Spinning joint scheduling strategy and its optimization method based on data and empirical knowledge

Abstract

Spinning end breakage is a major factor limiting the efficiency of the spinning process, and this paper proposes a digital method of spinning joint management. Based on the broken ends data collected by a single spindle monitoring system and guided by the empirical knowledge obtained from a factory investigation, a genetic algorithm-based spinning joint scheduling model is built with the minimum spinning machine idle time as the optimization objective. Three different heuristic rules are introduced in generating the initial population, and their relationship with the distribution of broken ends is discussed; to curb the potential efficiency loss, the broken ends are classified by the data obtained from the single spindle monitoring, and the priority joint task is introduced in the model. The experimental results show that, compared with the traditional S-tour, the model with heuristic rule 2 can reduce the machine idle time by 43% on average, and the priority-based model can reduce it by 42% on average. They both have comparable optimization capabilities, but the priority-based model avoids more serious production loss and is the superior choice.

Keywords

Spinning end breakage single spindle monitoring joint scheduling heuristic rules broken ends topology priority-based genetic algorithm

Yarn yield and quality are the main performance indicators of a spinning factory's management level and production capacity.¹ Spinning end breakage is a key influence, as if it is not handled in time, the spinning machine will idle and cause output loss.² The impact is reflected in raw materials, labor, machinery and others. For example, a flying cotton wad will adhere to a nearby sliver, resulting in yarn nep.³ For machines without a roving self-stop device, the continuously input roving goes directly into the cotton suction, resulting in increased cotton consumption.^4,5 A worker takes 80% working time to tour and eliminate broken ends. The breakage frequency is strongly positively correlated with the labor cost and the work intensity of the workers. Chain broken ends cause certain damage to machines.^6,7 Serious damage to spinning machines or shutting them down should be avoided, as this will cause significant losses to the overall efficiency of the workshop.⁸ The above analysis shows the necessity of spinning end breakage management from the perspective of product quality, production efficiency and cost and benefit.

The solutions to broken end management can be divided into two categories: one is to reduce the breakage rate, and the other is to improve joint efficiency. Theoretically, it is difficult to propose a complete model to avoid breakage,⁹ due to the complex coupling relation in the spinning system. In practice, reducing end breakage will lower the spinning speed.¹⁰ Therefore, this paper focuses on an efficient joint. We divide the spinning jointing task into three main steps: step 1 is to find and locate the broken end; step 2 is to move it to the spindle; and step 3 is to finish the joint. For step 1, spinning broken end monitoring is a typical technology.^11–13 Researchers have explored the monitoring system through different monitoring forms,¹⁴ involving patrol monitoring and single spindle monitoring,^15–17 with an inductive sensing system or a photoelectric sensing system. From the Uster Ring Data to the Uster Ring Exper, Uster prefer inductive technology.^18,19 The photoelectric monitoring is represented by the ISM system of Rieter, whose latest product is ISM premium on G38, which can reduce the labor cost by about 5%.²⁰ The status quo is the data obtained from the above sensing technology that still remains in a simple statistic state.²¹ We found that the frequency, distribution and other information extracted from the above data can be used for the scheduling of joint tasks, reasonably planning the joint path, and realizing the lean management of the spinning end breakage. Step 3, “finish joint task,” is mainly done by hand. This manual joint mode has the problems of high labor intensity and low efficiency. Therefore, Rieter, Premier and JINGWEI Textile Machinery have released automatic joint robots.^22,23 For step 2, sequencing of the spinning joint task, in most spinning workshops, the joint path of the worker basically maintains the habit of an S-tour, which is a comprehensive search. Kang²⁴ of Donghua University proposed a joint scheduling method to notify workers to go to the joint once the broken ends signal is lighted. Due to an inaccurate signal or the strong subjectivity of the path selection made by workers, the intervention effect of this method is weak. Ma et al.²⁵ proposed an expression to calculate the importance of broken ends, and took this as the scheduling basis of the joint unit. This method is more concerned with the individual spindle and lacks planning for overall production efficiency.

The joint scheduling strategy is similar to finding the shortest path, and people mostly cope with this problem using modern heuristic algorithms. The mainstream algorithms mainly include the following²⁶: the tabu search (TS) algorithm,²⁷ which is characterized by marking objects corresponding to the searched local optimal solutions and trying to avoid these objects in further iterative searches. However, the TS algorithm has a strong dependence on the initial solution and the iterative search process is serial, not parallel, which greatly affects the efficiency of optimization. The simulated annealing (SA) algorithm is a random search algorithm based on the annealing principle²⁸; it is difficult to choose the appropriate parameters in the annealing process. The SA algorithm is suitable for large-scale practical problems, so its disadvantage is low optimization efficiency. The ant colony algorithm (ACA) is a heuristic search algorithm that simulates ant foraging behavior,²⁹ and it has the excellent characteristics of positive feedback and parallel searching, but it is only in the stage of simulation in the application, and there is no complete theory, as well as doubts about its priority. The genetic algorithm (GA) is a more general optimization algorithm,³⁰ wherein the encoding technique and genetic operation are relatively simple, and it is also more effective for the traveling salesman problem (TSP). The advantage of the GA is that the problem to be solved is coded into chromosomes and then optimized without the constraints of the function; the search process starts from a set of problem solutions instead of a single individual, which has the implicit parallel search property. The disadvantage of the GA is that for complex combinatorial optimization problems, the search time is long and sensitive to the initial population. The joint scheduling in this paper is simple in structure and adopts the GA for optimization. For its drawbacks, it will combine heuristic rules to find a balance between improving the convergence speed and seeking global optimization.

This study mainly discusses the optimization of the joint path. On the one hand, it is an extension of the value of single spindle monitoring technology. On the other hand, every joint unit, whether a joint robot, worker or worker with a scooter, will all need to be scheduled. This research helps to realize the continuity of the spinning process, and paves the way for unmanned factories with robot operation in the future. Combined with the on-line data of single spindle monitoring and the practical experience of the spinning process, this paper deeply analyzed the spinning joint scheduling task. Using the GA to optimize the joint path, the influence of different topologies, different heuristic rules and different broken ends attributes on the optimization effect is discussed.

Theoretical analysis

Indicators of the efficiency for spinning broken ends management

There are three main layouts of ring spinning machines in factories, as shown in Figure 1. According to the operation method of the tour route for workers, who adopt the method of a single line tour and double-sided care for the single row spinning machine arrangement, called the traditional S-tour, as shown in Figure 2. In some factories with a single spindle monitoring system, warning lights are installed at both ends of the machine, or a display screen is installed on the wall at one end of the workshop to assist in displaying the broken ends count. These devices assist the joint unit to find the broken ends earlier during the tour, without the need to check the condition of each spindle.

Figure 1.
Layout of the ring spinning machine: (a) ring spinning machine in a single row arrangement; (b) ring spinning machine in a double row arrangement and (c) spinning winding union in a single row arrangement.

Figure 2.
Traditional S-tour: (a) aisle by aisle and (b) skip aisle.

During the preliminary research experiments, we believe that the spinning joint scheduling problem is a nondeterministic polynomial (NP) problem,²⁶ and the joint path optimization is the same as the classical TSP. If there are n broken ends in the current area, the goal of path selection is to find the shortest distance D_c for the joint unit, where $D_{c} = \sum_{1}^{n} D_{i}$ , D_i refers to the distance from the (i–1)th to the ith joint spindle position. The research object of this paper has certain universality, and the conclusions are applicable to joint robots, scooters and workers that perform joint tasks.²⁷ We collectively call them a joint unit, which will not be repeated later. Compared to finding the shortest joint path distance, we are more concerned about the lost working time; in other words, the total idle time of the spinning machine. If there are n broken ends in the current area, let the total idling time be T, where T is the sum of the current n broken spindle’s lost working time, $T = \sum_{1}^{n} T_{i}$ , where, T_i refers to the idle time of the ith broken spindle, including the joint time of all previous broken spindles T_JT and the tour time of joint units T_TT. Here, t_JT is the time for a joint unit to finish one joint and V is the tour speed of the joint unit
$T_{i} = T_{T T} + T_{J T} = \frac{\sum_{1}^{i} D_{i}}{V} + (i - 1) t_{J T}$
(1)

$D_{s} = D_{1} + (D_{1} + D_{2}) + (D_{1} + D_{2} + D_{3}) + \dots + (D_{1} + D_{2} + D_{3} + \dots + D_{n})$
(2)

$T = \frac{D_{s}}{V} + \frac{n (n - 1)}{2} t_{J T}$
(3)

From Equation (3), it is clear that when $D_{s}$ obtains the minimum value $T$ reaches the minimum. Besides, $D_{s} - D_{c} = (n - 1) D_{1} + (n - 2) D_{2} + (n - 3) D_{3} + \dots + D_{n - 1}$ . Obviously, D_i has different percentages in D_c or D_s, and the conditions for both D_c and D_s to reach the minimum are different. This indicates that spinning joint scheduling is similar to the TSP, but not equivalent to the TSP. In order to minimize the D_s, D_n_–1 has a greater impact than D_n, which tells us the choice of starting point is very important. Therefore, we treat the spinning scheduling problem as a deformed TSP, and take the minimum value of machine idling time T as the optimization goal.

Topology of broken ends spindle distribution

Our preliminary research found that the efficiency improvement of the scheduling strategy based on the GA is highly dependent on the distribution of the broken ends.³¹ Comparing the case where there is a local concentration of broken spindles and the case where the distribution of broken ends is more dispersed, there is a significant difference in the optimization effect of the algorithm. Therefore, we use the average nearest neighbor index to measure the spatial aggregation degree of broken ends, and discuss the relationship between the distribution and the algorithm parameter settings.

The average nearest neighbor is a purely spatial clustering model, which can obtain an index indicating the degree of aggregation, including three specific indicators: observed mean distance $\bar{D_{o}}$ , expected mean distance $\bar{D_{E}}$ and nearest neighbor ratio ANN. If ANN > 1, this indicates dispersion, and vice versa indicates agglomeration. The evaluation results of all the distributions involved in this paper are shown in Table 1. The specific distribution will be presented later.

Table 1.
Topology classification of spinning end breakage distribution

Distribution D_O D_E ANN z Type

1 1774.00 2038.51 0.87 –1.63 Agglomeration

2 1820.00 2363.04 0.77 –2.49 Agglomeration

3 3364.00 2440.54 1.38 3.96 Dispersion

4 4654.00 2197.58 2.12 13.01 Dispersion

5 1030.00 2227.90 0.46 –6.17 Agglomeration

6 1612.00 2259.50 0.71 –3.24 Agglomeration

Classification and grading of broken ends

Spinning end breakage is an abnormal phenomenon in the spinning process, suggesting a failure in the previous process and signaling a loss in yarn quality. We found that the data obtained from the single spindle monitoring system mainly includes the absolute value related to production management, such as the broken ends alarm, spindle position, spindle speed, running efficiency, output, etc. We can analyze the above data and extract high-level information, such as frequency and distribution type, and use these information to optimize the traditional spinning end breakage management model. Table 2 shows the information that can be obtained by in-depth analysis of single spindle monitoring data, mainly including different types of spinning end breaks, and lists the consequences of each type, which will directly affect the joint scheduling strategy.

Table 2.
Analysis of broken end properties

No. Broken end properties Possible reasons Consequences

A Continuous multi-spindle breakage Flying cotton winding on top roller Chain broken ends

B Repeated breakage of adjacent spindles at the same time Cradle failure Group spindle discontinuation and cradle repair

C Repeated breakage of a single spindle Parts failure Single spindle shut down for maintenance

D Failure of adjacent spindles on both sides of the machine Spindle belt breakage Group spindle discontinuation and spindle belt replacement

The situation with continuous multi-spindle breakage is classified as level 1, a priority joint. According to the empirical knowledge of the spinning process, when the cotton wad is winding on the top roller, the control of the roller on the fiber becomes unstable and the fiber gradually accumulates with the roller rotation. Once the load is exceeded, and the air pressure changes due to the suction fan, the cotton mass wound on the roller and its associated flotsam will break away from the roller and the flotsam scattered around will be attracted by the moving yarn on the spindle and cause the end breakage. More seriously, due to the 70 mm spacing between the spindles and the random flight path of the flotsam, the flotsam usually causes other broken ends near its own spindle, leading to chain broken ends and multiplying the efficiency loss. Then, even if the flotsam does not cause end breakage, it will still affect the yarn quality and cause knots. Therefore, when the algorithm detects end breakage occurring in adjacent spindles, it assigns them to level 1 and orders the joint unit in the scheduling model to prioritize the jointing task for these spindles.

In the spinning process, there will be a situation in which a certain spindle breaks repeatedly; usually 2–5% of the abnormal spindles will cause 30% of the broken ends, which shows that the spindle has a certain mechanical or process failure. If the joint unit keeps working on the same spindle repeatedly, on the one hand, it increases the work load of the joint unit and besides it is ineffective work; on the other hand, the low-quality yarn produced will be degraded and there is efficiency loss. Therefore, the spindle that is determined by the system to be repeatedly broken will not enter the scheduling process, and the spindle position information goes directly to the mechanic terminal. When it is repaired, it will be reintegrated into the scheduling algorithm. In the design of the system parameters for identifying repeated broken spindles, we obtained statistics using the production data from a factory in Henan, China. We collected 24 hours of broken ends data of 115,200 spindles for 96 spinning machines, and randomly selected 16,424 data of 48 machines. The statistical object is the frequency of breakage per spindle in 24 hours, and the statistical values of every six spinning machines were set as a group of analysis samples, for a total of eight groups. Using the Box-whisker plot to observe the data, and the statistical outliers were considered as anomalous spindles.³² The statistical results are shown in the Figure 3, where a spindle is broken more than three times in the measurement time, then the system determines a level 3, suspended joint.

Figure 3.
Statistics of repeated breakage determination.

According to the above analysis about the impact of different end break types on the scheduling strategy, we introduce a priority-based GA in the scheduling model, and the ranking results are listed in Table 3.

Table 3.
Leveling of joint tasks

Level Action Broken end properties

1 Priority Continuous multi-spindle breakage >2 (A)

2 Normal Others

3 Suspended Failure of adjacent spindles on both sides of the machineRepeated breakage of adjacent spindles at the same time (D) Repeated breakage of single spindle >3 (B, C)

Experimental research

Description of the algorithm case

In this study, a spinning workshop was taken as the research object, 10 spinning machines in a single row are used as a case, where each contains 1200 spindles, and the layout is shown in Figure 4. The length of the machine is 47,650 mm, the spindle distance is 70 mm and the distance between the machines is 1500 mm. A coordinate system is established with the machine length direction as the X-axis and the vertical direction as the Y-axis, and each spindle is represented by a separate coordinate. When the joint unit enters an aisle, it can perform on both sides of the aisle, so the spindles belonging to different machines in one aisle have the same Y value. In the actual production process, the time and position of spinning end breakage have strong randomness. Based on the historical database of the single spindle monitoring system, we randomly selected six distributions, shown in Figure 5, from the database as cases for the experiment. The variety is JCF60S, and the spinning end breakage of 1000 spindles per hour is 17.

Figure 4.
Spinning machine layout.

Figure 5.
Distribution of spinning end breakage.

Model for the scheduling algorithm

Assumptions and definitions

In order to abstract the proposed spinning joint scheduling problem into a mathematical model, we assume that each joint unit manages a fixed group of spinning machines, takes the same time to complete each joint and has a 100% success rate, and has a constant speed for switching between broken spindles. In priority-based scheduling, the joint unit completes the high-level task first and proceeds to the secondary task.

Optimization goal

With the machine idling time $T$ as the optimization goal, the following functions are constructed. Here, $T_{i}$ indicates the idle time of the ith joint spindle, n indicates the total number of broken ends, $t_{i}$ indicates the idle time of the ith spindle more than the (i–1)th spindle, $D_{i}$ refers to the distance from the (i–1)th to the ith joint spindle position, $t_{J T}$ is the time for a joint unit to finish one joint and $V$ is the tour speed of the joint unit
$T = \sum_{1}^{n} T_{i}$
(4)

$T_{i} = T_{i - 1} + t_{i}$
(5)

$t_{i} = \frac{D_{i}}{V} + t_{J T}$
(6)

Since both sides of the spinning machine are free to pass, Equation (7) ensures the algorithm takes the shortest distance when the joint unit goes to the next aisle. Here, $L_{M}$ indicates the length of a spinning machine and $(x_{i}, y_{i})$ indicates the ith broken spindle coordinates
$D_{i} = {\begin{cases} | x_{i} - x_{i - 1} |, y_{i} = y_{i - 1} \\ x_{i} + x_{i - 1} + | y_{i} - y_{i - 1} |, y_{i} \neq y_{i - 1} \cap x_{i} + x_{i - 1} \leq L_{M} \\ 2 L_{M} - (x_{i} + x_{i - 1}) + | y_{i} - y_{i - 1} |, y_{i} \neq y_{i - 1} \cap x_{i} + x_{i - 1} > L_{M} \end{cases}$
(7)

On the assumption that $t_{J T}$ and $V$ are constant, $T$ can be simplified to the corresponding route length $L$ . The final optimization goal is Equation (8). Here, $L_{i}$ indicates the simplified $T_{i}$ of the ith joint spindle and $l_{i}$ indicates the simplified $t_{i}$ , the distance from the (i–1)th to the ith joint spindle position
$L = \sum_{1}^{n} L_{i}$
(8)

$L_{i} = L_{i - 1} + l_{i}$
(9)

Heuristic rules

We discussed that the path optimization of joint scheduling is a NP problem, and the time complexity is extremely high, even reaching O(n!), factorial complexity. Besides, the general GA generates the initial population randomly, so the search time is long. If the rules intervene in the process of generating the initial population, the GA combines heuristic rules to make the initial population contain better individuals, which can improve the computational efficiency of the model. After summarizing the practical experience of the cooperative factory, we agreed that going to the aisle with a high number of broken ends relatively earlier is more conducive to reducing the total efficiency loss, so we designed three different heuristic rules, shown in Table 4. If the heuristic rule intervenes completely in all populations, to form a rule domination, then the algorithm has a high risk of falling into a local optimum. Therefore, only a certain percentage of individuals in the initial population is generated by the heuristic rule intervention, and the rest of the individual genes are randomly generated sequences of numbers. In the experimental design, trials with different usage proportions, from 10%, 20% and 30% to 100% in 10 groups, were set up to determine the appropriate usage proportions of the heuristic rule.

Table 4.
Heuristic rules

Rule number Content of heuristic rules

GA-H1 The starting point of the path selects the aisle with the larger quantity of broken ends; when there are two or more aisles with the same quantity of broken ends, choose the aisle with the smaller vertical coordinate; for the broken ends in one aisle, choose the spindle with the smaller horizontal coordinate.

GA-H2 On the basis of GA-H1, for the broken ends in one aisle, choose the nearest one.

GA-H3 On the basis of GA-H2, when there are two or more aisles with the same quantity of broken ends, choose the nearest one.

GA: genetic algorithm.

Fitness function

The fitness function is shown in Equation (10), where $f_{m}$ is the fitness function of the mth individual and $L_{m}$ is the objective function value calculated by the mth individual
$f_{m} = \frac{L_{\max} - L_{m}}{L_{\max} - L_{\min}}$
(10)

Experimental environment and parameters

Applications have been implemented in the MATLAB environment following the flow of the GA in Figure 6. The experimental parameters were set as follows: the population size was set to 100, the crossover probability was 0.9, the mutation probability was 0.1 and the number of iterations was 1000. To avoid randomness in the experimental results, each set of experiments was conducted 100 times. Each set of experiments initially generates 100 sequences, which include two parts, part of which is randomly generated sequences and part of which is generated by heuristic rule intervention; thus, for each distribution, a total of 10 sets of experiments are conducted according to the heuristic rule proportion from 10% to 100%. The same experimental parameters are used in the priority-based GA scheduling model.

Figure 6.
Flow of the genetic algorithm.

Results and discussion

Efficiency improvement effect of the models

In Figure 7, We compiled the statistical results for Distributions 1–4 under different scheduling strategies. The different scheduling strategies include three main types, the traditional S-tour (S in Figure 7), the general GA scheduling (GA in Figure 7) and the GA with heuristic rule intervention, which contains three heuristic rules (GA-H1, GA-H2, GA-H3 in Figure 7), and the statistics for each heuristic rule contain the average of 10 sets of experiments using a percentage of 10% to 100%. Obviously, for the optimization of the traditional S-tour, compared with the GA, the scheduling strategy with heuristic rule intervention has a higher efficiency improvement effect. The optimization effect of the GA is less stable, and there is even an increase in machine idle time for Distribution 4. The improvement effect of GA-H1 is between 20% and 58% compared to that of the S-tour, while GA-H2 is between 23% and 61% and GA-H3 is between 24% and 60%. This shows that, by adding the intervention of heuristic rules, the optimization effect of the GA for spinning end breakage management is significantly enhanced, which can reduce the equipment idling time by half, and the enhancement effect of different heuristic rules is different. In general, the optimization effect of GA-H2 and GA-H3 is similar, which is higher than that of GA-H1.

Figure 7.
Results of five models.

Figure 8 and 9 are Box-whisker plots of the experimental results of the above four different scheduling strategies, where each group of experiments includes the computational results of 100 random sequences. From the figures, it can be seen that the GA gets more kinds of optimization results after iteration, the gap between the results is greater, the data distribution is scattered, the uncertainty of the optimization effect is higher and the convergence speed of the optimization process is slower. For example, in Distribution 1, the span of optimization results obtained by the GA is between 6000 and 11,000, and the optimization efficiency is between –15% and 30%, where there is a 24% possibility that no optimization will be produced, even extending the idling time of the machine, and a 50% possibility that more than 10% optimization efficiency will be achieved, with unstable optimization results. GA-H1, GA-H2 and GA-H3 all exhibit less variety of optimization results, the gap between results is smaller, the data distribution is concentrated, the stability of the optimization effect is better and the convergence of the optimization process is faster. For Distribution 1, the optimization results obtained for GA-H1 span between 5350 and 5750, with an optimization efficiency of more than 36%; the optimization results for GA-H2 and GA-H3 span between 5343 and 5360, with all results producing an optimization effect of more than 40%. The optimization efficiency is stable and obvious.

Figure 8.
Statistical results of the genetic algorithm.

Figure 9.
Statistical results of three heuristic rules. Distribution 1: (a) GA-H1; (b) GA-H2; (c) GA-H3. Distribution 2: (d) GA-H1; (e) GA-H2; (f) GA-H3. Distribution 3: (g) GA-H1; (h)GA-H2; (i) GA-H3. Distribution 4: (j) GA-H1; (k) GA-H2 and (l) GA-H3. GA: genetic algorithm.

Selection and use of heuristic rules

From the perspective of optimization efficiency and optimization stability, the GA and GA-H1 are eliminated. Figure 9 shows that in the process of initial population generation, the proportion of different heuristic rules has a weak effect on the computational results and no obvious law. To further compare the optimization effects of GA-H2 and GA-H3, Figure 10 provides detailed statistics on the results of the experiments. There are 11 different computational results of Distribution 1; when using GA-H2, there is a 71–82% probability of obtaining the six smaller results, while when using GA-H3, there is only a 65–79% probability. Similarly, there are seven different computational results of Distribution 2; there is a 75–84% probability of obtaining the six smaller results, while when using GA-H3, there is only a 69–78% probability. Obviously, like the two cases that are localized with concentrated broken ends, GA-H2 gives a higher probability of obtaining a better solution.

Figure 10.
Comparative analysis of GA-H2 and GA-H3: (a) Distribution 1 and (b) Distribution 2. GA: genetic algorithm.

For Distributions 3 and 4, where the broken ends are more dispersed, the experimental results show that GA-H3 enables the algorithm to obtain a better solution. For Distribution 3, only 4943.88 was obtained using GA-H2, and the worst result was 4923.08 using GA-H3. Similarly, for Distribution 4, the best result using GA-H2 is 6954.62, which is also larger than the worst result using GA-H3, 6835.58. The experimental results show that the calculation of Distribution 3 by GA-H2 and Distribution 4 by GA-H3 only obtained one value, both of which occurred due to the over-excellence of the heuristic rule, which greatly reduces the selection range of joint paths and allows the algorithm to fall into a local optimal solution. Overall, the optimization effect of the heuristic rules is affected by the distribution of the broken ends; GA-H2 is more suitable for the agglomeration distribution and GA-H3 is more suitable for the dispersion distribution.

Priority-based genetic algorithm model effect

Firstly, in Figure 11, we compiled the statistical results for Distributions 1, 2, 5 and 6 under the traditional S-tour, GA-H2 and priority-based GA models (Priority-GA in Figure 11). Compared to the traditional S-tour, priority-GA can still significantly reduce the device idle time, but the optimization is not necessarily better than that of GA-H2. For Distributions 1 and 5, priority-GA's optimization efficiency is reduced by 13% and 1%, respectively, compared to GA-H2, and for Distributions 2 and 6, priority-GA's optimization efficiency is improved by 2% and 8%, respectively, compared to GA-H2. This is because the addition of priority changes the optimization object of the model. The optimization object of GA-H2 is the current distribution, but priority-GA’s is the two distributions after dividing the broken ends into grades. In other words, the existence of priority is to avoid greater production losses in the future, for the current distribution of all broken ends, but this is not necessarily the best scheduling method, which may produce a detour or may find better solutions. For example, in Distribution 6, broken ends of level 1 exist in aisle 2 (with six breaks) and aisle 6 (with 12 breaks), and aisle 7 (10 breaks) is the aisle with most broken ends; in GA-H2, the joint unit will cross the whole aisle in the order of aisle number 6 → 7 → 2 → 4 → 5 → 9, while in the priority-GA, after the joint task of level 1 is finished, the number of broken ends in aisle 6 becomes eight, which is smaller than the 10 in the aisle 7, so the joint unit enters aisle 6 twice from one machine side, which reduces the number of passes through the whole aisle and obtains better optimization.

Figure 11.
Results of the three models. GA: genetic algorithm.

Secondly, it is clear from Figure 12 that in the priority-GA model, when the proportion of heuristic rules is 10%, the overall algorithm results are better. The algorithm tends to fall into a local optimum dilemma when the proportion is 20% or more.

Figure 12.
Statistical results of priority-based genetic algorithm.

Cost–time comparison

As for the time cost of the models, it can be seen from Table 5 that there is no significant difference in the time cost of different heuristic rules. GA-H3 is more complex than GA-H2, and the solution time is also slightly increased. The solution time of priority-GA is about twice that of GA-H2. Similarly, the addition of priority makes the algorithm perform the optimization process twice, so increasing the time cost, but this does not affect the actual production.

Table 5.
Time cost of the algorithms

Distribution Cost–time (s)

GA-H2 GA-H3 Priority-GA

1 3.77 3.83 7.03

2 3.34 3.39 6.56

3 3.28 3.31 \

4 3.54 3.57 \

5 3.55 \ 6.69

6 3.54 \ 6.63

GA: genetic algorithm.

Conclusion

This study proposes a priority-based heuristic algorithm model for spinning joint scheduling, based on the data collected by a single spindle monitoring system and empirical knowledge from a factory. Firstly, we find that the path optimization problem of the joint task is not only a problem of finding the shortest path, but also a management problem that requires comprehensive consideration of spinning production efficiency, and takes the minimum idle time of the spinning machine as the optimization goal. Secondly, combining specific spinning scenarios and empirical knowledge, we develop a series of scheduling optimization models based on GAs, the main difference in which lies in the intervention of three different heuristic rules for initial population generation.

The experimental results show that, compared with the traditional S-tour, the addition of heuristic rules can reduce the machine idle time by 37% on average, while the degree of efficiency improvement is influenced by the broken ends distribution, and GA-H2 is better optimized when the break distributions are agglomeration. Furthermore, when we study the production problems exposed by the breakages, we divide the joint task into different emergency degrees and design a priority-based scheduling optimization model, combined with the empirical knowledge of the factory. The experimental results show that compared with the traditional S-tour, the priority-GA can reduce the machine idle time by 42% on average and the GA-H2 model can reduce it by 43% on average, and there is no superiority or inferiority between the two for the optimization of the current distribution of broken ends. This shows that the priority-GA and GA-H2 have comparable optimization capabilities, but the priority-GA prioritizes broken end positions with potential risk, avoiding more serious production losses, so the priority-GA is the better choice for longer-term considerations of spinning workshop production. In the priority-GA, when the heuristic rule accounts for 10%, the algorithm can get better results, while the other proportion will make the algorithm fall into the dilemma of the local optimum. This study lays the foundation for lean management of spinning end breakage. In the future, this strategy will be widely applied to spinning production in different mills to continue optimizing the model for multi-variety production or multi-objective optimization scenarios.

Distribution	D_O	D_E	ANN	z	Type
1	1774.00	2038.51	0.87	–1.63	Agglomeration
2	1820.00	2363.04	0.77	–2.49	Agglomeration
3	3364.00	2440.54	1.38	3.96	Dispersion
4	4654.00	2197.58	2.12	13.01	Dispersion
5	1030.00	2227.90	0.46	–6.17	Agglomeration
6	1612.00	2259.50	0.71	–3.24	Agglomeration

No.	Broken end properties	Possible reasons	Consequences
A	Continuous multi-spindle breakage	Flying cotton winding on top roller	Chain broken ends
B	Repeated breakage of adjacent spindles at the same time	Cradle failure	Group spindle discontinuation and cradle repair
C	Repeated breakage of a single spindle	Parts failure	Single spindle shut down for maintenance
D	Failure of adjacent spindles on both sides of the machine	Spindle belt breakage	Group spindle discontinuation and spindle belt replacement

Level	Action	Broken end properties
1	Priority	Continuous multi-spindle breakage >2 (A)
2	Normal	Others
3	Suspended	Failure of adjacent spindles on both sides of the machineRepeated breakage of adjacent spindles at the same time (D) Repeated breakage of single spindle >3 (B, C)

Rule number	Content of heuristic rules
GA-H1	The starting point of the path selects the aisle with the larger quantity of broken ends; when there are two or more aisles with the same quantity of broken ends, choose the aisle with the smaller vertical coordinate; for the broken ends in one aisle, choose the spindle with the smaller horizontal coordinate.
GA-H2	On the basis of GA-H1, for the broken ends in one aisle, choose the nearest one.
GA-H3	On the basis of GA-H2, when there are two or more aisles with the same quantity of broken ends, choose the nearest one.

Distribution	Cost–time (s)
1	3.77	3.83	7.03
2	3.34	3.39	6.56
3	3.28	3.31	\
4	3.54	3.57	\
5	3.55	\	6.69
6	3.54	\	6.63

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by the Fundamental Research Funds for the Central Universities (2232022G-01), the Applied Basic Research Programs of “Glory of Textiles” (grant no. J201807) and the Fundamental Research Funds for the Central Universities and Graduate Student Innovation Fund of Donghua University (no. CUSF-DH-D-2022026).

ORCID iDs

Sudao Zhang

Yongshan Gao

Shanshan He

References

Alakent

Kunduracıoğlu Issever

Exploratory and predictive logistic modeling of a ring spinning process using historical data. Text Res J 2017; 87: 1643–1654.

Lappage

End breaks in the spinning and weaving of weavable singles yarns – Part 1: end breaks in spinning. Text Res J 2005; 75: 507–511.

Lappage

End breaks in the spinning and weaving of weavable singles yarns – Part 2: end breaks in weaving. Text Res J 2005; 75: 512–517.

Guo

Han

, et al. Discussion of spinning process intelligent development status. Cotton Text Tech 2020; 48: 81–84.

Hori

A statistical analysis of yarn breakage on spinning frame. J Text Mach Soc Jpn 1955; 1: 54–57.

Huang

Oxenham

Predicting end breakage rates in worsted spinning. 1. Measuring dynamic yarn strength and tension. Text Res J 1994; 64: 619–626.

Huang

Oxenham

Grosberg

Predicting end breakage rates in worsted spinning. 2. A new model for end break prediction. Text Res J 1994; 64: 717–722.

Purushothama

A practical guide to quality management in spinning. New Delhi: Woodhead Publishing, 2011, pp.186–187.

Ghosh

Ishtiaque

Rengasamy

, et al. The mechanism of end breakage in ring spinning: a statistical model to predict the end break in ring spinning. AUTEX Res J 2004; 4: 19–24.

10.

Ghosh

Majumdar

Characterizing the tensile properties of spun yarns using bivariate normal distribution. Fiber Polym 2010; 11: 642–647.

11.

Liu

Innovative development of monitoring technology for ring spinning breakage. Text Accessor 2019; 46: 42–48.

12.

Liu

Zhang

The innovation and development of yarn breakage and detection. Text Accessor 2016; 43: 60–63.

13.

Gong

The latest development in broken-end detecting technology on ring-spinning machine. China Text Lead 2012; 41: 100–104.

14.

Jin

, et al. On-line detection device for ring spun-yarn breakage based on infrared sensor. Infrared Laser Eng 2018; 48: 333–337.

15.

Detection of ring spun yarn breakage based on detecting and analyzing sound signal. J Text Res 2015; 36: 142–146.

16.

Wang

Gao

Liu

Position recognition of spinning yarn breakage based on convolution neural network. J Text Res 2018; 39: 136–141.

17.

Wang

Liu

Spinning breakage detection based on optimized Hough transform. J Text Res 2018; 39: 36–41.

18.

Gao

Liang

USTER®SENTINEL comprehensively optimizes ring spinning. China Text 2017; 68: 73 (in Chinese).

19.

Wang

Xiao

Application of Premier Ultimo single spindle spinning detection system. Cotton Test Tech 2015; 43: 77–81.

20.

Zihan Z. Rieter Group: focusing on “digitization” with a brand new image. China Text 2018; 11: 18–19.

21.

, et al. Broken yarn monitoring and data display for ring spinning frame based on database. J Text Res 2018; 39: 123–129.

22.

Anon. Ring spinning automatic joint device exhibited at Milan exhibition in 1975. Shanghai Text Sci Tech 1975; 51: 21–22.

23.

Development and prospect of automatic splitter for ring spinning frame. Text Accessor 2021; 48: 54–60.

24.

Kang

Beheaded monitoring system of research design of ring spun spinning frame. MD Thesis, Donghua University, China, 2015.

25.

Cheng

Quan

, et al. Scheduling method of joint car in spinning workshop and system using this scheduling method. Patent CN109706564A China, 2018.

26.

Fox

GC.

Physical computation. Concurr Comp Pract E 1991; 3: 627–653.

27.

Glover

Future paths for integer programming and links to artificial intelligence. Comput Oper Res 1986; 13: 533–549.

28.

Kirkpatrick

Gelatt

Vecchi

MP.

Optimization by simulated annealing. Science 1983; 220: 671–680.

29.

Colorni

Dorigo

Maffioli

, et al. Heuristics from nature for hard combinatorial optimization problems. Int T Oper Res 1996; 3: 1–21.

30.

Holland

JH.

Adaption in natural and artificial system. Ann Arbor, MI: The University of Michigan Press, 1975, pp.150–195.

31.

Cai

K-Q

Tang

Y-W

Zhang

X-J

, et al. An improved genetic algorithm with dynamic topology. Chinese Phys B 2016; 25: 7.

32.

Krummenauer

I: Box whisker plots–flexible alternative to “MSE Plots”. Klin Monatsbl Augenh 2002; 219: 613–615.