Improving the Search Performance of Genetic Algorithm to Solve Assembly Line Balancing Problem

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1 International Journal of Business and Manageent Invention (IJBMI) ISSN (Online): , ISSN (Print): X Volue 7 Issue 4 Ver. II April PP Iproving the Search Perforance of Genetic Algorith to Solve Assebly Line Balancing Proble Mazouzi Mohaed 1,Belassiria Iad 1 1 (Mechanical departent, ENSEM/ Hassan II University, Casablanca-Morocco) Corresponding Author: Mazouzi Mohaed ABSTRACT: Assebly line balancing belongs to a class of intensively studied cobinatorial optiization probles known to be NP-hard in general. For the resolution of such proble, a genetic algorith (GA) is ipleented to solve type E of assebly line balancing proble (ALBP). The paper copares two kinds of GA, one is hybrid GA which hybridized traditional schee of GA with heuristic priority rule-based procedure, and other one is GA adopted with strategy of localized evolution. Through coputational experients using ten test probles collected fro literature, the search perforance of traditional GA is iproved and the coparisonresults between GAs is reported. Keywords: Assebly line balancing proble; genetic algorith; hybrid; strategy of localized evolution; perforance coparison Date of Subission: Date of acceptance: I. INTRODUCTION An assebly line consists of a set of sequential workstations in which repetitive sets of tasks are perfored in a liited tie called cycle tie. The classical proble of assigning tasks to the workstations, while one or ore objectives are optiized without violating to respect ain constraints and soe specific restrictions iposed on the assebly line is called the assebly line balancing proble (ALBP). In the literature, the ALBP is divided into four types of probles, these types are related to the objective function which evaluates the quality of feasible solutions. The basic optiization probles of ALPB are type I and type II, where the type I proble (ALBP-I) is the iniization of the nuber of workstations () for a given cycle tie (c), and the type II proble (ALBP-II) is used to iniize the cycle tie for a given nuber of workstations. While ALBP type E (ALBP-E) is ipleented to axiize line efficiency (E) considering the interrelationship between and c. Last kind of ALBP is a feasibility proble (ALBP-F) which is to establish whether or not a feasible line balance exists for a given cobination of and c. Researchers have published any studies on the solution for the ALBP type I, e.g., (Bautista and Pereira [1], Özcan and Toklu [2], Essafi et al. [3], Kilincci [4]). However, the ALBP-I frequently occurs when the organization desires to design new assebly lines and the production deand can be easily estiated, therefore, the cycle tie is pre-specified as a fixed input data. In the other words, the ai is to eploy as few workstations (nuber of operators) as possible while eeting a requested level of production rate. Unlike ALBP type I, the goal of ALBP type II is to iniize the cycle tie in order to axiize the level of production rate of an existing assebly line with a specific nuber of workstations. This type of proble ay exist when there are soe liitations in the assebly line which restricts the nuber of workstations, so that, the redesigns of an existing assebly line can be perfored without utilizing new workstations, or when the organization tends to produce the axiu nuber of products by using existing resources without expansion. This type also has got a great attention in the literature, e.g., (Gao et al. [5], Kulak et al. [6], Ki et al. [7], Kilincci [8], Seyed- Alagheband et al. [9]). The ALBP type E is ore general proble which cobines the ALBP type I and type II [10]. Therefore, the type E proble is presented when the production syste is flexible enough to change the nuber of workstations and cycle tie as well. However, it can be no possible to change those paraeters arbitrarily. By deand rate, a axiu cycle tie, which is the reciprocal of the production rate, is defined. Furtherore, the space available ay set an upper liit on the nuber of workstations. Line efficiency can be defined with and c being variables in certain ranges. This type of proble is less studied in literature because of its nonlinear for, such studies are treated in Wei and Chao [11], Scholl and Klein [12], Belassiria et al. [13]. In this paper, the objective function of the proble is a bi-objective function which ais to axiize line efficiency and balance workload between workstations siultaneously. Due to the cobinatorial nature of the ALBP which falls into NP-hard class of cobinatorial optiization probles. The coplexity to find an optial solution increases when the instances include ore 28 Page

2 than a few tasks and/or workstations. Furtherore, in real-life situations one can observe nuerous restrictions which ake the ALBP ore difficult to solve. Therefore, it can be tie consuing for optiu seeking ethods to obtain an optial solution within this vast search space. However, any research efforts have been conducted towards the developent of heuristics and eta-heuristics approaches such as siulated annealing (Suresh and Sahu [14]), tabu search (Peterson [15]) and genetic algoriths (Falkenauer and Delchabre [16]). Genetic algorith (GA) is one of eta-heuristics approaches and sees to be the ost popular algorith aong the. GA received an increasing attention since it perfors well for any types of optiization probles by using directed rando searches to locale optiu solutions in coplex probles. However, the standard schee of GA ay lack the ability of exploring the solution space effectively as probles get larger and ore coplex as in real life. Often, the pure GA is copleted with soe ethods to iprove its search ability. Over the last years, hybridization of GA has been considered as an iportant efficiency enhanceent technique of GA [17]. In this paper, we present a hybrid GA (h-ga) in which the heuristic priority rule-based procedure is sequentially hybridized with GA, this kind of hybridization is used in Belassiria et al. [13]. Another approach that it can proote search efficiency is a localized evolution of genetic algorith which is called a neighborhood GA (n-ga), this algorith is adapted fro Ki et al. [18]. This article copares the results obtained by h-ga and those obtained by n-ga at solving test probles which are widely used for ALBP. The rest of this paper is organized as follow. The atheatical odel is presented in section 2. Section 3 describes the two copared algoriths. Section 4 provides the experiental design and results. Conclusion is highlighted in section 5. II. FORMULATION OF ALBP-E The siplealbp usually takes into account two constraints (the precedence constraints and the cycle tie). In industry there are ore realistic situations which ake the ALBP hardly applicable. Therefore, we tackle here soe of additional constraints, which coonly has been used in real practices, in order to help line anagers to deal with assignent difficulties. The notations and atheatical odel used in this paper for the two algoriths are adapted fro Belassiria et al. [13]. 1. Notation I: set of tasks; I = {1, 2,.., i,., n}. J: set of workstation; J = {1, 2,., j,, }. C: cycle tie. t i : processing tie for task i. F i : set of successors of task i. P 0 : set of tasks that has no iediate predecessors; P 0 = {i I P(i) = }. W j : subset of all tasks that can be assigned in workstation j. W j : nuber of tasks that can be assigned in workstation j. 2. Matheatical odel Decision variables: x ij = { 1 if task i is assigned to workstation j 0 otherwise. U ij = { 1 if task i can be assigned to workstation j 0 otherwise. The ALBP-E odel cobines the SALBP-I and SALBP-II which is defined as = t su, so the idle tie C is ( C) t su.the objective function of the proble is to axiize assebly line efficiency and siultaneously iniize the idle tie, and furtherore it can be achieved by iniizing the nuber of workstations and cycle tie. WE = n i=1 t i ; i I (1) C The assebly line efficiency is always in the value of (0, 1) and it is a axiization function. When the efficiency closer to 1, the assebly line will has better perforance in which it has lower idle tie. Max F = WE (2) In addition to the cycle tie and precedence constraints, we have considered additional constraints, in which we can find in realistic situations. So the constraints of the atheatical odel are as follows: Subject to j=1 x ij = 1, i I (3) j=1 x bj j=1 x aj 0 a I, b F a (4) 29 Page

3 n i=1 (t i x ij ) + s j C (5) j=1 x aj j=1 x bj = 0, (a, b) ZP (6) x aj x bj 1, (a, b) ZN, j = 1,, (7) i I x ij W j U ij 0 (8) x ij {0, 1}, i I, j J (9a) s j 0, j J (9b) Constraint (3) ensures that each task is assigned to only one workstation. Constraint (4) describes that the assignent of a task ust be follow the precedence constraint, i.e. a task can only be assigned when its entire predecessors are finished. Constraint (5) ensures that the su of processing tie and idle tie in a workstation ust be saller than or equal to the cycle tie. Constraint (6) is copatibility zoning constraint, this type of constraints are norally related with the use of coon equipent or tooling. For exaple, if two tasks need the sae equipent or have siilar processing conditions it is desirable to assign these tasks to the sae workstation. Constraint (7) is incopatibility zoning constraint. These constraints are usually iposed when a set of tasks require different equipent, thus they cannot share the sae workstation. Or when it is not possible to perfor soe tasks in the sae workstation for safety reasons. Constraint (8) ensures that specific tasks need to be assigned into specific workstation. This is usually due to soe kind of heavy equipent that would be too expensive to ove elsewhere in the shop.equations (9a)-(9b) define doain of the decision variables. III. GENETIC ALGORITHM FOR SOLVING ALBP-E As entioned above, GAs have been proven to be very efficient and powerful in a wide variety of application particularly in cobinatorial optiization probles. Another advantage is that GA has the strength that it is flexible in dealing with various types of optiization criteria and constraints. 1. Hybrid genetic algorith (h-ga) Since the ALB proble in this study considers a large nuber of tasks and precedence restrictions. The solution of the algorith should seek to assign tasks to workstations in order to find the optial objective function, the algorith s efficiency is highly dependent on the initial solution. Therefore, by using a heuristic priority rule-based procedure, ixed with generating rando solutions a ore rich initial seeds is created. The task assignent rules used in our h-ga is proposed by Baykasoglu and Özbakir [20], and a list of task assignent rules is shown in Table 1. The flow chart of the proposed h-ga is presented in Fig. 1. The initialization of h-ga contains the creation of the initial individuals by heuristic priority rule-based procedure and rando individuals. Besides, genetic operators are used to iprove the solution quality. The proposed hga is outlined step by step as follows: Step 1: Generate an initial population of individuals obtained by the task assignent rules. Step 2: Decode all individuals and evaluate the fitness function of their corresponding solutions. Step 3: Deterine pairs which define which chroosoes will undergo crossover (selection) Step 4: Apply crossover operator to the selected pairs in order to obtain new pairs of chroosoes (offsprings). Step 5: Apply utation operator to one parent Step 6: Decode all offspring and evaluate the fitness function of their corresponding solutions Step 7: Decide which chroosoe will for new generation; to preserve the diversity of the population, the offspring, which has not duplicated with any solution in the population, replace with the poor solution. Step 8: If terination criterion is satisfied go to Step 9, else go to Step 3. Step 9: Terinate the algorith and present best solution. 2. Neighborhood genetic algorith (n-ga) Flow diagra of the proposed n-ga is depicted in Fig. 2. Initialisation of the n-ga contains generating the initial population randoly. Afterword, we adopt the strategy of localized evolution, presented by (Ki et al. [18]), that we expect can proote population diversity and search efficiency. The population fors a two diensional structure of toroidal grids. The structure of a 3 3 neighborhood is used here for the localized evolution. Let NHst denote the neighborhood including individual (s, t) and its eight neighbors in the population. The evolution of NHst proceeds while interacting with individuals within NHst. The procedure of the n-ga is outlined step as follows: 30 Page

4 Fig. 1. Flow diagra of the proposed hybrid genetic algorith TABLE I. LIST OF TASK ASSIGNMENT RULES Rule Task assignent rules no. 1 Shortest Processing Tie (SPT) 2 Longest Processing tie (LPT) 3 Miniu Total Nuber of Successor Tasks (MiTNST) 4 Maxiu Total Nuber of Successor Tasks (MaTNST) 5 Miniu Total Tie of Successor Tasks (MiTTST) 6 Maxiu Total Tie of Successor Tasks (MaTNST) 7 Miniu Total Nuber of Predecessor Tasks (MiTNPT) 8 Maxiu Total Nuber of Predecessor Tasks (MaTNPT) 9 Miniu Total Tie of Predecessor Tasks (MiTTPT) 10 Maxiu Total Tie of Predecessor Tasks (MaTTPT) Step 1: Generate a rando initial population of population. Step 2: Decode all individuals and evaluate the fitness function for each individual. Set fbest to the best individual. Step 3: Divide the population into nuerous cell. Step 4: An arbitrary cell (s, t) is selected, which sets up NHst. Step 5: Evolution of NHst Step 5.1: The fitness of each individual in NHst is evaluated. Step 5.2: Apply crossover operator to the selected parents in order to produce two offsprings. Step 5.3: Two individuals which have the worst fitness in NHst are replaced with the offspring newly produced. Step 4: An arbitrary cell (s, t) is selected, which sets up NHst. Step 5: Evolution of NHst Step 5.1: The fitness of each individual in NHst is evaluated. Step 5.2: Apply crossover operator to the selected parents in order to produce two offsprings. Step 5.3: Two individuals which have the worst fitness in NHst are replaced with the offspring newly produced. Step 5.4: Apply utation operator to the individuals in NHst. 31 Page

5 Fig. 2. Flow diagra of neighborhood genetic algorith Step 5.5: The fitness function is coputed for the newly produced individuals using the decoding ethod. If the best fitness in the newly evaluated individuals bigger than fbest, then fbest is updated with the new best fitness. Step 5.6: If the terination criteria for NHst is et, then go to Step 6. Otherwise, go to Step 5.1. Step 6: If the terination criteria is satisfied, then stop. Otherwise, go to Step 4. IV. REPRESENTATION AND INITIALISATION For solving the ALBP-E by h-ga and n-ga, a well-known task based representation is eployed to represent chroosoe structure (Sabuncuoglu et al. [19]). An individual is a string of length n (the nuber of tasks), and each gene of the chroosoe represents a task. Therefore, tasks assignent to the workstations is according to the task sequence in the chroosoe. For exaple, Fig.3. illustrates assignent of tasks to workstations according to a chroosoe for a sall-sized proble consists of 13 tasks. Fig. 3. Assignent procedure according to chroosoe 32 Page

6 To generate individuals in the initial population task assignent heuristics ethod, the following procedure is iterated. Step 1: All tasks that have not been assigned are idendified. Find a set of tasks, F, such that all their predecessors have been assigned.. Step 2: Selecting a task i in F based on the selected task assignent rule. If there are ore than one task with the sae priority, a task is selected randoly. Step 3: checking all the task constraints. Step 4: If all constraints are fulfilled, task i is assigned to the workstation and then go to step 5. Otherwise, reove the task fro F, and then go to step 2. Step 5: If all tasks have been assigned, then stop. Otherwise, go to step Genetic operators a. Crossover operator We use a special two-point crossover ethod adapted fro Belassiria et al. [13] as shown in Fig 4. in order to generate offspring fro parents, in which these two points are randoly generated. The procedure of the crossover operation is described as follows. Step 1: One integer value r between [1, n-1] are generated randoly. Step 2: The genes with values of [1, r] are copied into the sae position in child. Step 3: The alteration procedure is used to fill the second part in Offspring 1. Step 3.1: Identifying all tasks that have not been assigned in the child, UT. Step 3.2: Starting right fro the cut point of the copied part. Step 3.3: Select task i in UT, using the order of the second parent. Step 3.4:Wrapping around at the end. Step 4: Analogous for the second child, with parent roles reversed. b. Mutation operator Here we use scrable utation adapted fro Belassiria et al. [13]. One nuber between 1 and the chroosoe length is arbitrarily generated. Chroosoe parent is separated into two sections: head and tail. The new utated offspring keeps the head part of the parent, and the tail part is filled using the sae procedure used to generate initial population with rando assignent. Fig 5. represents a scrable utation ethod. Fig. 4. Recobination two point crossover 33 Page

7 Line Efficiency (WE) Fig. 5. Scrable utation V. THE EXPERIMENTS AND RESULTS In order to assess the efficiency of the copared algoriths, it is tested on the data set taken fro Scholl [21]. This proble set involves ten test probles and the suaryof the data set is given in Table 2. For each proble, we give the nuber of tasks N, the cycle tie C and the inial nuber of workstation *. If * is not equal to the theoretical iniu nuber of workstation in : = [t su /C], the sybol + is added. All experients are executed on a personal coputer with an EliteBook HP with 2.50 GHz i5-2520m CPU. The algoriths were coded by C# 6.0 (visual studio 2013). We set a genetic paraeters used for h-ga and n-ga as follows: crossover rate = 0.5, utation rate = 0.15, and the population size P z = 100. The nuber of necessary iterations is varied related to size proble. Mediusize Proble No TABLE II. COMPUTATIONAL RESULTS FOR THE TEST PROBLEMS N C Graph * Pure GA h-ga n-ga WE(%) WE(%) WE(%) Heskia , , , Lutz , , , Gunter , , ,333 Large-size Hahn , , , Warnecke , , , Tonge , , , Lutz , , , Mukherje , , , Bartholdi , , , Scholl , , , Proble No Pure GA h-ga n-ga Fig. 6. Coparison of solution quality obtained by genetic algoriths Table 2 exhibits results obtained for the 10 probles by the pure GA, h-ga and n-ga in ters of the line efficiency (WE%). To axiize line efficiency one of the paraeters or c is to odify. In this case, the cycle tie is given and the nuber of workstation is iniized. 34 Page

8 The experients for the copared GAs are repeated 10 ties and the best solution is taken. In the experiental results show that for the ost of experiental proble, the two GAs (h-ga and n-ga) provide better outcoes than pure GA, which confors that the hybridization technique and local search strategy applied to GA aintain the global diversity and iprove search perforance of pure GA to find a better perforance specially in ore coplex probles. On the other hand, if the line efficiency obtained by h-ga and n-ga for probles 1, 2, 3, 4, 5, 6, 7 and 8 are copared, the h-ga outperfors the n-ga for the large probles 9 and 10. Therefore, Sequential hybridization can provide ore perforance for large size proble. To analysis the effect of hybridization technique and strategy of localized evolution adapted to GA on the genetic search. Fig 6. shows the perforance coparison of the copared GA techniques. The curves in Figure 6 correspond to the line efficiency of the best solution attained by the three GAs over each one of the test probles. As can be seen fro this figure, seeding the initial population with good solution using a ixed quantity of solutions obtained by the assignent rules heuristics and rando assignent iproves significantly the search perforance of h-ga resulting to higher quality solutions for the large probles. VI. CONCLUSION This paper addressed ALBP type E with the objective of axiizing line efficiency. Through coputational experients, we presented a coparison of two faous technique applied to genetic algorith to iprove search perforance: hybridization and localized evolutionary. Although the h-ga and n-ga showed a better perforance than traditional GA for all test probles, which confors the effectiveness of these techniques to iprove the solution quality of traditional GA. Copared between the two techniques, it s observed that h-ga increase the solution quality especially for large-size probles. REFERENCES [1] Bautista, J., Pereira, J., A dynaic prograing based heuristic for the assebly line balancing proble. European Journal of Operational Research 194 (3), [2] Özcan, U., & Toklu, B. (2009). Balancing of ixed-odel two-sided assebly lines.coputers & Industrial Engineering, 57, [3] Essafi, M., Delore, X., Dolgui, A., & Guschinskaya, O. (2010). A MIP approach for balancing transfer line with coplex industrial constraints. Coputers &Industrial Engineering, 58, [4] Kilincci, O., Firing sequences backward algorith for siple assebly line balancing proble of type 1. Coputers & Industrial Engineering 60 (4), [5] Gao, J., Sun, L., Wang, L., Gen, M., An efficient approach for type II robotic assebly line balancing probles. 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