R P Abeysooriya, 2 T G I Fernando. Lecturer, Department of Textile and Clothing Technology, University of Moratuwa, Sri Lanka 2

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1 Canonical Genetic Algorithm To Optimize Cut Order Plan Solutions in Apparel Manufacturing 1 R P Abeysooriya, 2 T G I Fernando 1 Lecturer, Department of Textile and Clothing Technology, University of Moratuwa, Sri Lanka 2 Lecturer, Department of Statistics and Computer Science, University of Sri Jayewardenepura, Sri Lanka ABSTRACT In practice, cutting large number of pieces with different shapes often requires a well plan of assigning number of shapes on the cut template. The working arrangement of the cut-template is treated as Cut order plan (COP). The aim is to optimize cutting templates of fabric cutting function in apparel manufacturing firms when the cut order requirement is known. This solving of cut order plan problem is usually a tedious procedure so a signi ficant amount of arithmetic operations are required if conventional heuristic algorithms being used. However, optimization of COP solutions is not guaranteed by the conventional heuristics. This study presents a canonical genetic algorithm (CGA) approach to the problems of cut order planning with the objective of finding the optimum size ratios for each cut template used to fulfill the cut order requirement. General CGA techniques were used to achieve better solutions under a self-tuning attached to the proposed algorithm. Several cut order cases were employed to justify the performance of the proposed approach. Experimental results indicated that the proposed method can yield better solutions compared to the available methodologies of generating cut-order plans available in apparel industry. Keywords: Canonical Genetic Algorithm, Cut order Plann 1. INTRODUCTION The work plan of the cutting department is termed as Cut Order Plan (COP). It entails the way certain units of material should be cut out, in order to obtain the requested number of cut-outs [1,2]. In simple terms, fabric-cutting is the process of transforming roll form fabrics into cut panels, according to the requirement of stitching production modules [1]. Wong & Leung [3] state COP as a planning process which determines the set of cut templates needed including the garment sizes in each cut template, quantities of garments from each size and number of fabric plies will be cut under each cut template [4]. The number of garments to be put on a cut template from selected sizes of the garment is defined as the size ratio of that particular cut template. In fact, size ratios are determined by cut planners to develop the corresponding cut templates for a given cut order, as the major function Previous studies of COP problem Scheduling of fabric spreading and cutting demands labour cost minimization, faster throughput, greater accuracy, higher fabric utilization and correct cut-piece fulfilment [3,5]. In research work, several authors highlight that difficulty of solving the COP problem when it entails with vast number of input parameters. The number of possible solutions propagates exponentially as the size of the problem increases [2]. Jacobs-Blecha [2] proposed heuristic approaches to solve COP problem with some assumptions and the problem was modelled to minimize the costs incurred; specifically, fabric cost, spreading cost, cutting cost and the marker making cost, in cutting process [2]. In 1998, Degraeve & Vanderbroek [6] have used linear integer programming solver to work out the objective function to determine the cutting setup cost with constrains such as cutting knife height, cutting table length. Degraeve & Vanderbroek [7] later improved their work and proposed non-linear integer programming solver to work out the same problem [5]. With the advancement of computer programming and simulation, Sykes & McGregor [8] proposed computer simulation model for cutting process in apparel manufacturing. Wong, Chan and Ip [4] generated a sequencing model for computerized spreading & cutting to minimize the idle time of the cutting department, and solved it using genetic algorithm Another study was found with the objective function of minimizing the number of cut templates for a given cut order which contains different sizes and different colours [9]. The problem was solved transforming the problem into a knapsack problem. According to the study, the solution algorithms were developed, embracing the evolutionary search optimal combinations to maximize the number of pieces of each cut template, while minimizing the number of cut templates Current Practices of COP Generation in Apparel Industry In apparel industry, COP solutions are derived in two ways. First method is the manual calculation which a cut order planner calculates and generates COP using either prescribed algorithm or random allocation of size ratios. In most cases solutions of COP problems are derived subjectively, based on the experience of production managers. Once managers realize any inefficacy in their 150

2 plan, they tend to adjust their plan in a trial-and-error approach [5]. This subjective nature wouldn t guarantee the optimal planning and scheduling of the process [5]. In second method, computer applications are used to solve COP problems based on their own heuristic algorithms. Out of those computer applications, some manufacturing firms use commercial software to generate COPs while others have developed their own software applications. Most software applications replace manual pen-and-paper planning methods with sophisticated computer-based applications [10] enabling optimized COPs with intensive calculation and faster cost predictions The COP Problem yy ii ) min aa ) jj iiii ii = 1, 2,, mm. jj The main objective of COP problem is to find YY ) = ) yy 1 yy ) mm for all k values while maximizing the ff YY ) under the given constrains. ) The corresponding size-ratio yy i ii, was used to calculate the corresponding ply numbers of the fabric layer. ) bb mmmmmm,jj = mmmmmm jj aa ) iiii yy ) ii ii = 1, 2,, mm. Definition of the cut-order (A): A particular order contains quantities of garments need to be cut in different sizes and different fabric types. m: Number of sizes AA = aa iiii mmmmmm n: Number of different fabric types i = 1, 2,,m j = 1, 2,,n Nomenclature: gg mmmmmm : Maximum number of garments in the cut template h mmmmmm : Maximum number of plies in the lay yy ii : Number of times a particular size (size i) appeared in the cut template The objective function is to optimize the number of garments included for each marker k in the cut-order and thereby minimize the cost. where subjected to ff YY ) = mmmmmm( yy ii ) bb jj ) ) YY ) = yy 1 ) mm ii=1 nn jj =1 yy mm ) cc ) ii = 0 iiii SSSSSSSS ii iiii nnnnnn uuuuuuuu 1 iiii SSSSSSSS ii iiii uuuuuuuu mm gg mmmmmm cc ) ) ii yy ii gg mmmmmm ii=1 ii, kk where jj = 1, 2,, nn 1.4 Genetic Algorithm kk = 1,2,. Genetic algorithm (GA) is a stochastic search technique which is categorized under evolutionary computation techniques [11]. GA follows the conditions of natural phenomena of evolution theory which designates the concept of survival of the fittest [12]. As a powerful solution search technique, GA has been used to find either optimal or near optimal solutions to many of real-world optimization problems [7]. One of the most challenging phenomena in optimizing a problem is that they get more complicated by the dense of the objective functions with number of constrains. In solving these complicated optimization problems, GA has been used because of its inherent searching ability which made GA more popular in both research and application areas than other stochastic search techniques. 1.5 Execution of GA Before starting the algorithm, there should be a mechanism to evaluate each possible solution in the optimization problem. As GA states, a possible solution is considered as a chromosome. The fitness function (cost function) defined at the beginning, evaluates each chromosome. Genetic parameters control the flow of algorithm, thus they are considered as inputs of GA. Number of chromosomes in the population, number of generations going to be executed, crossover probability, mutation probability, number of chromosomes exposed to elitism are some input parameters defined when the algorithm starts [13]. As the second step, GA generates random population of n chromosomes and set of possible solutions is encoded to the algorithm, with the aim of finding out the optimum or near optimum solution [14]. Then the corresponding solutions (encoded chromosomes) in population are evaluated via the fitness f(x) of each chromosome x in the population. Based on the fitness values of chromosomes, a predefined number of chromosomes are selected for mating 151

3 using an appropriate selection criterion. Selected chromosomes are then exposed for mating and some of them are undergone crossover operation at the defined crossover probability [13]. All the children chromosomes are evaluated and the children chromosomes with higher fitness values than parents, replace their parents. Number of chromosomes is also subjected to the mutation operation, according to the mutation probability [15]. Similar to crossover, highly fitted chromosomes are derived through the mutation and they replace the lower fitted parent chromosomes in the population. In basic GA, when the two main genetic operators; crossover and mutation, are executed, population is being revaluated as the fitness function to see that updated population has better fitness values than the previous population of chromosomes [16]. The new population is considered as generation 2. This population is the input population to derive generation 3. At the beginning of each generation, convergence for optimum is checked [16]. This cycle continues until either a defined number of generation or the user receives satisfactory level of optimality [15]. 2. METHODOLOGY Methodology of this study is examined under 4 subtopics; Encoding Chromosomes, Mating, Crossover & Mutation Operations for Mating Chromosomes and Elitism Encoding Chromosomes A candidate solution was encoded as a integer string to form a chromosome. For example, is one possible chromosome when five sizes of garments are in the cut order. A certain size ratio allocated for a cut template was treated as an initial potential solution for that cut template. cchrrrrrrrrrrrrrrrr yy 1 ) yy mm ) In order to generate possible chromosomes, sequence of genes was generated under a self-tuning mechanism to alter an infeasible chromosome [17]. Step4: Go to Step1. Step5: Return the correct gene to the population. The chromosome was defined randomly according to the constrains discussed under the title of the COP Problem. Then the algorithm could be used in finding the chromosome which got the maximum fitness value of each chromosome given by the fitness function ff CChrr ) Selection The selection policy employed a combination of the roulette wheel selection strategy and the elitism strategy. Both strategies ensure the chromosomes with higher fitness are more likely to become parents of new chromosomes and can strengthen the surviving ability of better chromosomes. Especially elitism strategy enables quick and distinct convergence in the algorithm [18]. Four chromosomes were selected including two elite chromosomes in each generation. Then, crossovers and mutations were employed to progression the pair of parent chromosomes to generate children Crossover & Mutation Operations for Mating Chromosomes Four random numbers were generated between 0 & 1, and each number was assigned to one particular mating chromosome. The mating chromosomes with the random number are less than the crossover probability [19] (P Crossover = 0.6), were selected as chromosomes to be crossover. Uniform order based crossover method has used with some fications modi to apply crossover operation, while satisfying the size ratio constrains mentioned in section 1.3. As uniform order based crossover, a mask string is defined randomly to control the gene are interchanged. Figure 1 explains the execution of crossover operator, while meeting the size ratio constrains mentioned in section 1.3. A mask string is fined de randomly to control the gene are inter-changed. In the figure 1, Step1: Generate a gene randomly Step2: Validate the value of the given gene in the partially filled chromosome with respective to the constrains given in section 1.3 Step2.1: If the gene satisfies the constrains, then assign it to the correct gene record; otherwise, 1 s of the mask string guides to fill the set of genes of child 1 by copying the genes from parent 1 (denoted in solid arrows). Zeros of the mask string guides fills the rest of genes in childe 1 by copying the genes from parent 2 (denoted in broken arrow), if child 1 chromosome satisfies the constrains. Step2.2: Put the gene into the interim space of bad gene. Generate another gene less than the gene in the bad gene. Go to Step2. Step3: Check the primary chromosome. If it is empt y, then go to Step5. Figure 1: Crossover operation 152

4 Similar procedure is followed to generate child 2 chromosome by copying the genes of parent first 2 and copied genes from parent 1 second. In the case of two mating chromosomes are selected, those two will be crossover with each other and will generate two children. When three mating chromosomes are selected for crossover, two highest fitted chromosomes will be taken for crossover. If there four mating chromosomes, proposed algorithm will generates two children from first and second chromosomes and another two children from third and fourth. Mutation operator is equipped to search global optima in the solution space. Mutation executes in bit wise or gene wise of the chromosomes in the population. Mutation probability defines the possibility of selecting particular chromosome for the mutation operation [18]. The mutation probability selected for the proposed algorithm was 0.1. The algorithm executes gene-wise until it finds a gene where corresponding random number is less than the mutation probability. If such gene is found, algorithm selects that chromosome for mutation. The mutation position of that chromosome is the gene position of the selected gene. Get the chromosome which a gene of it falls less than the mutation probability Select the gene position for mutation Check for other possibilities that gene can be under the constrains of size ratio (chromosome) Select possible values for gene other than existing Randomly fix one value out of possible values selected Move for the next chromosome Figure 2: Convergence Performance of the algorithm This evidences that chromosomes were being updated by the algorithm, with the aim of generating high fitted chromosomes Performance of Proposed Algorithm Compared to the Commercial COP Software Available Usage of GA indicates a significant improvement of optimizing the solutions obtained from 15 different COP problems in the industry (Figure 3). The results depict that proposed GA has more economical performance than the existing methodologies in the Sri Lankan apparel industry, in solving COP problems gg mmmmmm = 4 New gene values = rand [0, (4 - (1+1))] 3. Results and Discussion 3.1. Evaluation of Convergence for Optimization The proposed GA approach can quickly find many feasible solutions for a given set of criteria. Running the algorithm several cycles makes the proposed algorithm yield better solutions. Figure 2 indicates the average fitness values of 10 chromosomes in each generation for a practical COP problem in the industry. Figure 3: Comparison of cost values based on two different approaches of optimizing the COP solution (population =30, generations =100) 4. CONCLUSIONS AND SUGGESTIONS 4.1. Conclusion The proposed methodology is executed to maximize the number of garments in the cut templates generated in 153

5 the COP, by searching optimized size ratios of the cut templates. As a powerful optimization technique, GA has implemented to search for better solutions of size ratios by defining them as chromosomes. Outcomes of several experiments in the study confirms that GA is capable in finding optimized solutions than the heuristic based commercial COP software available in the market Limitations and future research The proposed SGA helps effectively solve the COP problems. However, in its current form, it is not efficient in solving the more complex COP problems. For instance, the proposed algorithm cannot obtain quality solutions in small population size or a smaller number of generations. Investigation of hybrid approach is suggested research which the properties of GA will be used to optimal solution and conventional heuristic methods of solving COP reduces the population size and number of generations which enables higher efficiency and greater effectiveness. [7] YoungSu Yun, "Hybrid genetic algorithm with adaptive local search scheme," Computers & Industrial Engineering, vol. 51, pp , [8] Supaporn Suwannarongsri and Deacha Puangdownreong, "Optimal assembly line balancing using tabu search with partial random permutation technique," International Journal of Management Science and Engineering Management, vol. 3, no. 1, pp. 3-18, [9] B Filipic, I Fister, and M Mernik, "Evolutionary search for optimal combinations of markers in clothing manufacturing," in GECCO, Washington, [10] Lectra. (2010) Optiplan - Cut-order Planning and Optimization. [Online]. ptiplan.html REFERENCES [1] T Peric and Z Babic, "Determining Optimal Plan of Fabric Cutting with the Multiple Criteria Programming Methods," in Proceedings of the International Multi-Conference of Engineers and Computer Scientists Hong Kong, 2008, pp [2] C Jacobs-Blecha, J C Ammons, A Schutte, and T Smith, "Cut order planning for apparel manufacturing," IIE Transactions, vol. 30, pp , [3] W Wong and S Leung, "Real-time GA-based rescheduling approach for the pre-sewing stage of an apparel manufacturing process," International Journal of Advanced Manufacturing Technology, vol. 25, pp , [4] W K Wong, C K Chan, and W H Ip, "Optimization of spreading and cutting sequencing model in garment manufacturing," Computers in Industry, vol. 43, pp. 1-10, [5] W K Wong, C K Kwong, P Y Mok, W H Ip, and C K Chan, "Optimization of manual fabric-cutting process in apparel manufacture using genetic algorithms," International Journal of Advance Manufacturing Technology, vol. 27, pp , [6] Z Degraeve and M Vanderbroek, "A Mixed Integer Programming Model for Solving a Cutting Stock Problem in the Fashion Clothing Industry," [11] Schwefel and Hans-Paul, Evolution and Optimum Seeking.: John Wiley & Sons Inc, [12] E C Brown and R T Sumichrast, "Evaluating performance advantages of grouping genetic algorithms," Engineering applications of artificial intelligence, vol. 18, pp. 1-12, [13] D E Goldberg, Genetic algorithms in search, optimization & machine learning.: Addison Wesley, [14] Y J Cao and Q H Wu, "teaching genetic algorithm using Matlab," International Journal of Electrical Engineering Education, vol. 36, pp , [15] Yeo Su Yuin Melinda, Genetic Algorithm and Acceleration Techniques, [16] Michael D. and Vose, The simple genetic algorithm: foundations and theory.: MIT Press, [17] Ruey-Shun Chen, Kun-Yung Lu, and Shien-Chiang Yu, "A hybrid genetic algorithm approach on multiobjective of assembly planning problem," Engineering Applications of Arti ficial Intelligence, vol. 15, pp , [18] Sue Ellen Haupt and Randy L. Haupt, Practical Genetic Algorithms.: Wiley-Interscience, [19] C Karr, Industrial applications of genetic algorithms. Boca Raton FL: CRC Press,