layer under each objective function has a different neighborhood radius. Let r ij is the objective function f i The neighborhood radius of the jth non-dominated layer is:

[0154]

[0155] In the formula, is the maximum value of all individuals in the j-th non-dominated layer under the i-th objective function, is the minimum value of all individuals in the j-th non-dominated layer under the i-th objective function, n is the number of individuals in the j-th non-dominated layer, and k is the neighborhood radius coefficient (k ≥ 1).

[0156] Since there are two objective functions, we can use the congestion calculation method in the NSGA-II algorithm to solve d(x,y), so:

[0157] N j (x) = {x, y∈X j :|f1(x)-f1(y)|r 1j ,|f2(x)-f2(y)|r 2j} (13)

[0158] In the formula, X j are all individuals in the jth non-dominated layer.

[0159] The present invention adopts a method of deleting other neighbor individuals in the neighborhood of an individual in each non-dominated layer to replace the use of congestion in the original algorithm.

[0160] like Figure 8As shown in the figure, after the fast non-dominated sorting stratification, starting from the 0th layer to the last layer, traversing from the first individual in each layer, if there are other individuals in the layer within the neighborhood of this individual, they will be deleted until the last individual in the layer.

[0161] from Figure 8 It can be seen that the improved method can not only prevent the appearance of a large number of duplicate individuals, but also make the individuals more evenly distributed.

[0162] The overall process of the improved NSGA-II algorithm is as follows: Fig. 9 shown.

[0163] Step 4. Rescheduling plan decision based on AHP

[0164] The analytic hierarchy process (AHP) is used to select the optimal solution from the Pareto solution set. The analytic hierarchy process (AHP) was proposed by Thomas Setty, an operations researcher at the University of Pittsburgh in the United States in the early 1970s. It is a hierarchical weighted decision analysis method that combines qualitative and quantitative methods to solve complex multi-objective problems using network system theory and multi-objective comprehensive evaluation methods.

[0165] Specifically, the rescheduling plan decision steps include:

[0166] Step 4.1. Build a hierarchical model

[0167] like Fig.10 As shown in the figure, a three-layer structural model is constructed, namely the overall goal layer, the sub-goal layer, and the solution layer. Among them, the overall goal layer is the purpose of solving the problem of co-linear installation and rescheduling decision-making of multi-model positioners, the sub-goal layer is the various sub-goals considered when evaluating various schemes against the goal, and the solution layer is a set of Pareto solutions generated in the rescheduling optimization stage based on the multi-objective evolutionary algorithm.

[0168] Step 4.2. According to the hierarchical model, construct a judgment matrix as shown in formula (14). The number of rows or columns of the matrix should be the number of targets. ij Represents the comparison result of the i-th target relative to the j-th target.

[0169]

[0170] Step 4.3. Calculate the eigenvector of the judgment matrix

[0171] The weight vector can be obtained by calculating the eigenvector of the judgment matrix. However, since the dimensions of each target are different, there is no unified standard and it is impossible to compare them. Therefore, before comprehensive evaluation, dimensionless processing is required, that is, the eigenvalues ​​of the target are uniformly transformed into the range of [0,1]. The specific unified quantification processing method is as follows.

[0172]

[0173]

[0174]

[0175]

[0176] In the above formula, i is the number of solutions in the Pareto solution set, i = 1, 2, ..., p; j is the optimization target f j The number of, j = 1, 2, ..., q; a ij Represents the solution X i The optimization objective f j The value of .

[0177] From formula (15), we can get the decision matrix B of the scheme = (b ij ) p×q ;

[0178] The matrix D for evaluating the satisfaction of the scheme can be obtained from formula (18).

[0179] Furthermore, in order to verify the effectiveness of the improved algorithm, the present invention performs simulation analysis through simulation experiments.

[0180] Experiment 1: Example Test Analysis

[0181] The improved NSGA-II algorithm is programmed in Python, and the program is run in the Windows 10 system, Intel(R) Core(TM) i7-10875H CPU@2.3GHz, and 16GB RAM.

[0182] This test example uses 5 types of products, 6 processes, and a total of 11 workstations for testing. Among them, since there are two parallel workstations for processes 2, 3, and 5, and there is only one workstation for the remaining processes, and the parallel workstations take the same time to process the same product and the same process, there are actually 9 test stations.

[0183] The product model, the corresponding batch number and the process information of each model product are shown in Table 2, the information of the optional workstations corresponding to each process is shown in Table 3, and the assembly time of each process of the product is shown in Table 4.

[0184] Table 2 Product Information

[0185]

[0186] Table 3 Optional workstation information table

[0187]

[0188] Table 4 Various product installation and adjustment time information table

[0189]

[0190] Its initial production schedule is as follows: Fig.11 shown.

[0191] The completion time of each product of the initial scheme is shown in Table 5, where the time when the product starts is defined as 0h.

[0192] Table 5 Completion schedule of each product in the initial plan

[0193]

[0194] The process and time information of self-inspection and military inspection of each product are shown in Table 6.

[0195] Table 6 Process and time information of self-inspection and military inspection of each product

[0196]

[0197] It can be seen from Table 5 that the first batch of product No. 2 in the initial plan is completed first, and its completion time is 5.15h, so self-inspection can be arranged for it. Assuming the self-inspection time is 5.5h, the planned completion times of each batch of each product are {11.5, 12.0, 8.0, 8.0, 12.0, 12.0, 12.5, 14.0} respectively.

[0198] The coefficient k of the neighborhood radius in the improved NSGA-II algorithm is set to 5, and the other parameters are the same as those of the traditional NSGA-II algorithm, namely, the crossover probability is 0.8, the mutation probability is 0.1, the population size is 100, and the number of iterations is 100.

[0199] The examples are solved using the traditional NSGA-II and the improved NSGA-II algorithm of the present invention, and the obtained Pareto frontiers are as follows: Fig.12 , Fig.13 shown.

[0200] Through the analysis in the figure, it can be seen that the number and quality of non-repetitive solutions in the Pareto solution set of the improved NSGA-II algorithm of the present invention are better than those of the traditional NSGA-II algorithm.

[0201] Experiment 2: Comparison of mutual dominance between Pareto optimal solutions

[0202] In order to further evaluate the performance of the improved NSGA-II algorithm of the present invention and the traditional NSGA-II algorithm, the solution set mutual coverage is used to compare the mutual dominance relationship between the Pareto optimal solutions generated by the two algorithms. The definition of solution set mutual coverage is as follows:

[0203]

[0204] In the above formula, X1 and X2 represent two different Pareto solution sets, and C(X1,X2) represents the proportion of solutions in the solution set X2 that are dominated by or equal to the solutions in X1 to the total solution set of X2, and its size is between [0,1]. C(X1,X2)=1 means that all solutions in X2 can find solutions in X1 that dominate or are equal to them; on the contrary, C(X1,X2)=0 means that no solution in X2 is dominated by a solution in X1.

[0205] By comparing in this way, we can clearly see the mutual dominance relationship between the solutions of different algorithms, that is, the superiority and inferiority of the algorithms. In a single operation, the mutual coverage of the solution sets of the improved NSGA-II algorithm and the traditional NSGA-II algorithm changes with the number of iterations as follows: Fig.14 shown.

[0206] from Fig.14 It can be seen that with the increase of the number of iterations, the non-dominated solution set obtained by the improved NSGA-II algorithm of the present invention can cover the non-dominated solution set of the traditional NSGA-II algorithm. When the number of iterations is greater than or equal to 22, C(X1,X2)=1, indicating that all the solutions generated by the traditional NSGA-II algorithm are dominated by the solutions generated by the improved NSGA-II algorithm of the present invention; at the same time, C(X2,X1)=0 indicates that the solutions generated by the improved NSGA-II algorithm of the present invention are not dominated by any solutions generated by the traditional NSGA-II algorithm.

[0207] The traditional and improved NSGA-II algorithms were run 10 times respectively, and the mutual coverage of the obtained solution sets is shown in Table 7.

[0208] Table 7 Comparison results of mutual coverage of algorithm solution sets before and after improvement

[0209]

[0210] It can be seen from Table 7 that in the 10 consecutive runs of the algorithm, the quality and quantity of the optimal solution of the improved algorithm are basically better than or equal to the optimal solution of the algorithm before the improvement; Fig.14 Table 7 can more accurately illustrate that the improved NSGA-II algorithm proposed in the present invention has better performance than the traditional NSGA-II algorithm.

[0211] The Pareto solution set obtained by the improved NSGA-II algorithm of the present invention in one operation is shown in Table 8.

[0212] Table 8 Pareto solutions obtained by the improved NSGA-II algorithm

[0213]

[0214] Experiment 3: AHP decision-making process analysis

[0215] The hierarchical analysis method is used to select a satisfactory solution from the Pareto solution set obtained by the improved NSGA-II algorithm of the present invention. The importance of the decision-making is the deviation of the solution and the total delay. 1 and 3 are used to represent the importance between the two targets f1 and f2, and the judgment matrix is ​​obtained:

[0216]

[0217] The calculated weight vector w = [0.25, 0.75];

[0218] From equations (15)-(18), we can get the matrix D = [0.25, 0.75, 0.37] for evaluating the satisfaction of the solution, where the maximum value is D2 = 0.75, indicating that the second solution in the Pareto solution set is the most satisfactory solution. The corresponding rescheduling Gantt chart is as follows: Fig.15 shown.

[0219] For the above rescheduling scheme, at 7.8h, it is necessary to arrange self-inspection and military inspection for the products that have been installed and adjusted normally and the products that have completed self-inspection, so it is necessary to reschedule again. That is, the above rescheduling scheme is used as the initial scheme, and rescheduling is performed again according to the above method. The rescheduling Gantt chart is as follows: Fig.16 shown.

[0220] After analysis, it is found that the improved rescheduling scheme of the present invention has reliable performance, the method is feasible and effective, and can meet the actual production scheduling needs of the workshop.

[0221] According to the characteristics that some products may be delayed in delivery due to self-inspection and military inspection in the actual assembly process, and the changes in the production schedule have an impact on the original plan, the present invention establishes a scheduling model with two objectives of minimizing the total delay and minimizing the plan deviation. Then, in view of the characteristics that the position marker has multiple models, each model has a number of batches, the same process has a number of parallel workstations, and there are three priorities, a four-layer encoding method and its decoding mechanism, as well as effective crossover and mutation operations are designed; in view of the phenomenon that there are a large number of individual repetitions in the actual application of the non-dominated sorting genetic algorithm, a neighborhood radius is set in each non-dominated layer and other neighbor individuals in the neighborhood of the individual in the layer are deleted; finally, the improved algorithm is applied to solve the assembly scheduling problem to obtain a set of Pareto solution sets, and the hierarchical analysis method is used to select the optimal solution. The simulation experiment is verified, and the results show that the improved algorithm is feasible and effective and can meet the actual production needs.

[0222] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A method for co-ordination and rescheduling of multi-model position coordinators based on an improved NSGA-II algorithm, characterized in that: The following steps are involved: Step 1. Read the scheduling-related information from the production system, establish constraints according to the product process, batch number, workstation and priority, set model parameters, establish objective function and constraint function, and then establish a dual-objective rescheduling model; Step 2. Use the NSGA-II algorithm to obtain the initial population of the coordinator collinear installation and rescheduling problem, then set the encoding method and the corresponding decoding method, classify and group the individuals in the population through encoding, and mark the categories, and obtain new individuals through crossover operations on the selected individuals through decoding, expand the search space through mutation operations and enhance the local search ability of the algorithm; Step 3. By setting a neighborhood radius in each non-dominated layer and deleting other neighbor individuals in the neighborhood of the individual in the layer, an improved NSGA-II algorithm is obtained, and the improved NSGA-II algorithm is applied to solve the rescheduling problem to obtain a Pareto solution set; the specific steps of step 3 are as follows: Assume the neighborhood radius is r, N(x) is the r-neighborhood of x, then: Since each non-dominated layer under each objective function has a different neighborhood radius, let r ij is the objective function f i The neighborhood radius of the jth non-dominated layer is: In the formula, is the maximum value of all individuals in the j-th non-dominated layer under the i-th objective function, is the minimum value of all individuals in the jth non-dominated layer under the i-th objective function, n is the number of individuals in the jth non-dominated layer, and k is the neighborhood radius coefficient (k ≥ 1); d ( x , y )The solution is: In the formula, X j are all individuals in the jth non-dominated layer; Finally, after the fast non-dominated sorting stratification, we start from the 0th layer to the last layer, starting from the first individual in each layer. If there are other individuals in the layer within the neighborhood of this individual, they will be deleted until the last individual in the layer. Step 4. Use the hierarchical analysis method to select the optimal solution from the Pareto solution set. First, build a hierarchical model, then construct a judgment matrix based on the hierarchical model, and calculate the eigenvector of the judgment matrix.

2. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 1 is characterized in that: In step 1, the heavy rescheduling needs to meet the following constraints: The assembly and production sequence of each product is determined by the process, and its procedures are known and cannot be changed; At the time of rescheduling, the ongoing process is still carried out at this workstation; Only one workstation can be selected for assembly or testing at the same time in the same process; Only one process can be processed at the same workstation at the same time; The processing of the same process cannot be interrupted; The specifications and functions of the parallel workstations are the same; There are sequence constraints between the processes of the same type and the same batch of products; There is no order constraint between different types or batches of products; When products of different priorities are being assembled at the same workstation, products with higher priority will be arranged first.

3. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 1 is characterized in that: In step 1, the two objectives considered in the dual-objective rescheduling model include: The first optimization goal is to minimize the total delay; The second optimization goal is to minimize the deviation of the rescheduling plan from the original plan.

4. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 1 is characterized in that: The objective function is set as follows: The total delay time function is （1） In the formula, is the actual completion time of the wth batch of product i, is the planned completion time of the wth batch of product i, i is the product number, w Number the batches of the same product. N is the total number of product models, P i Total number of batches of product i; The solution deviation function is （2） In the formula, is the start time of the jth process of the wth batch of the ith product before rescheduling, is the start time of the jth process of the wth batch of the i-th product after rescheduling, i is the product number, w is the batch number of the same product, j is the process number, N is the total number of product models, P i The total number of batches of product i, e iw is the number of processes for the wth batch of the ith product; The constraint function is: （3） （4） （5） （6） （7） （8） （9） In the formula, is the start time of the jth process of the wth batch of product i, is the end time of the jth process of the wth batch of product i, is the processing time of the jth process of the wth batch of the i-th product at the kth station, is a sufficiently large constant, m is the total number of workstations, and k is the workstation number; Among them, formula (3) and formula (4) represent 0 and 1 variables; formula (5) indicates that the start processing time and the overall completion time of a process should not be greater than the completion time of the process; formula (6) is used to restrict the subsequent process to start work only after the previous process is completed; formula (7) and formula (8) are used to restrict each workstation to process only one process of a batch of products at the same time; formula (9) is used to restrict each process to be processed at only one workstation, and the workstation cannot be changed in the middle.

5. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 1 is characterized in that: In step 2, the coding adopts a four-layer coding method, the first layer represents the priority corresponding to each product, the second layer represents the process information of each model of product, the third layer represents the batch number information of the workpiece, and the fourth layer represents the work station information corresponding to each process; The decoding method adopts a hierarchical decoding strategy, that is, the chromosome is divided into at most three parts according to the priority, and then the chromosomes with lower priority are decoded by insert greedy decoding.

6. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 5 is characterized in that: In step 2, the specific steps of the crossover operation include: Step 2.1.

1. Randomly select several positions in the second layer of the two chromosomes of the parents; Step 2.1.

2. Copy the genes at these positions on the second layer of the parent chromosome to the same positions in the offspring; Step 2.1.

3. Fill in the genes missing from the second layer of the maternal chromosome in order; Step 2.1.

4. Adjust the genes of the first and third layers of chromosomes of the offspring. Adjust the third layer genes of the offspring individuals according to the third layer genes corresponding to the order of the genes encoding each process in the second layer of the paternal or maternal individuals. The adjustment method of the first layer chromosomes is the same as that of the third layer; Step 2.1.

5. Adjust the fourth-layer genes of the offspring by adjusting the fourth-layer genes in the offspring individuals according to the correspondence between the second-layer and third-layer genes and the fourth-layer genes in the paternal or maternal individuals.

7. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 6 is characterized in that: In step 2, the specific steps of the mutation operation include: Step 2.2.

1. First, mutate the process, randomly select two positions in the individual process sequence, and exchange the genes at these two positions; Step 2.2.

2. Adjust the first, third, and fourth layer genes of the mutant individuals in the same way as the crossover operation; Step 2.2.

3. Randomly select a position in the process sequence and mutate the gene at this position to a position in the optional position set.

8. The method for co-ordination and rescheduling of multi-model coordinators based on the improved NSGA-II algorithm according to claim 1 is characterized in that: In step 4, the constructed hierarchical structure model is a three-layer structure model, which includes the overall goal layer, the sub-goal layer, and the solution layer; The overall target layer is to solve the problem of co-ordination and rescheduling decision-making of multiple types of coordinators; The sub-goal layer is the various sub-goals considered when evaluating various plans against the goal; The solution layer is a set of Pareto solutions generated in the rescheduling optimization phase based on a multi-objective evolutionary algorithm.

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