A genetic algorithm for searching weaving parameters for woven fabrics

Lin, Jeng-Jong

ABSTRACT

In this study, an intelligent R&D design system is used to obtain the best combination of weaving parameters for woven fabric designs. The searching mechanism, developed in the Turbo C programming environment, and the theory, based on a genetic algorithm, can find several desired solutions of weaving parameters to produce woven fabrics within controlled costs. In addition, the system can simultaneously calculate the fractional cover of the fabric for each set of surveyed solutions in order to provide the designer with options for the functionality of these fabrics. With this system, the weaving mill can integrate the resources of different divisions (e.g., design, production, and financial divisions) to achieve perfect designs for woven fabrics and enhance the enterprise’s competitive power.

Before the industrial revolution, textile design was almost wholly controlled by the makers themselves. Moreover, in addition to design, quality control, production management, sales, and marketing were all included. As highly diversified as the modern textile industry has become, such situations seem impossible now. In addition, when designing textiles, one cannot neglect all the information and knowledge related to the manufacturing process in textile engineering. Otherwise, the design work will not go smoothly through all the processes of manufacturing, and quality problems can eventually halt manufacturing.

Recent applications of computer technology in the textile field have spread widely. For example, implementing automation techniques for production processes and management procedures has become increasingly important in textile engineering. Current studies have also investigated applications of computer techniques in the design field [4, 8, 9], e.g., simulation systems for color matching, computer aided design (CAD) systems for static and dynamic states, and semantic color-generating systems for garment design. In this study, we propose an intelligent searching system theory based on a genetic algorithm to search for weaving parameters. There are five weaving parameters, i.e., warp yarn count, weft yarn count, warp yarn density, weft yarn density, and total yarn weight, which are all correlated to one another in weaving. If two or more than two parameters are unknown among them, there will be many available combinations. This study focuses mainly on using the genetic algorithm, which has an excellent searching capacity, to facilitate fabric design to obtain the best combinations of parameters while considering both manufacturing costs and quality.

It is essential for a fabric of good quality to have an appropriate weaving density. If the weaving density is too low, the fabric will obviously be too sparse to have good strength. Yet the higher the weight consumption of material yams, the higher the manufacturing costs. In the mean time, marketing and sales will become more difficult. On the other hand, lessening the weight of the material yams can decrease their consumption, but that will damage the good quality of the fabrics. How to strike a good balance between the cost and the essential weight consumption of the material yams is a key issue, and both cost and quality are taken into consideration in design.

Our system can provide several appropriate combination sets of weaving parameters that can meet a designer’s exact demand without the necessity of advance lab– manufacturing. With this system, a fabric designer can efficiently determine what the yarn count and the density of the warp and the weft yarns should be to manufacture the desired width, length, and total weight of the fabric at a pre-controlled cost. Thus, the design, production, and financial divisions can be integrated. Moreover, the fractional cover value, directly related to the air permeability and heat retaining properties of fabrics, can be calculated simultaneously for the designer to refer to when developing novel fabrics. Manufacturers can benefit from the quick response capability provided by this system, and can then enhance their own competitive abilities.

Theory

SEARCHING MECHANISM

The main goal of this study is to explore an effective way to help a fabric designer obtain several appropriate combination sets of weaving parameters in a short time. These sets are composed of four variables, warp yarn count, weft yarn count, weaving density of the warp yarn, and weaving density of the weft yarn. We know that the cost of the fabric is directly related to the weight consumption of the material yams. The more weight consumption, the higher the cost of manufacturing the fabric. In addition, the greater the weight consumption of the material yarns, the heavier the fabric, so much so as to be uncomfortable to wear.

Let’s suppose there is a weaving mill that develops a fabric whose total weight consumption is preset as 5.6 X 10^sup -7^ (lb) per square inch. For simplification, the shrinkage of the fabric during weaving is neglected. There exist many combinations of weaving parameters (i.e., both yarn count and weaving density of the warp and weft), that can be used for preset weight consumptions of the material yarns. For instance, samples A, B, and C, shown in Table I, all answer these demands. The areas of these three fabric pieces are similar-1 square inch-but they have different yam counts and weaving densities. Now the question is how a designer can easily and immediately obtain a lot of available combination sets of these four weaving parameters. In other words, it’s difficult for a designer to acquire all the possible combination sets of weaving parameters simply through common sense. In addition, in order to speed up the production rate, the weft yam count used in weaving is usually smaller than the warp yam count. Thus the weaving density of the warp yarns is usually larger than that of weft yarns during implementation. Sample D’s weaving density of warp yarn is smaller than that of its weft yam. Sample E’s warp yam count is smaller than its weft yam count. Sample F’s weaving density of warp yarn is smaller than its weft yam, and its warp yam count is smaller than its weft yarn count. Therefore, Sample D-F shown in Table I are not available for practical use in weaving engineering.

To realize the relationships between these weaving parameters, we have adopted a search method, which is a way to find the maximum or minimum point in a multidimensional space. A genetic algorithm (GA) [1, 2, 5] is a search method based on the mechanism of genetic inheritance. A genetic algorithm maintains a set of trial solutions, called a population, and operates in cycles called generations. Each individual in the population is called a chromosome, representing a solution to the problem at hand. A chromosome is a string of symbols, usually, but not necessarily, a binary bit string.

During each generation, three steps are executed. Step 1: Each member of the population is evaluated and assigned a fitness value, which serves to provide a ranking of the members. Step 2: Some members are selected for reproduction. Step 3: New trial solutions are generated by recombination operators applied to those members, which construct the new population after reproduction. The genetic algorithm is shown in Figure 1, and a brief discussion of the three basic operators of the GA is given next.

GENETIC OPERATIONS

Crossover

Crossover is the main genetic operator. It operates on two chromosomes at a time and generates offspring by combining both chromosomes’ features. A simple way to achieve crossover would be to choose a random cut-point in one parent chromosome and generate the offspring by combining the segment of one parent to the left of the cut-point with the segment of the other parent to the right of the cut-point, as shown in Figure 2. This genetic algorithm method depends to a great extent on the performance of the crossover operator used.

Example

In this study, we use our system to search for weaving parameters while the predetermined specifications are set and listed in Table III, i.e., Width = 64 in., Length = 120 yd, Total weight = 58 lb. Based on Equation 9, we can choose a known parameter (i.e., Width, L or W) to set to the left side of the equal sign of the equation. First, we choose the total weight of the material yarn (ie., W) as an already known parameter and set it to the left side of the equal sign of Equation 9. Second, using a binary coding method, we encode the unknown parameters. Generally speaking, it is not necessary for the number of bits for each variable to be the same. Nevertheless, for simplification, the four unknown parameters are all set at 4 bits in this study. By putting the searching index k^sub i^ obtained after processing the genetic algorithm into Equation 1, we can decode and obtain the four weaving parameters, i.e., N^sub 1^, N^sub 2^, n^sub 1^, n^sub 2^.

Then, putting these four parameters into Equation 9, we can determine the required weight of the raw material yams. Using Equation 10, we can compare the calculated weight W^sub g^ and the previously set weight W. The smaller the difference between the two, the closer the value of fitness to “1”. Thus, a fitness function can be formulated as Equation 10. If the fitness value is close enough to 1, we can decide whether it is necessary to go through more generations or not.

The survey results after ten generations are shown as Table IV. In this instance, if the user is not satisfied with the search result of the best fitness value 0.7531 for the first chromosome for the tenth generation shown in Table IV, he can just reset the generations, say at 20. The same (but it is not necessary to be the same) initial population, crossover probability, and mutation probability of 30, 0.6, and 0.033, respectively, remain, and he can then run the system again to search for another combination of bit strings. He expects that there exists a chromosome with a better fitness value than 0.7531.

ACCURACY AND EFFICIENCY OF IMPLEMENTATION

With the assistance of this system, many solution sets, consisting of weaving parameters (e.g., N^sub 1^, N^sub 2^, n^sub 1^, n^sub 2^), are obtained in a short time to help the designer make a decision more easily when exploring innovative fabrics. Furthermore, the system will figure out the fractional cover (i.e., C) of each solution set depending on the combination of weaving parameters generated after the iterative operation of the GA. For instance, the example shown in Table III, has a GA whose operation conditions of crossover probability, mutation probability, and initial population are set to 0.6, 0.033, and 30, respectively. The results of the tenth generation are shown in Table IV. The decoded value of the ninth chromosome (i.e., 0100010010010100) from right to left per four bits is 30.7 (= N^sub 1^, 0100), 44.0 (= N^sub 2^, 1001), 70.7 (= n^sub 1^, 0100), and 70.7 (= n^sub 2^, 0100), respectively. By putting these four decoded values into Equation 5, we can obtain the fractional cover as 0.6394, yet it conflicts with the constrained conditions mentioned above that N^sub 1^ (= 30.7) be smaller than N^sub 2^ (= 44.0). Thus, the fitness of this solution is set at zero. Among the thirty chromosomes, a fabric designer can easily choose several solution sets, whose fitness values are closer to 1 and are of appropriate fractional cover, from the results shown in Table IV to apply to the tt&D of fabric design. Thus, the designer can avoid designing a woven fabric that cannot be manufactured by the production division. Furthermore, the designer can achieve the goal of considering many essential design factors such as cost, functionality (e.g., hand, air permeability, and heat retaining properties, etc.), and the possibility of weaving during the design stage.

SHRINKAGE OF YARNS

Since our goal is to control the total consumption of yarn in the fabric, we must not neglect the shrinkage of warp and weft yams. It may be possible that different, reasonably good sets of weaving parameters (n^sub 1^, n^sub 2^, N^sub 1^, N^sub 2^) result in widely differing shrinkage values S^sub 1^ and S^sub 2^. Such shrinkage would affect the actual total weight W and thus the relative fitness of the members of the population. Based on Pierce’s model of a plain weave [3], we can obtain an equation derived by Pierce as h/p = (413)(sqaure root of)CR, where h (=(d^sub 1^ + d^sub 2^)/2) denotes crimp height, p (= 1/n) denotes thread spacing, and CR denotes crimp ratio. By taking h = (d^sub 1^ + d^sub 2^)/2 (d^sub 1^ and d^sub 2^ denote the diameters of the warp and weft yams respectively), p = 1/n (n denotes the weaving density of warp or weft yam (yams/in.), and CR = S/(1 – S) (S denotes shrinkage of warp and weft yarns (%)) into the equation hlp = (4/3)(sqaure root of)CR, we can obtain a reformulated equation, S = 9 X n^sup 2^ X (d^sub 1^ + d^sub 2^)^sup 2^/(64 + 9 X n^sup 2^ X (d^sub 1^ + d^sub 1^)^sup 2^). Using this equation, we can estimate the shrinkage of the warp and weft yarns for each solution set generated after the iterative operation of the GA. For instance, the shrinkage in the warp yarn for the first population of the tenth generation (i.e., N^sub 1^ = 52, N^sub 2^ = 22.7, n^sub 1^ = 70.7, n^sub 2^ = 70.7, C = 0.6946, and fitness = 0.7531) presented in Table IV can be estimated as 9.8% by taking n = 70, d^sub 1^ = 1/(28(sqaure root of)N^sub 1^) = 1/ (28(sqaure root of)52), and d^sub 2^ = 1/(28(sqaure root of)N^sub 2^) = 1/(28(sqaure root of)22.7) into the reformulated equation (i.e., S = 9 X n^sup 2^ X (d^sub 1^ + d^sub 2^)^sup 2^/(64 + 9 X n^sup 2^ X (d^sub 1^ + d^sub 2^)^sup 2^)), and the weft yam can be estimated as 9.8%. The decoded weight of the first population (i.e., W^sub g^) can be calculated at 45.36 (lb) using Equation 9. Finally, Equation 10 can determine the fitness of the first population to be 0.7821. Comparing the fitness value obtained by the randomly set shrinkage ratio 6.3% used in the example in Table III to that obtained by the estimated 9.8% using Pierce’s geometric model, we see that there indeed exists a little difference as expected, for one is 0.7531 and the other is 0.7821. The less accurate the randomly set shrinkage, the more different from the genuine fitness of the population. Therefore it is risky for the designer to randomly set a shrinkage ratio for the warp (i.e., S^sub 1^) and weft (i.e., S^sub 2^) yams in the fabrics during the design stage.

In order to make our system more available for practical manufacturing conditions, we are trying to collect gray fabric samples manufactured with various looms and raw material yarns. First, collections are to be divided into several groups according to loom type (e.g., air jet, rapier, gripper, etc.), material yarn ingredients, and fabric structural class to measure the shrinkage ratio of warp and weft yarns. Then, using the statistical regression method, we calculate the respective regression functions for the relationship between fractional cover C and the shrinkage ratio of the warp yarn S^sub 1^ (or the weft yam S^sub 2^) in each group. The relation equations about the influence on S^sub 1^ and S^sub 2^ can thus be simplified and achieved using only C to represent the complicated combination relationships of n^sub 1^, n^sub 2^, N^sub 1^, and N^sub 2^, which are highly related to the genuine value of S^sub 1^ and S^sub 2^ during weaving. Using Equation 5, we can calculate the fractional cover C by each known combination solution set of weaving parameters generated after iterative operation of the GA. Finally, the genuine shrinkage of warp and weft yams with specific manufacturing conditions can be estimated by using each respective calculated regression function (consisting of C and S^sub 1^, or S^sub 2^) instead of just being randomly set at a certain constant such as 6.3% by the designer for warp and weft yarns in the example shown as Table III.

Conclusions

In this study, we have successfully set up a searching mechanism based on a genetic algorithm for efficiently finding appropriate combination sets consisting of weaving densities and yam counts of material warp and weft yams to be used in manufacturing. The searching mechanism of the design system has an excellent search capacity to allow the fabric designer to obtain the best combinations of weaving parameters during manufacturing, considering costs. In addition, by integrating our R&D design system with the commercialized computer aided design system for weave structure, it becomes possible for designers to display the profile of the woven fabric from the weaving parameters surveyed by the GA directly on the monitor to enhance convenience and efficiency during design. The entire system of the design, production, and financial divisions of a company can thus be integrated.

ACKNOWLEDGMENT

We thank the National Science Council for the financial aid for this study.

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Manuscript received October 2, 2001; accepted June 28, 2002.

JENG-JONG LIN

Department of Textile Science, Van Nung Institute of Technology, Chung-Li, Tao-Yuan,

Taiwan, Republic of China

Copyright Textile Research Institute Feb 2003

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