Improved production scheduling method for weaving flexible workshop based on NSGA-II

Abstract

The present invention discloses a production scheduling method for a weaving flexible workshop based on an improved NSGA‑II, comprising the following steps: determining a description of the production scheduling problem of a weaving flexible workshop; constructing a mathematical model of the production scheduling problem of a weaving flexible workshop; in the improved NSGA‑II algorithm, combining the rapid search capability of an artificial bee colony algorithm to preliminarily search the initial population, combining simulated annealing to perform a local search on the Pateto solution, and solving the model to obtain a flexible production scheduling scheme for a weaving flexible workshop. The present invention improves the problem of increased computational time overhead caused by an excessively large initial population, while enhancing the search capability of the optimal solution, retaining secondary solutions to enhance population diversity, and avoiding the problem of a large number of repeated individuals in the later stage of the calculation; optimizing the production scheduling scheme from four dimensions: maximum completion time, number of times the same equipment changes varieties, time penalty, and total processing time, and is more suitable for lean production than algorithms with a single solution target.

Description

Technical Field

[0001] The invention relates to the technical field of textile manufacturing, and more specifically to a flexible weaving workshop production scheduling method based on NSGA-II improvement. Background Art

[0002] With the widespread application of digitalization in the business community, the various possibilities it provides are changing the competitive position of companies; in the information age, the trade trend of "short, frequent and fast" production orders has made the manual scheduling method of traditional weaving companies unable to meet today's employment conditions and changing order forms, and the competitiveness of traditional production methods is decreasing at a very fast rate. Therefore, driven by the current situation of survival and interests, the textile industry has gradually transformed from traditional production workshops to information workshops, and intelligent production scheduling systems have replaced manual scheduling.

[0003] The flexible job shop scheduling problem (FJSP) refers to finding the most ideal process and production equipment for each workpiece on the line under the actual scheduling constraints. FJSP is a multi-objective problem to adapt to complex production conditions. When solving multi-objective task scheduling problems, the NSGA-II algorithm adopts the strategy of fast non-dominated sorting and crowding distance, which has good convergence and is therefore widely used. However, when dealing with large-scale complex problems, the NSGA-II algorithm may have problems such as early convergence, time overhead affected by the population size, and excessive repetition of individuals in the later stages of calculation.

[0004] Therefore, in order to solve the above technical problems, it is necessary to provide an innovative weaving flexible workshop production scheduling method based on NSGA-II improvement. Summary of the invention

[0005] The purpose of the present invention is to overcome the above-mentioned deficiencies of the prior art and provide a weaving flexible workshop production scheduling method based on NSGA-II improvement.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] The weaving flexible workshop production scheduling method based on NSGA-II improvement includes the following steps:

[0008] Step 1, determine the description of the production scheduling problem of the weaving flexible job shop;

[0009] Step 2, constructing a mathematical model for the production scheduling problem of a weaving flexible job shop;

[0010] Step 3, in the improved NSGA-II algorithm, the rapid search capability of the artificial bee colony algorithm is combined to conduct a preliminary search of the initial population, and the simulated annealing is combined to conduct a local search of the Pateto solution, and the solution model is used to obtain a flexible production scheduling plan for the weaving flexible workshop.

[0011] Furthermore, step 2 specifically includes:

[0012] 2.1. Minimizing the Maximum Completion Time Model

[0013]

[0014] In the formula, i is the weaving beam number, y is the total number of weaving beams, and Ji is the processing completion time of weaving beam i;

[0015] 2.2. Minimum number of times of changing products for the same equipment model

[0016]

[0017] In the formula, m is the device number, z is the total number of devices, is the processing sequence number in the queue of weaving beams to be processed on the equipment, Mam is the total number of weaving beams to be processed on equipment m, Produced for device m Whether to continue to produce the same variety after the end, 0 if yes, 1 if not;

[0018] 2.3 Minimizing Time Penalty Model

[0019]

[0020] In the formula, i is the weaving beam number, y is the total number of weaving beams, λ i is the time difference penalty coefficient of weaving beam i, is the processing completion time of weaving beam i, and is the delivery date of weaving beam i;

[0021] 2.4. Minimizing the total processing time model

[0022]

[0023] In the formula, o is the order number, h is the total number of orders, p is the variety number, Lpo is the number of varieties in order o, i is the weaving beam number, y is the total number of weaving beams, m is the equipment number, z is the total number of equipment, Tz m,p is the time it takes for weaving beam i to produce variety p on equipment m, X i,o is whether the weaving beam i is used to produce order o, if yes, it is 1, otherwise it is 0, P i,p Is the weaving beam i used to produce variety p? If yes, it takes 1; otherwise, it takes 0. V m,p Whether equipment m is used to produce product p, it takes 1 if yes, and 0 otherwise. i,m Is the weaving beam i produced on m, which takes 1 if yes and 0 otherwise;

[0024] 2.5. The above target model functions are combined into a multi-objective optimization function, as follows:

[0025] min[f 1 , f 2 , f 3 , f 4 ]

[0026] In the formula, f 1 To minimize the maximum completion time, f 2 is the minimum number of times the same equipment is changed, f 3 To minimize the time penalty; f 4 To minimize the total processing time;

[0027] 2.6. Add constraints based on actual production scheduling requirements

[0028]

[0029] Formula (2-1) indicates that weaving beam i can only be assigned to order o, that is, a weaving beam can only be assigned to one order at the same time;

[0030]

[0031] Formula (2-2) indicates that weaving beam i can only be processed by equipment m, that is, a weaving beam can only be processed by one equipment at the same time;

[0032]

[0033] Formula (2-3) indicates that weaving beam i can be allocated to order o to produce variety p, that is, to ensure that the order and variety of workpieces are allocated correctly;

[0034]

[0035] Formula (2-4) indicates that weaving beam i can produce variety p on equipment m, that is, ensuring that the processing equipment allocation of the weaving beam is correct;

[0036]

[0037] Formula (2-5) indicates that the total time for weaving beam i to produce variety p by equipment m at a certain moment is less than the completion time of workpiece i;

[0038]

[0039] Formula (2-6) indicates that the start time of producing the i+1th weaving beam on equipment m is greater than the production completion time of the i-th weaving beam;

[0040]

[0041] Formula (2-7) indicates that when the first After the production of the first workpiece is completed, the production of the When there are two workpieces, if the products of the two workpieces are different, the value is 1, and if they are the same, the value is 0, which limits the value of the decision variable.

[0042]

[0043] Formula (2-8) represents the first After the production of the first workpiece is completed, the production of the The preparation process time for each workpiece is limited, and the corresponding production time is indicated. When the varieties of the two workpieces produced are different, a variety change operation needs to be performed. When the varieties are the same, only the warp tying operation needs to be performed. That is, the preparation process for the subsequent processing of the weaving beam is limited, and the corresponding production time is indicated.

[0044] Furthermore, in step 3, the improved NSGA-II algorithm specifically includes:

[0045] 3.1. Initialize the parameters of the improved algorithm: including initialization of basic parameters of each algorithm and initialization of conversion rate Pf;

[0046] 3.2. Population initialization: The weaving workshop scheduling problem is converted into algorithm coding through double-chain symbiotic coding, and then the artificial bee colony algorithm is initially iterated to a specified number of times to obtain a new generation of initialization population. After the preliminary screened population is obtained, the new generation of population is used as the initial population of the next stage of NSGA-II;

[0047] 3.3, Mutation operation: First, use the discrete DE / rand / 1 operator to mutate the encoding device segment, and use the insertion method to mutate the sequence segment;

[0048] 3.4. Crossover operation: Use multi-point crossover and sequential crossover to perform crossover operations on device segments and sequential segments respectively;

[0049] 3.5. Selection operation: merge the new individuals generated by crossover mutation with the original individuals into a new population, and then sort the population by Pareto; then, select the frontier solution from the sorted Pareto solution set to enter the new generation population, and use simulated annealing to select individuals with large fitness values ​​for the solutions with large crowding in the non-frontier Pareto solutions of the same level to enter the new generation population;

[0050] 3.6. Repeat the iterative operation until the number of iterations set by the parameter is reached, and output the Pareto solution of the last iteration.

[0051] Furthermore, in the double-stranded symbiotic encoding of step 3.2

[0052] Before coding, it is necessary to first determine the number of weaving shafts corresponding to the required output of each variety for each order, and the weaving shaft is used as the production unit during coding; secondly, the order number O is arranged from small to large, and the variety number P corresponding to the order O is arranged from small to large. The number of variety P corresponding to the order O in the gene coding is the number of weaving shafts required in advance, and the number of order O is the sum of the number of weaving shafts required for all varieties; the orders P arranged in sequence are used as the order layer of the gene symbiotic part, and the varieties P arranged in sequence are used as the variety layer of the gene symbiotic part; for each variety, the processing equipment is selected from the processable equipment set as the equipment segment in the double-chain part; finally, the processing sequence is selected for the weaving shaft corresponding to each variety as the sequence segment in the double-chain part; in the double-chain symbiotic gene, only the double-chain part participates in crossover and mutation, and the symbiotic part does not participate in crossover and mutation; the symbiotic part only serves as corresponding information, but its gene coding position changes with the change of the gene coding position of the double-chain part. In the coding process, each gene coding value in the four parts of GO, GP, GM, and GR corresponds to each other.

[0053] Furthermore, in the artificial bee colony algorithm of step 3.2

[0054] The fitness value needs to be calculated during the iteration process. The fitness value is calculated as follows:

[0055]

[0056] In formula (5-1), fi represents the value of the i-th objective function, Af i 、If i Respectively represent the population in the same generation f i The maximum and minimum values ​​of Zf i represents the normalized value of the objective function fi; in formula (5-2), θ i It represents the weight coefficient of the i-th objective function, and Zr is the fitness value.

[0057] Furthermore, in the selection operation of step 3.5

[0058] The hybrid selection method of fast non-dominated sorting with elite strategy and simulated annealing search includes two parts. The first part is Pareto solution selection, which gives priority to selecting Pareto frontier solutions as new populations. The second part is non-Pareto solution selection, which gives priority to eliminating individuals with smaller domination times. Secondly, individuals with small crowding degree are eliminated at the same level. Finally, the cooling function and acceptance probability of modular annealing algorithm are used as simulated annealing parameters in the population selection of this paper to conduct local search for the individuals with the largest crowding degree at the same level of Pareto non-frontier solutions.

[0059] The beneficial effects of the present invention are:

[0060] 1. In the present invention, the initial population is preliminarily searched by combining NSGA-II with the fast search capability of the artificial bee colony algorithm to improve the problem of increased computing time overhead caused by the initial population being too large. At the same time, the Pateto solution is locally searched in combination with simulated annealing to enhance the search capability of the optimal solution, and the secondary solution is retained to enhance the population diversity and avoid the problem of a large number of repeated individuals in the later stage of the calculation.

[0061] 2. In the present invention, the production scheduling plan is optimized from four dimensions: maximum completion time, number of product changes with the same equipment, time penalty and total processing time. Compared with algorithms with a single solution target, it is more suitable for lean production. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flow chart of the production scheduling method of a weaving flexible workshop improved based on NSGA-II in this embodiment;

[0063] Figure 2 It is an optimal value diagram of the objective function during the iteration process in this embodiment;

[0064] Figure 3 A Gantt chart for finally determining the optimal scheduling solution in this embodiment;

[0065] Figure 4 A comparison chart of the algorithm performance in this embodiment. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] This embodiment provides a weaving flexible workshop production scheduling method based on NSGA-II improvement, comprising the following steps:

[0068] Step 1, determine the description of the weaving flexible job shop production scheduling problem; wherein, in the production system, the problem of processing n workpieces on m equipment is defined as a flexible job shop scheduling problem, that is, each workpiece has its fixed process steps and process number, the process number and process steps of different workpieces may be different, each equipment can perform one or more processes on different workpieces, and the same process of the same workpiece may have different processing times on different equipment;

[0069] Step 2: Construct a mathematical model for the production scheduling problem of a weaving flexible workshop, that is, establish target models by minimizing the maximum completion time, minimizing the number of times the same equipment is changed, minimizing time penalties, and minimizing the total processing time. Specifically:

[0070] 2.1. Minimizing the Maximum Completion Time Model

[0071]

[0072] In the formula, i is the weaving beam number, y is the total number of weaving beams, and Ji is the processing completion time of weaving beam i;

[0073] 2.2. Minimum number of times of changing products for the same equipment model

[0074]

[0075] In the formula, m is the device number, z is the total number of devices, is the processing sequence number in the queue of weaving beams to be processed on the equipment, Mam is the total number of weaving beams to be processed on equipment m, Produced for device m Whether to continue to produce the same variety after the end, 0 if yes, 1 if not;

[0076] 2.3 Minimizing Time Penalty Model

[0077]

[0078] In the formula, i is the weaving beam number, y is the total number of weaving beams, λ i is the time difference penalty coefficient of weaving beam i, is the processing completion time of weaving beam i, and is the delivery date of weaving beam i;

[0079] 2.4. Minimizing the total processing time model

[0080]

[0081] In the formula, o is the order number, h is the total number of orders, p is the variety number, Lpo is the number of varieties in order o, i is the weaving beam number, y is the total number of weaving beams, m is the equipment number, z is the total number of equipment, Tz m,p is the time it takes for weaving beam i to produce variety p on equipment m, X i,o is whether the weaving beam i is used to produce order o, if yes, it is 1, otherwise it is 0, P i,p Is the weaving beam i used to produce variety p? If yes, it takes 1; otherwise, it takes 0. V m,p Whether equipment m is used to produce product p, it takes 1 if yes, and 0 otherwise. i,m Is the weaving beam i produced on m, which takes 1 if yes and 0 otherwise;

[0082] 2.5. The above target model functions are combined into a multi-objective optimization function, as follows:

[0083] min[f 1 , f 2 , f 3 , f 4 ]

[0084] In the formula, f 1 To minimize the maximum completion time, f 2 is the minimum number of times the same equipment is changed, f 3 To minimize the time penalty; f 4 To minimize the total processing time;

[0085] 2.6. Add constraints based on actual production scheduling requirements

[0086]

[0087] Formula (2-1) indicates that weaving beam i can only be assigned to order o, that is, a weaving beam can only be assigned to one order at the same time;

[0088]

[0089] Formula (2-2) indicates that weaving beam i can only be processed by equipment m, that is, a weaving beam can only be processed by one equipment at the same time;

[0090]

[0091] Formula (2-3) indicates that weaving beam i can be allocated to order o to produce variety p, that is, to ensure that the order and variety of workpieces are allocated correctly;

[0092]

[0093] Formula (2-4) indicates that weaving beam i can produce variety p on equipment m, that is, ensuring that the processing equipment allocation of the weaving beam is correct;

[0094]

[0095] Formula (2-5) indicates that the total time for weaving beam i to produce variety p by equipment m at a certain moment is less than the completion time of workpiece i;

[0096]

[0097] Formula (2-6) indicates that the start time of producing the i+1th weaving beam on equipment m is greater than the production completion time of the i-th weaving beam;

[0098]

[0099] Formula (2-7) indicates that when the first After the production of the first workpiece is completed, the production of the When there are two workpieces, if the products of the two workpieces are different, the value is 1, and if they are the same, the value is 0, which limits the value of the decision variable.

[0100]

[0101] Formula (2-8) represents the first After the production of the first workpiece is completed, the production of the The preparation process time for each workpiece is limited, and the corresponding production time is indicated; when the products of the two workpieces are different, the product change operation needs to be performed, and when the products are the same, only the warp tying operation needs to be performed, that is, the preparation process for the subsequent processing of the weaving beam is limited, and the corresponding production time is indicated;

[0102] Step 3, in the improved NSGA-II algorithm, the rapid search capability of the artificial bee colony algorithm is combined to conduct a preliminary search of the initial population, and the simulated annealing is combined to conduct a local search of the Pateto solution, and the solution model is used to obtain a flexible production scheduling plan for the weaving flexible workshop;

[0103] Among them, the improved NSGA-II algorithm specifically includes:

[0104] 3.1. Initialize the parameters of the improved algorithm: including initialization of basic parameters of each algorithm and initialization of conversion rate Pf;

[0105] 3.2. Population initialization:

[0106] (1) The weaving workshop scheduling problem is converted into algorithmic coding through double-chain symbiotic coding. Before coding, the number of weaving shafts corresponding to the required output of each variety for each order must be determined first, and the weaving shaft is used as the production unit during coding. Secondly, the order numbers O are arranged from small to large, and the variety numbers P corresponding to the order O are arranged from small to large. The number of weaving shafts required for the variety P corresponding to the order O in the gene coding is the number of weaving shafts required in advance, and the number of orders O is the sum of the number of weaving shafts required for all varieties. At this time, the sequentially arranged orders P are used as the order layer of the gene symbiotic part, and the sequentially arranged varieties P are used as the order layer of the gene symbiotic part. The species P is used as the variety layer of the gene symbiotic part; in addition, for each variety, a processing device is selected from the processable equipment set as the equipment segment in the double-stranded part; finally, a processing sequence is selected for each variety corresponding to the weaving axis as the sequence segment in the double-stranded part; in the double-stranded symbiotic gene, only the double-stranded part participates in crossover and mutation, and the symbiotic part does not participate in crossover and mutation; the symbiotic part only serves as corresponding information, but its gene coding position changes with the change of the gene coding position of the double-stranded part. In the coding process, each gene coding value in the four parts of GO, GP, GM, and GR corresponds to each other one by one;

[0107] (2) After the artificial bee colony algorithm is initially iterated for a specified number of times, a new generation of initialization population is obtained. After the preliminary screened population is obtained, the new generation of population is used as the initial population of the next stage of NSGA-II;

[0108] Among them, the fitness value needs to be calculated during the iteration process of the artificial bee colony algorithm:

[0109]

[0110] In formula (5-1), fi represents the value of the i-th objective function, Af i 、If i Respectively represent the population in the same generation f i The maximum and minimum values ​​of Zf i represents the normalized value of the objective function fi; in formula (5-2), θ i represents the weight coefficient of the i-th objective function, and Zr is the fitness value;

[0111] 3.3, Mutation operation: First, use the discrete DE / rand / 1 operator to mutate the encoding device segment, and use the insertion method to mutate the sequence segment;

[0112] 3.4. Crossover operation: Use multi-point crossover and sequential crossover to perform crossover operations on device segments and sequential segments respectively;

[0113] 3.5. Selection operation: merge the new individuals generated by crossover mutation with the original individuals into a new population, and then sort the population by Pareto; then, select the frontier solution from the sorted Pareto solution set to enter the new generation population, and use simulated annealing to select individuals with large fitness values ​​for the solutions with large crowding in the non-frontier Pareto solutions of the same level to enter the new generation population;

[0114] 3.6. Repeat the iterative operation until the number of iterations set by the parameter is reached, and output the Pareto solution of the last iteration.

[0115] The following is an analysis of two orders produced by a weaving company:

[0116] (1) Simulation Example

[0117] Table 1 shows two orders produced by a weaving enterprise. Each order includes the required varieties, the required output of each variety, the order date, the delivery date, and the daily penalty for exceeding the delivery date. Table 2 shows the processing equipment assigned to the order by the weaving enterprise, including the number of the processable equipment corresponding to each variety. Table 3 shows the processing time of each equipment for each variety, and Table 4 shows the output of one weaving shaft produced by the loom for each variety in the weaving enterprise. The time data and output data are statistical values ​​of the data acquisition system database of this article. The enterprise stipulates that the change of varieties on the same equipment must be completed within half a shift. The daily shifts of the enterprise are divided into three shifts: morning, midday, and evening, each shift is 8 hours. In scheduling, this article takes the maximum value of 4 hours for the operation time of changing varieties.

[0118] Table 1 Order example table

[0119]

[0120]

[0121] Table 2 Correspondence between varieties and processable equipment examples

[0122]

[0123] Table 3 Scheduling problem table for a weaving flexible job shop example

[0124]

[0125] Table 4 Shaft production examples

[0126]

[0127] (2) Results Analysis

[0128] Since there is plenty of production time from the order placement time to the delivery date, in order to better implement the time penalty objective function, the delivery date of all orders is set to 100 hours after the order placement date. The penalty coefficient for order 1 is set to 0.4, and the penalty coefficient for order 2 is set to 0.6.

[0129] In the algorithm solution process, the values ​​of the four objective functions change with the number of iterations as shown below: Figure 2 ,The figure shows that each objective value is optimized with the increase of iteration times, indicating that the ,improved algorithm in this paper has good convergence in solving the ,weaving workshop scheduling problem.

[0130] After the algorithm solves the weaving workshop scheduling problem, a set of Pareto solutions will be obtained. In this set, the four objective function values ​​of maximum completion time, number of product changes, time penalty, and total processing time corresponding to each individual have their own advantages and disadvantages. When selecting the final scheduling plan, use formula (3-2) to calculate the fitness value of the Pareto solution set and select the optimal solution. In this example, the total processing time and time penalty are more important, and the objective function value weight θ is set. 1 =0.1,θ 2 =0.2,θ 3 =0.3,θ 4 =0.4. The optimal solution scheduling scheme selected by fitness value calculation is as follows Figure 3 .

[0131] In order to verify the effectiveness of the improved algorithm in this paper in solving the weaving workshop scheduling problem, the NSGA-II algorithm and the improved algorithm were used to solve the example under the same parameter settings and the same experimental environment. Figure 4 ,The improved algorithm has a faster convergence speed and better solutions when solving the problem than the NSGA-II algorithm.

[0132] The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. The improved weaving flexible workshop production scheduling method based on NSGA-II is characterized by: The following steps are involved: Step 1, determine the description of the production scheduling problem of the weaving flexible job shop; Step 2, constructing a mathematical model for the production scheduling problem of a weaving flexible job shop; Step 3, in the improved NSGA-II algorithm, the rapid search capability of the artificial bee colony algorithm is combined to conduct a preliminary search of the initial population, and the simulated annealing is combined to conduct a local search of the Pateto solution, and the solution model is used to obtain a flexible production scheduling plan for the weaving flexible workshop; Step 2 specifically includes: 2.

1. Minimizing the Maximum Completion Time Model In the formula, i is the weaving beam number, y is the total number of weaving beams, and Ji is the processing completion time of weaving beam i; 2.

2. Minimum number of times of changing products for the same equipment model In the formula, m is the device number, z is the total number of devices, is the processing sequence number in the queue of weaving beams to be processed on the equipment, Mam is the total number of weaving beams to be processed on equipment m, Produced for device m Whether to continue to produce the same variety after the end, 0 if yes, 1 if not; 2.3 Minimizing Time Penalty Model In the formula, i is the weaving beam number, y is the total number of weaving beams, λ i is the time difference penalty coefficient of weaving beam i, is the processing completion time of weaving beam i, and is the delivery date of weaving beam i; 2.

4. Minimizing the total processing time model Where o is the order number, h is the total number of orders, p is the variety number, Lpo is the number of varieties in order o, i is the weaving beam number, y is the total number of weaving beams, m is the equipment number, z is the total number of equipment, Tz m,p is the time it takes for weaving beam i to produce variety p on equipment m, X i,o is whether the weaving beam i is used to produce order o, if yes, it is 1, otherwise it is 0, P i,p Is the weaving beam i used to produce variety p? If yes, it takes 1; otherwise, it takes 0. V m,p Whether equipment m is used to produce product p, it takes 1 if yes, and 0 otherwise. i,m Is the weaving beam i produced on m, which takes 1 if yes and 0 otherwise; 2.

5. The above target model functions are combined into a multi-objective optimization function, as follows: min[f1,f2,f3,f4] In the formula, f1 is the minimum maximum completion time, f2 is the minimum number of times the same equipment is changed, f3 is the minimum time penalty; f4 is the minimum total processing time; 2.

6. Add constraints based on actual production scheduling requirements Formula (2-1) indicates that weaving beam i can only be assigned to order o, that is, a weaving beam can only be assigned to one order at the same time; Formula (2-2) indicates that weaving beam i can only be processed by equipment m, that is, a weaving beam can only be processed by one equipment at the same time; Formula (2-3) indicates that weaving beam i can be allocated to order o to produce variety p, that is, to ensure that the order and variety of workpieces are allocated correctly; Formula (2-4) indicates that weaving beam i can produce variety p on equipment m, that is, ensuring that the processing equipment allocation of the weaving beam is correct; Formula (2-5) indicates that the total time for weaving beam i to produce variety p by equipment m at a certain moment is less than the completion time of workpiece i; Formula (2-6) indicates that the start time of producing the i+1th weaving beam on equipment m is greater than the production completion time of the i-th weaving beam; Formula (2-7) indicates that when the first After the production of the first workpiece is completed, the production of the When there are two workpieces, if the products of the two workpieces are different, the value is 1, and if they are the same, the value is 0, which limits the value of the decision variable. Formula (2-8) represents the first After the production of the first workpiece is completed, the production of the The preparation process time for each workpiece is limited, and the corresponding production time is indicated; when the products of the two workpieces are different, the product change operation needs to be performed, and when the products are the same, only the warp tying operation needs to be performed, that is, the preparation process for the subsequent processing of the weaving beam is limited, and the corresponding production time is indicated; In step 3, the improved NSGA-II algorithm specifically includes: 3.

1. Initialize the parameters of the improved algorithm: including initialization of basic parameters of each algorithm and initialization of conversion rate Pf; 3.

2. Population initialization: The weaving workshop scheduling problem is converted into algorithm coding through double-chain symbiotic coding, and then the artificial bee colony algorithm is initially iterated to a specified number of times to obtain a new generation of initialization population. After the preliminary screened population is obtained, the new generation of population is used as the initial population of the next stage of NSGA-II; 3.3, Mutation operation: First, use the discrete DE / rand / 1 operator to mutate the encoding device segment, and use the insertion method to mutate the sequence segment; 3.

4. Crossover operation: Use multi-point crossover and sequential crossover to perform crossover operations on device segments and sequential segments respectively; 3.

5. Selection operation: merge the new individuals generated by crossover mutation with the original individuals into a new population, and then sort the population by Pareto; then, select the frontier solution from the sorted Pareto solution set to enter the new generation population, and use simulated annealing to select individuals with large fitness values ​​for the solutions with large crowding in the non-frontier Pareto solutions of the same level to enter the new generation population; 3.

6. Repeat the iterative operation until the number of iterations set by the parameter is reached, and output the Pareto solution of the last iteration.

2. The improved weaving flexible workshop production scheduling method based on NSGA-II according to claim 1 is characterized in that: In the double-stranded symbiotic encoding of step 3.2 Before coding, it is necessary to first determine the number of weaving shafts corresponding to the required output of each variety for each order, and the weaving shaft is used as the production unit during coding; secondly, the order number O is arranged from small to large, and the variety number P corresponding to the order O is arranged from small to large. The number of variety P corresponding to the order O in the gene coding is the number of weaving shafts required in advance, and the number of order O is the sum of the number of weaving shafts required for all varieties; the orders P arranged in sequence are used as the order layer of the gene symbiotic part, and the varieties P arranged in sequence are used as the variety layer of the gene symbiotic part; for each variety, the processing equipment is selected from the processable equipment set as the equipment segment in the double-chain part; finally, the processing sequence is selected for the weaving shaft corresponding to each variety as the sequence segment in the double-chain part; in the double-chain symbiotic gene, only the double-chain part participates in crossover and mutation, and the symbiotic part does not participate in crossover and mutation; the symbiotic part only serves as corresponding information, but its gene coding position changes with the change of the gene coding position of the double-chain part. In the coding process, each gene coding value in the four parts of GO, GP, GM, and GR corresponds to each other.

3. The improved weaving flexible workshop production scheduling method based on NSGA-II according to claim 1 is characterized in that: In the artificial bee colony algorithm of step 3.2 The fitness value needs to be calculated during the iteration process. The fitness value is calculated as follows: In formula (5-1), fi represents the value of the i-th objective function, Af i 、If i Respectively represent the population in the same generation f i The maximum and minimum values ​​of Zf i represents the normalized value of the objective function fi; in formula (5-2), θ i It represents the weight coefficient of the i-th objective function, and Zr is the fitness value.

4. The improved weaving flexible workshop production scheduling method based on NSGA-II according to claim 1 is characterized in that: In the selection operation of step 3.5 The hybrid selection method of fast non-dominated sorting with elite strategy and simulated annealing search includes two parts. The first part is Pareto solution selection, which gives priority to selecting Pareto frontier solutions as new populations. The second part is non-Pareto solution selection, which gives priority to eliminating individuals with smaller domination times. Secondly, individuals with small crowding degree are eliminated at the same level. Finally, the cooling function and acceptance probability of modular annealing algorithm are used as simulated annealing parameters in the population selection of this paper to conduct local search for the individuals with the largest crowding degree at the same level of Pareto non-frontier solutions.

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