# Production Scheduling Optimization of Garment Intelligent Manufacturing System Based on Big Data

Authors: Ning Sun; Botao Cao
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

In order to improve the efficiency of cloth laying and cutting integrated production process, this article proposes a method of optimal scheduling of cloth laying and cutting garment production system process based on big data and genetic algorithm. The chromosomes in the algorithm are expressed by real strings. The method of bit string crossover and mutation is used to solve the premature problem of the algorithm. The experimental results show that the actual cutting time of the plan is 736 min, and the total idle time is 113 min. The idle time occurs in processes 25, 28, 34, 35, and 31, respectively. The cutting time of the plan arranged by the genetic algorithm is 627 min, and there is no idle time.Conclusion. This method can effectively solve the optimal scheduling problem of the cloth laying and cutting production process.


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## Body

## 1. Introduction

Recently, many major changes have taken place in information technology and industrial fields such as cloud computing, big data, industrial robots, and 3D printing. The deep integration of industrialization and informatization has formed intelligent manufacturing. Governments of various countries pay great attention to and attach great importance to intelligent manufacturing. The United States, Germany, France, and other countries have successively formulated the national strategy of advanced manufacturing industry, the French plan for new industry, industry 4.0, etc [1]. Today, China’s economic development has entered a new normal, and the constraints of resources and environment on the manufacturing industry are constantly strengthening.In the clothing industry structure, the clothing industry occupies an important position, which to a large extent promotes the country’s economic growth, labor employment, and foreign exchange earnings through exports and meets industry market demand. It is an important traditional industry in my country. In recent years, with the continuous increase in the demand for clothing in the global market, my country’s clothing industry has achieved rapid development. According to statistics from the National Bureau of Statistics, clothing production has more than doubled from 2017 to 2018; enterprises in the clothing industry achieved a total of 13.177 billion pieces of clothing production in 2018. Statistics show that due to the in-depth development of the economy, the demand for clothing market is increasing. However, many garment enterprises in my country still use the traditional management mode in the past and have not realized the optimization and upgrade of the management mode, which makes the production capacity, product quality, response mode, and control method a relatively backward state, and it is difficult to keep up with the development of the company and the progress of the times. The pace of this is easy to be eliminated by the market industry. Under the general environment of the clothing manufacturing industry, how to strengthen the production management ability, improve the production efficiency, and reduce the growing production and operation costs are the problems faced and need to be solved by a large number of clothing enterprises at this stage. Traditional garment manufacturing mainly focuses on mass production. With the development of economy and society, most customers are no longer satisfied with single commodities and begin to pursue distinctive diversified and personalized products. The traditional production management mode of few varieties and large quantities cannot meet the new needs of the market. In addition, the current industrial products are becoming cheaper. In this case, the advantages of the traditional production management mode have become defects [2]. Under the traditional production management mode, the products produced by enterprises are easy to form a large amount of inventory. With the continuous reduction of product prices, the inventory continues to depreciate, which has brought huge losses to enterprises. Based on the Internet of things technology, intelligent manufacturing transforms traditional clothing production into informatization and opens up the information flow from product development to raw material procurement and order production, so that enterprises can effectively manage the main production and operation links and help enterprises respond quickly. Market demand improves the management ability and production efficiency of enterprises [3].


## 2. Literature Review

Rahman and others explained the relevant theories of intelligent manufacturing management. He analyzed the intelligent methods in project management, innovation management, and logistics management and also involved the intelligent management of intelligent scheduling and control [4]. Constantin and others believed that an intelligent manufacturing system is the inevitable requirement of production flexibility, process flexibility, and production scheduling flexibility in the twenty-first century (Figure 1). Therefore, it is necessary to integrate the architecture of manufacturing software and hardware, so as to automatically collect production information, make decisions, and then arrange production [5]. Kaltenbrunner and others proposed that in order to deal with the threat of low-cost advantages of developing countries to the U.S. textile industry, they proposed to integrate existing information technologies, such as online product catalog, CAD system, cam system, CIM system, FMS system, so as to make a rapid response to the market and reduce inventory and cost [6]. Long and others believed that an intelligent manufacturing system is an automatic manufacturing process based on information. Through information technology, the data are extracted from the basic production links, and the processed data will be used as the basis of a production scheduling plan [7]. Zhaof and others believed that as products become more and more complex, it is required to improve production efficiency and save resource investment. Therefore, the manufacturing industry must change its mode of production. An effective solution is to embed flexible manufacturing technology (FMS) into an intelligent reconfigurable manufacturing system (RMS), which is essentially the same as intelligent manufacturing [8]. Ahmed and others analyzed the development of intelligent manufacturing abroad and believed that the main research hotspots abroad were intelligent design, intelligent production, intelligent management, intelligent service, etc. Therefore, the two scholars believed that the development of intelligent manufacturing abroad is more mature than that at home. At the same time, it is pointed out that the current research on the theory, development path, and development mode of intelligent manufacturing in China is not deep enough, and the attention to the changes in organizational structure and management mode caused by intelligent manufacturing is not enough, and it is blank in cross fields such as intelligent management and intelligent service [9]. Courtois and others constructed the theoretical system of intelligent manufacturing from the perspective of management. They believed that the intelligent manufacturing system is composed of intelligent activities, intelligent manufacturing capability, knowledge management, and intelligent alliance [10]. By comparing the current forms, it is considered that China’s manufacturing industry should adopt the market following strategy in intelligent devices and the differentiation strategy in technology application and knowledge management. Most researches are only limited to the optimal scheduling problem of the sewing production process, and no one has studied the scheduling problem of cloth laying and cutting integrated production process.Figure 1
Clothing intelligent manufacturing system.


## 3. Research Methods

### 3.1. Production Scheduling Problem

It is an efficient arrangement of the production process. It is an important module in production management. It can comprehensively plan all production processes and links. It is the key of modern production and manufacturing system. A scientific and efficient production scheduling optimization technology can improve production efficiency to a great extent [11]. The production scheduling problem is to issue production instructions for a decomposable business on the premise of maximizing the constraints such as delivery time, process, and equipment and facility resources; allocate corresponding equipment and facility resources for each production link program; and arrange production time and process, so as to realize the optimization of production cost or time. The general job shop scheduling problem can be explained by the three-parameter or four-parameter method.Considering the differentiation of additive methods, in a workshop production system, the production scheduling problem can be divided into the following categories:(1)
Single machine scheduling problem: the batch to be processed only needs one process flow and one instrument, and the whole production and processing process is completed based on these conditions. This is the simplest form of all scheduling problems [12].(2)
Parallel machine scheduling problem: the batch to be processed only needs one process flow and multiple parallel instruments with the same attributes and functions, no matter which machine can be used to process and produce workpieces.(3)
Flow shop scheduling problem: the batch to be processed requires multiple process flows. Each process has only one machine, and the institutional functions in the process are different. Each workpiece must undergo a unified process flow according to the inherent order.(4)
Flexible flow shop scheduling problem: the batch to be processed requires a number of process flows. Each process is equipped with multiple machines that cannot produce. Each workpiece must undergo a unified process flow according to the inherent order. The flexible flow shop scheduling problem is closer to the specific production status, so it is most widely used.(5)
Job shop scheduling problem: the batch to be processed requires multiple process flows. All processes must be operated on their own designated machines, and the specific process procedures of the workpiece can be different.(6)
Open shop scheduling problem: there is no restriction of an operation sequence in all workpiece processing. Based on this, the scheduling scheme is very easy to obtain. However, due to the lack of constraints, it is easy to obtain a large number of scheduling schemes that can be adopted, which makes it more difficult to select the best.If the two processing times of a machine and a workpiece do not overlap, and the production constraints can be met, the scheduling is effective. Optimal scheduling refers to the effect that the scheduling-related indicators meet the optimal level. There are many specific evaluation indicators.As can be seen from the above definition, if we want to organize production for the production processPi, we only need to determine a linear combination of its production organization C1i,C2i,…,Cjpi; the production time of the production process Pi is ti=TiT⋅Ki, the production cost of the production process Pi is ti=CiT⋅Ki, we can construct an optimal scheduling model.


### 3.2. Computer Cloth Laying and Garment Cutting Production Process

The traditional clothing production process of cloth laying and cutting mainly includes the following steps: cloth laying plan ⟶ cutting plan ⟶ cloth laying ⟶ cutting ⟶ unloading ⟶ binding [13].Usually, in the process of garment production, computers are only used to control all production links, such as computer-controlled cloth laying system, computer cutting system, etc., but the modern production process should integrate all subsystems controlled by computers to construct a computer-integrated manufacturing system. However, as far as the whole system is concerned, there is still a lack of effective management and use [14, 15]. References pointed out that once the computer automatic cutting and laying system is adopted, the more important task is how to plan the laying sequence, so as to shorten the process time of the laying and cutting system and improve the production efficiency of the process. In fact, if the laying and cutting sequence is not reasonably arranged, the idle time of the equipment will be generated, thus reducing the use efficiency of the equipment. The usual practice is to produce a feasible but not optimal laying and cutting sequence through experience and artificial operation. In this way, in order to complete the daily production task, workers and machines must increase their working hours, thus increasing the production cost. The working process is as follows: the cloth paver first paves the cloth on the cloth paving table, then moves forward for a certain distance (called “position”) and then puts the cloth layer on the cutting working face for cutting. After the first “position” is cut, the cut cloth is moved to the binding table, and the next “position” of the cloth is transferred to the cutting working position. After the cutting machine cuts a piece of clothing, it will be transferred from the existing position to the next position to be cut, and so on until all pieces of clothing are cut.


### 3.3. Optimization Method Based on Genetic Algorithm

The genetic algorithm takes the coding of decision variables as the operation object and can directly operate on structural objects such as sets, sequences, matrices, trees, and graphs. On the one hand, this method helps to simulate the process of biological genes, chromosomes, and genetic evolution and facilitates the use of genetic operators. On the other hand, the genetic algorithm has a wide range of application fields, such as function optimization, production scheduling, automatic control, image processing, machine learning, data mining, and other fields. The genetic algorithm directly uses the objective function value as the search information. It only uses the fitness function value to measure the goodness of the individual and does not involve the process of derivation and differentiation of the objective function value. Because many objective functions are difficult to derive in reality, even though there is no derivative, the genetic algorithm shows a high degree of superiority. The genetic algorithm has the characteristics of group search. Its search process starts from an initial groupP (0) with multiple individuals; on the one hand, it can effectively avoid searching for some unnecessary points. On the other hand, because the traditional single-point search method is easy to fall into a local extreme point of a single peak when searching the search space of multimodal distribution, the group search feature of the genetic algorithm can avoid such a problem, so it can reflect the parallelization of genetic algorithm and better global search.Finally, all the species that survive are those with strong adaptability to nature, and those with poor adaptability will eventually be eliminated, which is “survival of the fittest.” Its essence is the process of continuous optimization and the development of intergenerational replacement of groups. It has important practical reference significance in the field of computing. The genetic algorithm (GA) is its inspiration [16]. The algorithm is based on the theory of the existence of adapters in the theory of biological evolution, forming a high-function random, parallel, and automatic adaptive optimization algorithm. GA has a good effect in large-scale complex optimization problems. It compares the process of solving the problem to the process of intergenerational evolution and survival of individuals in the group. Finally, the best adaptive person is the best solution of the problem.In this method, the solution space of the optimization problem is transformed into the coding space, and the fitness function is used to evaluate the individual. Through repeated intergenerational evolution for many times, the optimal individual with the best value of the objective function is the optimal solution. GA is a very popular optimization algorithm, and its coding and operation methods are very convenient and fast. At present, this method has been successfully applied to many fields such as image processing, control optimization, production scheduling, neural network, and machine learning and has strong universality [17].


#### 3.3.1. Problem Expression

The preparation time and processing time of each process are different, and the laying sequence and cutting sequence may be different. Therefore, the chromosome consists of two parts: one is the cutting process and the other is the laying sequence. If real numbers are used to represent the process, laying order and cutting order, the expression of a feasible problem is a numeric string, which is called chromosome. Set chromosomeXnj, where: n=1,2,…,N; j=1,2,…,J.Table1 shows the laying sequence and cutting sequence of the process, which can be represented by a feasible chromosome: 1 (5) (4), 2 (4) (5), 3 (9) (8), 4 (7) (7), 5 (1), (1), 6 (8) (10), 7 (10) (9), 8 (3) (2), 9 (2) (3), and 10 (6) (6). Figure 2 shows the time of each process.Table 1
Laying and cutting sequences of the process.
Working procedureLaying sequenceLaying time/minClipping orderCutting time/min151046249563978647679514166846101571018910831721092737106667Figure 2
Time of each process.


#### 3.3.2. Initialization of Population

All the processes are arranged in random order, which is a solution to the problem. Firstly, the algorithm randomly generates a certain number of populations. The method of generating the initial population is as follows:(i)
Step 1: initialize the parameters. sequence numberq=1; population number s (generally 50) and population set p=.(ii)
Step 2: randomly generate a real number string, that is randomly arrange a sequence of laying and cutting.(iii)
Step 3: if it is a feasible arrangement order, turn to step 4; otherwise, turn to step 2.(iv)
Step 4: if it is a new chromosome,p=p+; q=q+1. Otherwise, go to step 2.(v)
Step 5: ifq>s, then p is the initialized population set as p=P1,P2,…; otherwise, go to step 2.


#### 3.3.3. Crossover and Mutation Operators

Crossover and mutation operators play a very important role in the genetic algorithm. The new offspring has the individual characteristics of two parents.The algorithm steps of crossover operation are as follows [18]:(i)
Step 1: a bit string is randomly generated(ii)
Step 2: the bit string is corresponding to the parent string(iii)
Step 3: if the bit string is 1, the corresponding parent 1 bit is reserved in the child stringIn Step 4, if the corresponding is 0, the remaining bits are filled into the children in the order of parent 2.(i)
Step 1: first two digital bits are generated, also known as variable ectopic(ii)
Step 2: the substrings of the two variation positions are reversed


### 3.4. Replication Method of Adaptation Function and Offspring

Fitness function is an evaluation function used to evaluate whether chromosomes can survive to the next generation. It is also an optimization model requiring a solution. Algorithm: firstly, the ratio of fitness function of each chromosome is calculated. A certain number of chromosomes with the minimum ratio are used as seeds to produce the next generation population. It should be noted here that the smaller the value of the assumed fitness function, the greater the survival probability of chromosomes [19].The system is provided with 3 cloth laying machines and 1 cutting machine, andX and Y are set as working procedures; i, j, and n are used to represent the order of arrangement; CXi is the completion time of process X in sequence i; SYj is the completion time of laying when process y is in sequence j; Xij is the cutting sequence i and laying sequence j of the process [20, 21].Then the adaptation function can be expressed as follows:(1)minf=∑i=1NIi;j=1,2,…,N,where(2)Ii=SYi−CXi,CXi≤SYi,0,CXi>SYi.Therefore, the goal of algorithm optimization is to minimize the idle time of cutting equipment. In order to avoid the idle time of cutting equipment and ensure the continuous cutting, the laying time must be less than or equal to the cutting time [22].In order to prevent the population from prematurity in the process of evolution, the Roulette wheel method is used to convert the evaluation value into the number of offspring population. The calculation formula is as follows:(3)Ns=fs∑s=1Pfs,where P is the total population and Ns and fs are the numbers of copies and fitness function value of s chromosome, respectively.


## 3.1. Production Scheduling Problem

It is an efficient arrangement of the production process. It is an important module in production management. It can comprehensively plan all production processes and links. It is the key of modern production and manufacturing system. A scientific and efficient production scheduling optimization technology can improve production efficiency to a great extent [11]. The production scheduling problem is to issue production instructions for a decomposable business on the premise of maximizing the constraints such as delivery time, process, and equipment and facility resources; allocate corresponding equipment and facility resources for each production link program; and arrange production time and process, so as to realize the optimization of production cost or time. The general job shop scheduling problem can be explained by the three-parameter or four-parameter method.Considering the differentiation of additive methods, in a workshop production system, the production scheduling problem can be divided into the following categories:(1)
Single machine scheduling problem: the batch to be processed only needs one process flow and one instrument, and the whole production and processing process is completed based on these conditions. This is the simplest form of all scheduling problems [12].(2)
Parallel machine scheduling problem: the batch to be processed only needs one process flow and multiple parallel instruments with the same attributes and functions, no matter which machine can be used to process and produce workpieces.(3)
Flow shop scheduling problem: the batch to be processed requires multiple process flows. Each process has only one machine, and the institutional functions in the process are different. Each workpiece must undergo a unified process flow according to the inherent order.(4)
Flexible flow shop scheduling problem: the batch to be processed requires a number of process flows. Each process is equipped with multiple machines that cannot produce. Each workpiece must undergo a unified process flow according to the inherent order. The flexible flow shop scheduling problem is closer to the specific production status, so it is most widely used.(5)
Job shop scheduling problem: the batch to be processed requires multiple process flows. All processes must be operated on their own designated machines, and the specific process procedures of the workpiece can be different.(6)
Open shop scheduling problem: there is no restriction of an operation sequence in all workpiece processing. Based on this, the scheduling scheme is very easy to obtain. However, due to the lack of constraints, it is easy to obtain a large number of scheduling schemes that can be adopted, which makes it more difficult to select the best.If the two processing times of a machine and a workpiece do not overlap, and the production constraints can be met, the scheduling is effective. Optimal scheduling refers to the effect that the scheduling-related indicators meet the optimal level. There are many specific evaluation indicators.As can be seen from the above definition, if we want to organize production for the production processPi, we only need to determine a linear combination of its production organization C1i,C2i,…,Cjpi; the production time of the production process Pi is ti=TiT⋅Ki, the production cost of the production process Pi is ti=CiT⋅Ki, we can construct an optimal scheduling model.


## 3.2. Computer Cloth Laying and Garment Cutting Production Process

The traditional clothing production process of cloth laying and cutting mainly includes the following steps: cloth laying plan ⟶ cutting plan ⟶ cloth laying ⟶ cutting ⟶ unloading ⟶ binding [13].Usually, in the process of garment production, computers are only used to control all production links, such as computer-controlled cloth laying system, computer cutting system, etc., but the modern production process should integrate all subsystems controlled by computers to construct a computer-integrated manufacturing system. However, as far as the whole system is concerned, there is still a lack of effective management and use [14, 15]. References pointed out that once the computer automatic cutting and laying system is adopted, the more important task is how to plan the laying sequence, so as to shorten the process time of the laying and cutting system and improve the production efficiency of the process. In fact, if the laying and cutting sequence is not reasonably arranged, the idle time of the equipment will be generated, thus reducing the use efficiency of the equipment. The usual practice is to produce a feasible but not optimal laying and cutting sequence through experience and artificial operation. In this way, in order to complete the daily production task, workers and machines must increase their working hours, thus increasing the production cost. The working process is as follows: the cloth paver first paves the cloth on the cloth paving table, then moves forward for a certain distance (called “position”) and then puts the cloth layer on the cutting working face for cutting. After the first “position” is cut, the cut cloth is moved to the binding table, and the next “position” of the cloth is transferred to the cutting working position. After the cutting machine cuts a piece of clothing, it will be transferred from the existing position to the next position to be cut, and so on until all pieces of clothing are cut.


## 3.3. Optimization Method Based on Genetic Algorithm

The genetic algorithm takes the coding of decision variables as the operation object and can directly operate on structural objects such as sets, sequences, matrices, trees, and graphs. On the one hand, this method helps to simulate the process of biological genes, chromosomes, and genetic evolution and facilitates the use of genetic operators. On the other hand, the genetic algorithm has a wide range of application fields, such as function optimization, production scheduling, automatic control, image processing, machine learning, data mining, and other fields. The genetic algorithm directly uses the objective function value as the search information. It only uses the fitness function value to measure the goodness of the individual and does not involve the process of derivation and differentiation of the objective function value. Because many objective functions are difficult to derive in reality, even though there is no derivative, the genetic algorithm shows a high degree of superiority. The genetic algorithm has the characteristics of group search. Its search process starts from an initial groupP (0) with multiple individuals; on the one hand, it can effectively avoid searching for some unnecessary points. On the other hand, because the traditional single-point search method is easy to fall into a local extreme point of a single peak when searching the search space of multimodal distribution, the group search feature of the genetic algorithm can avoid such a problem, so it can reflect the parallelization of genetic algorithm and better global search.Finally, all the species that survive are those with strong adaptability to nature, and those with poor adaptability will eventually be eliminated, which is “survival of the fittest.” Its essence is the process of continuous optimization and the development of intergenerational replacement of groups. It has important practical reference significance in the field of computing. The genetic algorithm (GA) is its inspiration [16]. The algorithm is based on the theory of the existence of adapters in the theory of biological evolution, forming a high-function random, parallel, and automatic adaptive optimization algorithm. GA has a good effect in large-scale complex optimization problems. It compares the process of solving the problem to the process of intergenerational evolution and survival of individuals in the group. Finally, the best adaptive person is the best solution of the problem.In this method, the solution space of the optimization problem is transformed into the coding space, and the fitness function is used to evaluate the individual. Through repeated intergenerational evolution for many times, the optimal individual with the best value of the objective function is the optimal solution. GA is a very popular optimization algorithm, and its coding and operation methods are very convenient and fast. At present, this method has been successfully applied to many fields such as image processing, control optimization, production scheduling, neural network, and machine learning and has strong universality [17].


### 3.3.1. Problem Expression

The preparation time and processing time of each process are different, and the laying sequence and cutting sequence may be different. Therefore, the chromosome consists of two parts: one is the cutting process and the other is the laying sequence. If real numbers are used to represent the process, laying order and cutting order, the expression of a feasible problem is a numeric string, which is called chromosome. Set chromosomeXnj, where: n=1,2,…,N; j=1,2,…,J.Table1 shows the laying sequence and cutting sequence of the process, which can be represented by a feasible chromosome: 1 (5) (4), 2 (4) (5), 3 (9) (8), 4 (7) (7), 5 (1), (1), 6 (8) (10), 7 (10) (9), 8 (3) (2), 9 (2) (3), and 10 (6) (6). Figure 2 shows the time of each process.Table 1
Laying and cutting sequences of the process.
Working procedureLaying sequenceLaying time/minClipping orderCutting time/min151046249563978647679514166846101571018910831721092737106667Figure 2
Time of each process.


### 3.3.2. Initialization of Population

All the processes are arranged in random order, which is a solution to the problem. Firstly, the algorithm randomly generates a certain number of populations. The method of generating the initial population is as follows:(i)
Step 1: initialize the parameters. sequence numberq=1; population number s (generally 50) and population set p=.(ii)
Step 2: randomly generate a real number string, that is randomly arrange a sequence of laying and cutting.(iii)
Step 3: if it is a feasible arrangement order, turn to step 4; otherwise, turn to step 2.(iv)
Step 4: if it is a new chromosome,p=p+; q=q+1. Otherwise, go to step 2.(v)
Step 5: ifq>s, then p is the initialized population set as p=P1,P2,…; otherwise, go to step 2.


### 3.3.3. Crossover and Mutation Operators

Crossover and mutation operators play a very important role in the genetic algorithm. The new offspring has the individual characteristics of two parents.The algorithm steps of crossover operation are as follows [18]:(i)
Step 1: a bit string is randomly generated(ii)
Step 2: the bit string is corresponding to the parent string(iii)
Step 3: if the bit string is 1, the corresponding parent 1 bit is reserved in the child stringIn Step 4, if the corresponding is 0, the remaining bits are filled into the children in the order of parent 2.(i)
Step 1: first two digital bits are generated, also known as variable ectopic(ii)
Step 2: the substrings of the two variation positions are reversed


## 3.3.1. Problem Expression

The preparation time and processing time of each process are different, and the laying sequence and cutting sequence may be different. Therefore, the chromosome consists of two parts: one is the cutting process and the other is the laying sequence. If real numbers are used to represent the process, laying order and cutting order, the expression of a feasible problem is a numeric string, which is called chromosome. Set chromosomeXnj, where: n=1,2,…,N; j=1,2,…,J.Table1 shows the laying sequence and cutting sequence of the process, which can be represented by a feasible chromosome: 1 (5) (4), 2 (4) (5), 3 (9) (8), 4 (7) (7), 5 (1), (1), 6 (8) (10), 7 (10) (9), 8 (3) (2), 9 (2) (3), and 10 (6) (6). Figure 2 shows the time of each process.Table 1
Laying and cutting sequences of the process.
Working procedureLaying sequenceLaying time/minClipping orderCutting time/min151046249563978647679514166846101571018910831721092737106667Figure 2
Time of each process.


## 3.3.2. Initialization of Population

All the processes are arranged in random order, which is a solution to the problem. Firstly, the algorithm randomly generates a certain number of populations. The method of generating the initial population is as follows:(i)
Step 1: initialize the parameters. sequence numberq=1; population number s (generally 50) and population set p=.(ii)
Step 2: randomly generate a real number string, that is randomly arrange a sequence of laying and cutting.(iii)
Step 3: if it is a feasible arrangement order, turn to step 4; otherwise, turn to step 2.(iv)
Step 4: if it is a new chromosome,p=p+; q=q+1. Otherwise, go to step 2.(v)
Step 5: ifq>s, then p is the initialized population set as p=P1,P2,…; otherwise, go to step 2.


## 3.3.3. Crossover and Mutation Operators

Crossover and mutation operators play a very important role in the genetic algorithm. The new offspring has the individual characteristics of two parents.The algorithm steps of crossover operation are as follows [18]:(i)
Step 1: a bit string is randomly generated(ii)
Step 2: the bit string is corresponding to the parent string(iii)
Step 3: if the bit string is 1, the corresponding parent 1 bit is reserved in the child stringIn Step 4, if the corresponding is 0, the remaining bits are filled into the children in the order of parent 2.(i)
Step 1: first two digital bits are generated, also known as variable ectopic(ii)
Step 2: the substrings of the two variation positions are reversed


## 3.4. Replication Method of Adaptation Function and Offspring

Fitness function is an evaluation function used to evaluate whether chromosomes can survive to the next generation. It is also an optimization model requiring a solution. Algorithm: firstly, the ratio of fitness function of each chromosome is calculated. A certain number of chromosomes with the minimum ratio are used as seeds to produce the next generation population. It should be noted here that the smaller the value of the assumed fitness function, the greater the survival probability of chromosomes [19].The system is provided with 3 cloth laying machines and 1 cutting machine, andX and Y are set as working procedures; i, j, and n are used to represent the order of arrangement; CXi is the completion time of process X in sequence i; SYj is the completion time of laying when process y is in sequence j; Xij is the cutting sequence i and laying sequence j of the process [20, 21].Then the adaptation function can be expressed as follows:(1)minf=∑i=1NIi;j=1,2,…,N,where(2)Ii=SYi−CXi,CXi≤SYi,0,CXi>SYi.Therefore, the goal of algorithm optimization is to minimize the idle time of cutting equipment. In order to avoid the idle time of cutting equipment and ensure the continuous cutting, the laying time must be less than or equal to the cutting time [22].In order to prevent the population from prematurity in the process of evolution, the Roulette wheel method is used to convert the evaluation value into the number of offspring population. The calculation formula is as follows:(3)Ns=fs∑s=1Pfs,where P is the total population and Ns and fs are the numbers of copies and fitness function value of s chromosome, respectively.


## 4. Result Analysis

All the experimental data come from a garment factory whose main products are men’s shirts and trousers. The cloth laying and cutting equipment of the factory are all controlled by computer and produce 18000 clothes every day. Table2 shows a production task with 53 processes, of which 29 processes are the production of men’s shirts and the other 24 processes are the production of men’s pants.Table 2
Production data sheet (min).
Working procedureLaying timeCutting time1106296376469546646157181081710977106711371012291513311014281015121016121017221018910191010208102141102245102333102421102571192679192780192880192979193071193179193222933911834189351093628937615385153959404641694271194346447119452615463947615483949171050101051431552289536319Table3 shows the cutting order and idle time of the actual arrangement plan. It can be seen that the cutting time is 736 min and the total idle time is 113 min. The idle time occurs in processes 25, 28, 34, 35, and 31. Table 4 shows the cutting order and idle time of the plan arranged by the genetic algorithm. The cutting time is 627 min and there is no free time.Table 3
Cutting sequence and idle time of actual arrangement plan (min).
Clipping orderCutting timeFree time1602603604905607100810091006701070121501110013100141001510016100171001810019100201002110022100231002410025194726190271902819472919030190329034933594311912369037150331803815039904060419043604515042190441904690471504890491005115050100531905290Table 4
Cutting order and idle time of the plan using genetic algorithm (min).
Clipping orderCutting timeFree time4060161004219056049014100241003715021100111004690311902819071001310025190501003605319081002210023100441901070201004715032901710034904910033180301903590271903690260451506150399041902919048904360191001215097052903815026190511501810015100160It can be seen from Table5 that the longest end time of manual scheduling is 207 h, and the total delayed delivery time is 44 h, of which the delay times of batches 4, 5, and 7 are 7 h, 27 h, and 10 h, respectively. The maximum end time and total delay time of the genetic algorithm scheduling are 179 h and 18 h, respectively, and the delay time of batches 3 and 7 are 7 h and 11 h, respectively. It can be seen that the genetic algorithm has more advantages than the former in both scheduling objectives, so it can be seen that the process connection of the genetic algorithm scheduling is more compact, the wasted waiting time is less, and the efficient use of production equipment and resources is also achieved.Table 5
Comparison between manual scheduling and genetic algorithm scheduling (unit: h).
BatchSchedule completion timeManual scheduling of the completion timeGenetic algorithm scheduling of the completion timeManual scheduling of the delay timeGenetic algorithm scheduling delay times1144941362144911263144120151741801879875180207178276168143105716817814410816816116291681641791110156127116111561401081215611057Subtotal712215654418


## 5. Conclusion

In this article, the optimal scheduling model of computer-controlled laying and cutting workshop is established, and the optimization results of laying and cutting solved by the genetic algorithm are given. The actual calculation shows that the scheduling result of the genetic algorithm is better than the actual manual arrangement method. The cutting time planned by the genetic algorithm is 627 minutes and there is no idle time. Therefore, this method can effectively solve the optimization scheduling problem in the production process of spreading and cutting garments. With the wide use of computer cloth laying and cutting equipment, the method introduced in this article can greatly improve the production efficiency and the utilization rate of equipment.



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*Source: 2293473-2022-08-21.xml*