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Applicationof Multi Criteria Decision-Making Approach and the Genetic Algorithmto Determine the Quality Value of ASFW and IMC Length-DiameterBlended Fibers
Applicationof Multi Criteria Decision-Making Approach and the Genetic Algorithmto Determine the Quality Value of ASFW and IMC Length-DiameterBlended Fibers
Abstract
TheInner Mongolia Cashmere (IMC) and the Australian Superfine MerinoWool (ASFW) are natural fibers that have variability in theirproperties. The quality of a ring of spun yarn is determined byseveral factors, including the fineness, length, strength, anduniformity of the diameter of the fiber. This implies that theprocess of determining the length-diameter relationships of the spanyarn is critically important. However, the process of determining thediameter-length blend of a span yarn is quite intricate and can beconsidered as the multi-criteria decision-making (MCDM) challenge.The purpose of the present study is to examine how the simultaneouschanges that take place in the diameter as well as the length of theanimal fiber affect the key features of the spun yarn that resultfrom that fiber. In the present study, the key properties of the yarnwere predicted at the blending ratios of 87, which were thelength-diameter blend groups. This prediction was accomplished usingthe software known as Yarnspec TM software. An algorithm fordetermining the overall quality of the length-diameter blend of theanimal fiber was proposed. The algorithm took account of fourproperties of the yarn, including the unevenness, tenacity,hairiness, and elongation of the yarn. The algorithm was utilized byamalgamating the Genetic Algorithm (GA) with the Technique for OrderPreference by the similarity to the similarity to an Idea Solution(TOPSIS). The yarn tenacity, which was considered as a uniqueobjective function, was placed in the way of objective optimization.The weight of the selected length-diameter blend groups features thatwere included in the decision criteria were optimized by GA. TheTOPSIS, on the other hand, was used to determine the overall qualityof the group features. This resulted in a conclusion that the rationis the best at approximately 3 % of the fiber’s length-diametercontent. The blending yarn was found to have the most appropriatetargets in general. The proposed approach produced a length-diameterblend quality that was consistent with the predicted yarn features.
Keywords: Length-diameter blending ratio, Australian Superfine Merino Wool,Yarn properties, Multi-criteria decision making, Genetic algorithm,Inner Mongolia Cashmere.
1.Introduction
Thesuperfine luxury fibers considered as the most significant naturalfiber. The superfine fiber constitutes about 3 % of the clothing andtextile material [1]. The cashmere and wool merchants often demandfor prices that are commensurate with the overall quality of thefiber [2, 3]. The manufacturers of fabric and yarn, on the otherhand, go for better quality of the fiber since they believe that theoverall quality of the span yarn is determined by the keycharacteristics of the fiber [4]. The quality of the length-diameterblend of the fiber is determined through a complex process. Theoutcome of this process is important to the manufacturers andtraders. The quality of the length-diameter groups is influenced bykey features of the fiber, including length, diameter, and variationsin the diameter as well as the length of the fiber. The level atwhich the length-diameter fiber blend influence the quality of theyarn is diverse and tends to change with the manufacturingtechnology.
Apartfrom the length-diameter, the fiber may have varying performancescores, which is measured in terms of the properties. For an instant,some blends may have more strength, but be coarser than othervarieties. This implies that the length-diameter blends cannot beranked the same. The different ranking of the blends complicates thesituation, which creates the need for the use of MCDM approach toproduce more plausible results. This solution should yield acomprehensive quality index by incorporating significant features ofthe length-diameter blends. However, the weight of the blendproperties is expected to be commensurate with the overall quality ofthe yarn. Researchers have attempted to develop a new algorithm forthe determination of length-diameter blends quality value. Theseresearchers consider key properties of the yarn, which includeelongation, unevenness, tenacity, hairiness simultaneously. Thisalgorithm works through the amalgamation of genetic algorithm andTOPSIS. The TOPSIS is mainly used in the determination of the blend’squality value under the MCDM framework. The overall weight ofdifferent properties of length-diameter blends are optimized usingthe genetic algorithm. The correlation coefficient between predictedproperties of the span yarn and the quality value of thelength-diameter blend is determined using the Yarnspec software. Thevalue obtained from this software can be used to formulate constraintequations and the objective function of the optimization problem.
1.1.MCDM and TOPSIS
TheMCDM is an operational research that deals with the decision changesthat involve a finite number of choices and several decisioncriteria. The key properties of the length-diameter blend areconsidered as the decision criteria, while the types of blends arethe available alternatives. Different MCDM techniques (including theAnalytical Hierarchy Process, TOPSIS, and Elimination and ChoiceTranslating Reality) are widely used in the fields of management andengineering. They are used to facilitate the decision-makingproblems, which depends on the complexity of a given situation. TheAnalytical Hierarchy Process is among the most popular MCDMapproaches [15, 16]. TOPSIS is more effective than AHP, especiallywhen there is a high number of an available alternative and theperformance score of all the available choices has been identifiedobjectively.
TheTOPSIS technique was developed in the year 1980s, and its basicphilosophy holds that the selected choices ought to have the shortestgeometric distance from the longest distance and the ideal solutionfrom the worst possible solutions. This is illustrated in Figure 1.The worst solution and the idea solution have the coordinates (0, 0,0) and (1, 1, 1) respectively, in the three dimensions. Two availablealternatives A and B have different distances from the worst solutionand the ideal solution. However, alternative B appears to have abetter solution as compared to alternative A since the former has arelatively greater distance from the worst solution and lowerdistance from the idea solution. The main steps that are involved inthe TOPSIS are considered below.
Step1
Thisstep involves the identification of the relevant goal, objectives,alternatives, and the decision criteria.
Step2
Thesecond step involves the production of the decision matrix ofalternative and criteria. If the number of cotton types is M and thatof the criteria (properties of the cotton) is N, then the matrix willhave an order MXN, which is prepared as shown in the subsequentsteps.
Step3
Thisstep involves the conversion of the decision matrix in order tonormalize it to an extent that the score obtained in various scalescan be compared. The element rij of the decision matrix that has beennormalized is computed as shown below
Step5
Thefifth step provides a positive ideal solution that is abbreviated asPIS (A*) and the negative idea solution that is abbreviated as NIS(A-).
Step6
TheEuclidean distance of the available alternatives is computed from theNIS and PSI as shown in step 3.
Step7
Thisinvolves the determination of the value of the relative closenessthat is abbreviated as Ci * of the available alternatives. This isusing an equation that is indicated in step 4. The value of closeness(Ci *) is found within the range of one and zero.
Thealternatives are then arranged in a descending order on the basis ofthe value of closeness Ci *. The alternative found on the top of thislist is more preferable.
1.2.Genetic algorithm (GA)
Thegenetic algorithm is a powerful and an orthodox optimization approachthat is based on the process of natural selection. This algorithm wasdeveloped in the 1970s at the University of Michigan [19]. Thegenetic algorithm can be used to solve mathematical functions thatare discontinuous, non-differentiable, or piecewise. The GA helps inthe creation of a population of individuals with some potentialsolution to the problem optimized. A string of binary numbers is usedto code these individuals. The GA modifies the population ofindividuals repeatedly. In addition, the GA algorithms select theaforementioned individuals from the parents or the current populationdepending on their fitness. A mating pool is established using theselected individuals. The mating pool is then used to produceoffspring for the subsequent generation. The evolution of thepopulation towards the optimal solution is ensured using mutation andcross-over operations in the GA. The GA program is then terminatedusing the maximum number of generations or another criterion that canindicate some improvements in performance. Variables that are encodedin the best string of individuals’ final generation are consideredas the solution to the optimization problem. The key details of theGA algorithm are found in the standard textbook [20, 21].
2.2.Formulation of optimization problem
Anoptimization problem was formulated in order to find the optimumcombination of the weights of the properties of the length-diameterblend groups. The objective function of the operation was to maximizethe correlation coefficient between tenacity of the yarn andlength-diameter quality. This is because the later is the mostimportant property that is considered when selecting the fiber forweaving and textile processes. The correlation between the yarn’selongation, unevenness, and hairiness and the length diameter blendswas added to act as a constraint in the optimization model. Thecorrelation between IMC and ASFW and tenacity of the yarn is positiveand but negative for the unevenness of the yarn. The enhanced qualityof the blends of the length-diameter fiber enhances the tenacitywhile reducing the unevenness. For the purposes of optimization,unevenness, tenacity hairiness, and elongation values of about87-length-diameter blending ring yarn were used.
Theformulated optimization problem was as shown below:
Fitnessfunction:
Theoptimization problem shown above was solved using by the GA using thePremium Solver toolbox. The significance of the correlationcoefficient that existed between the yarn properties and thelength-diameter blends was computed using the equation below. The t0value was then compared with the t-distribution for (n-2) degrees offreedom.