Application of Intelligence Based Genetic Algorithm for Job Sequencing Problem on Parallel Mixed-Model Assembly Line

Transcription

1 American J. of Engineering and Appied Sciences 3 (): 5-24, 200 ISSN Science Pubications Appication of Inteigence Based Genetic Agorithm for Job Sequencing Probem on Parae Mixed-Mode Assemby ine A. Norozi, M.K.A. Ariffin and N. Ismai Department of Mechanica and Manufacturing Engineering, University Putra Maaysia, UPM Serdang, Maaysia Abstract: Probem statement: In the area of gobaization the degree of competition in the market increased and many companies attempted to manufacture the products efficienty to overcome the chaenges faced. Approach: Mixed mode assemby ine was abe to provide continuous fow of materia and fexibiity with regard to mode change. The probem under study attempted to describe the mathematica programming imitation for minimizing the overa make-span and baancing objective for set of parae ines. Resuts: A proposed mixed-integer mode ony abe to find the best job sequence in each ine to meet the probem objectives for the given number of job aotted to each ine. Hence using the proposed mathematica mode for arge size probem was time consuming and inefficient as so many job aocation vaues shoud be checked. This study presented an inteigence based genetic agorithm approach to optimize the considered probem objectives through reducing the probem compexity. A heuristic agorithm was introduced to generate the initia popuation for inteigence based genetic agorithm. Then, it started to find the best sequence of jobs for each ine based on the generated popuation by heuristic agorithm. By this means, inteigence based genetic agorithm ony concentrated on those initia popuations that produce better soutions instead of probing the entire search space. Concusion/Recommendations: The resuts obtained from inteigence based genetic agorithm were used as an initia point for fine-tuning by simuated anneaing to increase the quaity of soution. In order to check the capabiity of proposed agorithm, severa experimentations on the set of probems were done. As the tota objective vaues in most of probems coud not be improved by simuated agorithm, it proved the we performing of proposed inteigence based genetic agorithm in reaching the near optima soutions. Key words: Inteigent based genetic agorithm, simuated anneaing, mixed mode assemby ine INTRODUCTION Evoutionary computing is a research area within computer science that used for soving combinatoria optimization and compex probems which they perform base on principes of generic popuation-based heuristic techniques (Eiben and Smith, 2003). With the emergence of meta-heuristic agorithms in recent years, so many compex probems have been studied and soved by metaheuristic search techniques such as Ant coony optimization, Tabu Search, Genetic Agorithm and Simuated Anneaing have been empoyed to dea with compex scheduing probems. Many Metaheuristic agorithms were appied to overcome the compexity of sequencing probems in assemby ines probems. Genetic agorithm is introduced by Godberg (989) as it works based on the procedure of natura mechanism and natura genetic. The popuation is composed of a coection of chromosomes which each string is encoded the probem soution as a finite-ength of gens. The entire evoution process works based on natura mechanism. Evoutionary computing agorithms usuay reach to the good soutions in the reasonabe amount of time though the achieved soution can be oca or goba optimum. A two-stage fow shop probems is considered by Johnson (954) and the proposed heuristic agorithm was deveoped to minimize the competion time. By increasing the compexity of practica probems in rea word, sequence-dependent setup times become one of the most favored assumptions in the area of scheduing researches (Naderi, et a. 2008). A mixed integer programming mode is deveoped by Wagner which minimizes the makespan in permutation fow shop Corresponding Author: A. Norozi, Department of Mechanica and Manufacturing, Engineering University Putra Maaysia, UPM Serdang, Maaysia 5

2 (F m /permu/c max ) with an arbitrary number of machines. This formuation focuses on minimizing the tota ide time on the ast machine which is associated with minimizing the tota ide time on the ast machine (Naderi, 2002). A comparison of two metaheuristic search in fow-ine manufacturing ce was done by (Skorin-Kapov and Vakharia, 993). The probem focuses on sequencing the part famiies with simiar setup time and the heuristic search techniques was deveoped based on Tabu search. The resuts prove the outperforming of deveoped search techniques in comparison to previous simuated anneaing. A hybrid Simuated Anneaing and Tabu search is introduced by (in and Ying, 2009) for scheduing the nonpermutation fowshop probems. The objective considered in this probem was focus on optimizing the make-span time for non-permutation fowshop scheduing. The performance of hybrid search agorithm was compared to severa metaheuristic agorithms such as Tabu Search, ant coony optimization and simuated anneaing and the resuts confirm the we performance of hybrid approach. Probem statement: The probem under study attempts to describe the mathematica programming imitation for soving set of parae ines. A mixed-integer mode was deveoped by Wagner (Pinedo, 2002) to find the best job sequence that minimize the make-span for a singe ine. The number of jobs assigned to each ine is predetermined for a singe ine probem, whie for set of parae ines different number of jobs can be assigned to each ine that minimizes the overa make-span time of system so the mathematica mode shoud be formuated for different vaues of job aocated to every singe ine. Meanwhie this study presented an inteigence based search approach to address the job aocation probem for parae mixed-mode assemby ine to minimize the overa makespan and aso baance the ines in way that a ines have amost equa processing time. A simpe evoutionary based agorithms ike GA, SA or etc aso faced with difficuties as there is no guaranty that which configuration of job aocation provides best soution so an inteigence based genetic agorithm is deveoped to decrease the probem compexity through providing some degree of proficiency in seecting the potentia. This study is organized as foows: A description of probem under study is provided to carify the probem s assumptions and the mathematica programming mode for probem under study is described. The compexity of probem under study is discussed to demonstrate Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 understanding of research probem and an inteigence based genetic agorithm is appied to overcome the probem compexity. A numerica exampe is iustrated in the foowing. Concusion and future research are presented in the ast part. MATERIAS AND METHODS Typicay, a mixed mode assemby ine is equipped with fexibe workstations which are capabe of producing variety of product modes simiar in product characteristics continuousy and concurrenty (Groover, 200). The probem under study incudes a number of parae mixed-mode assemby ines and each ine consists of number of workstations which are capabe of serving any job. A workstation in any ine shoud be setup for the new materias requirement to be abe to serve the new set of products. Initia setup time is essentia for the first job of sequence and change over time is required to change the settings between jobs in the same ine. The foowing assumptions are considered in this research: A the assemby ines perform assemby operation independenty. The workstation time for every singe job at a workstations are specified. Once the job aocated to any ine, jobs are not aowed to shift to other assemby ines. No ine shoud be eft without job assignment. Each assemby ine represents type of fow shop system and the workstations representative of invoved machines in the fow shop system and in a arger prospect, the whoe system ikes parae machine scheduing probems. Each assemby ine acts as fow ine system in which the overa make-spam for set of parae ines is determined by the ongest competion of ine so minimizing the competion time of a ines directy effect on overa make span of system. Mode diagram of probem under study is iustrated in Fig.. Fig. : Mode diagram of parae ines 6

3 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 Mathematica programming for job aocation: The proposed mixed-integer programming mode is buit based on fow shop mode which is deveoped by Wagner (Pinedo, 2002) and it is expanded to consider the effect of initia setup time and sequentia change over time for mutipe ines. The mathematic formua is as foow: Min (Max{Cmax }) + Subject to: m n Bek () e= k= e+ k Ide time = (X * p ) + j,, ij m, j, i= j= j= ; =,, (2) k n n Setup = (C + S ) * (X ) * (X ); (3) ij ik i,k j,,k +, k= i= j i= =, n k j,k mj, (4) j= k = Process = X * P ; =,... Cmax = Setup + Ide time +Process ; =, (5) B = T T ;e =,... (6) ek e k k = e+ n k T = X *t ; =,... (7) j,k, j j= k = n X = ;k =,...k, =,... (8) j= k k = j,k, X ; j =,...n, =,... (9) k = k = j, k, X = ; j =,...n (0) j, k, i,k, j,k ij i, j +, i,k +, i,k, j,k, + j= j= i+,k, n + X * P + W W X * P = 0;K =,...,k,i =,...m, =,... n () W i = 0; i =,.. m-, =, (2) k, = 0; k =,. n-, =, (3) 7 S ik = 0; k = 2 n- (4) W 0, I 0 X ijk 0, X jk = If job j is the kth job in the sequence in ine I ik = Idea time on machine i between the processing of job in the kth and (k+)th position in assemby ine W ik = Waiting time of the job in the kth position in between machine i and i+ in the th assemby ine m = Number of workstations in assemby ine n = Number of jobs in fow shop system S ik = Initia setup time for job i in the kth position of job sequence C ij = Change over time between job i and j Ide time = Tota ide time at the ast workstation for th assemby ine. Setup = Tota setup time for th assemby ine Cmax = Competion time for th assemby ine Process = Processing time at the ast workstation of th assemby ine B ek = Tota absoute difference among process time of ine e and rest of ines t j = Tota Process time for job j T i = Tota process time of th assemby ine k = Number of jobs aocated to th assemby ine = Number of assemby ine P ij = Process time of job j at workstation i = Process time of job j at workstation m P mj The first term of objective function () attempts to minimize the overa make-span of this system is by minimizing the ongest competion time of ines. The second term of objective function attempts to baance workoad among a assemby ines by considering a jobs process time for every singe job. Minimizing the absoute vaue of tota differences in process time of a assemby ines is the procedure that is used for achieving this goa. Constraint expanation: Minimizing the makespan time in (F m /permu/c max ) is associated with minimizing the tota ide time on the ast workstation. The second set of Equation 2 is used to obtain the minimum tota ide time at the ast workstation for every singe assemby ine. Equation 3 cacuates the tota setup time by summing the initia setup time and the change over time between the different jobs in sequence for each

4 assemby ine. It is obvious that initia setup time is ony considered for the first job of sequence. Equation 4 determines the processing time at the ast workstation for every assemby ine. Generay in the simpe fow shop system, the competion time is achieved by summing the process time and ide time on the ast workstation of the corresponding ine. Equation 5 cacuates the tota competion time for every singe assemby ine by adding job s initia setup time and change over time to the fow time of the corresponding ine. Equation 6 heps to find the difference in tota process time for mutipe ines by computing the absoute difference in tota process time for ines. Equation 7 is used to attain the process time for every singe ine which is determined by summing a the jobs aocated to the assemby ines. The tota process time for every singe assemby ine is attained by summing the process times of a the jobs aocated to that assemby ine. Constraint (8) is used to dedicate a jobs to the avaiabe positions in which each job is paced at the unique position of that assemby ine. Constraint (9) ensures that each job can be paced in ony one of the avaiabe positions of sequence for each assemby ine. Constraint (0) ensures that from a the avaiabe positions in the system, each job must be processed in ony one of a avaiabe positions of sequences. The ast set of constraints show the inevitabe reation between the ide time and waiting time in each assemby ine. It represents the ogica concept of invove variabes in fow shop system. Equation 2 reveas that the waiting time for the first job in a sequence is aways equa to zero for any assemby ine. Equation 3 shows that the first workstation is aways ready to process the first job of a sequence in any assemby ine. Equation 4 iustrates that the initia setup time is ony considered for the first job of sequence and for the rest of jobs is zero. Compexity theory: The proposed mixed-integer mode is abe to find the best job sequence in each ine to meet the probem objectives for a predetermined vaue of k. specifying the best vaue of k that provides opportunity for mixed integer mode to be soved by exact methods are quite time consuming and inefficient whie the probem shoud be formuated for a possibe vaue of k. The tota permutation of job aocation to set of parae ines can be computed as foows: N c Totapermutation = n! (5) C= Am. J. Engg. & Appied Sci., 3 (): 5-24, N c = Set of configurations for job aocation to assemby ines N = Number of jobs It shoud be noted that the different number of jobs can be aocated to each ine so the tota permutations for this probem is obtained by summing the a possibe configurations of job aocation. Due to massive permutations of job aocation, inteigence based genetic agorithm is appied to probe the soution space to find the near optima soutions through reducing searching space by choosing the set of potentia members of N c that provides best job aocation and sequence that meet both probem objectives. In this case, the probem compexity is tended to n!. Probem soving procedure: A jobs invoved in the system can be assigned to set of parae assemby ine in different way in which the tota summation of a aocated jobs are fixed. This process provides different configuration of job aocation which increases the compexity of parae mixed assemby ine probems so different number of jobs can be aocated to each ine, whie ony one of them can provides potentia situation that may conduce to the best sequence of aocated jobs to meet the presumed objectives. The proposed mixedinteger mode gives the optimum soution for the given configuration of job aocation for each ine whie checking a the possibe vaue of k for arge size probems requires huge probem formuation and massive computation by exact methods. A simpe genetic agorithm aso faces with difficuties as there is no guaranty that which configuration of job aocation provides the best soution, because it s directy associated with job s process time so a configuration of job aocation shoud be checked. As can be seen from Eq. 5, this vaue can dramaticay increases in arge size probem, so checking a the configurations of job aocation woud be so time consuming. In this case, an inteigence based evoutionary agorithm shoud be appied to sove the probem and find the soutions in efficient way. In a usua genetic agorithm, the fitness function is a particuar function which quantifies the quaity of generated chromosome and these functions are usuay predetermined and specified with regard to objectives of the corresponding probem and they are usuay expressed in terms of mathematica equations or even set of rues. As in each configuration of job aocation, severa permutations of job aocation and job sequence are avaiabe so in the proposed inteigence based genetic agorithm, GA-2 is executed as a cost evauation function to find the minimum

5 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 attainabe cost for the corresponding chromosome. In this regard, the fitness function for GA- is not a specified function but the best resut that can be achieved by GA-2 is considered as a reated cost. The tota configurations of job aocation are obtained by soving the Eq. 6: = n 2, Integer (6) = Represents number of jobs assigns to the th assemby ine n = Shows the tota number of jobs in the system The best configuration of job aocation is directy depends on jobs process time so a shoud be checked to find the best soution. In order to tacke the compexity of this probem, an inteigence based genetic agorithm is proposed which provides some degree of inteigence to seect the best configuration of job aocation and et the GA-2 to find the best sequence of aocated job based on the given job aocation configuration to avoid checking a the potentia soution which is so time consuming. As iustrated in Fig. 2, a popuation of potentia soution which can meet the condition (Eq. 6) is randomy generated. The cost computation for each chromosome is done by GA-2 through finding the best sequence of jobs which is accompanied with the best job aocation. The chromosomes are sorted according to their cost vaue and proceed to the genetic operators in (GA-) for further evoution. In this process, GA- attempts to find the potentia configuration of job aocation that has higher probabiity for better job aocation and sequencing. Meanwhie this probabiity is computed by GA-2 through finding the optimum job aocation and job sequence that optimize the presumed objective functions. This process continues unti the optimum vaue is achieved. In the fina step, a simuated anneaing is used to fine-tune the best resuts obtained by inteigence based genetic agorithm to improve the quaity of soutions. GA- aims to inteigenty decrease the N c and chose those configurations of job aocation that there is a higher possibiity of optimum soution. It ets the GA-2 to mainy focus on specific vaue of N c which is directy conduced to a better near optima soution through reducing the search space. The fowchart of inteigence based GA and fine-tuning is shown in Fig. 2. As mentioned in probem soving section, GA- aims to find the best configuration of job aocation by GA-2 for finding the optimum job sequence that minimizes the objective function. The possibe soution for Equation 6 can be set of integer vaue between to n as it satisfies the condition. A chromosome for GA- is a string of ength where it is composed of some integer vaues as the tota summation of distributed jobs among ines is equa to tota number of jobs in system. The chromosome for GA- is shown in Fig. 3. P = n (7) = P = Represents number of jobs assigns to the th assemby ine n = Shows the tota number of jobs in the system Exampe: In order to distribute 0 jobs among 4 ines, the chromosome can be initiated as foows: [4, 3, 2, ] or [5, 2, 2, ] or [3, 3, 2, 2]. Fig. 2: Diagram of inteigence based genetic agorithm and fine-tuning process P P 2 P 3 Fig. 3: Chromosomes of integer numbers for GA- P Initia popuation generation: In order to generate the initia popuation for GA-, a simpe heuristic agorithm is proposed to generate possibe soutions for different configuration of job aocation which as foows: The foowing inear Programming (P) modes capabe of determining the upper and ower bounds of possibe soutions for distributing n jobs among 9

6 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 assemby ine. p aims to maximize the maximum vaue of any invoved variabes as much as possibe so it ony force one of the variabes to reach to the maximum whie the rest of variabes get the minimum vaue. The vaue obtained form P is caed upper bound for job aocation which guaranty that no ines is eft without job assignment: P { { } } Max max x ; =,..., x = n i= (8) x x ; =, + x ; =, x Integer P2 attempts to maximize the minimum vaue of a variabes so a intend to be in a minimum vaue difference. The soution achieved by P2 is caed ower bound: P2 { { } } Max max x ; =,..., x = n (9) i= x x ; =, + x ; =, x Integer In order to generate new soutions, a particuar combining technique is appied to construct new data points within the range of upper and ower point. The equation (20) and (2) are abe to generate new points where α and β are arbitrary coefficient: Z = [ α * ( X ) + ( α ) * ( Y ); = 2,, (20) z = n Z (2) = 2 α = Random number on the interva [0, ] X = th variabe in the upper bound set Y = th variabe in the ower bound set Z = th variabe in the new generated point A set of new generated points provide an initia popuation for GA- to start the inteigence based genetic agorithm An exampe is provided to carify the impemented techniques for generating new points. Twenty jobs are assigned to 4 ines in which each ine must serve at east one job: = , Integer The soution obtained by P and P2 are iustrated as foows: P = Upper bound = [x = 7, x 2 =, x 3 =, x 4 = ] P2 = ower bound = [y = 5, y 2 =5, y 3 = 5, y 4 = 5] For a given α = 0.3, a new generated point is Z 2 = [0.3*()+(-0.3)*(5)]; = 2,,4 then [Z 2 = 4, Z 3 = 4 4, Z 4 = 4] and finay Z = 20 Z 2 = 8. Meanwhie = the new generated point is [Z = 8, Z 2 = 4, Z 3 = 4, Z 4 = 4] which is produced by inear interpoating of n- variabes. The first variabe is not engaged in interpoation process to keep the number of jobs fix during the whoe generation process. A popuation of new points can be produced by generating a random vaue of α. Crossover operator: As the entire agorithm moves forward those generated points that have minimum vaue of cost function have higher probabiity to be a part of candidate region around the optimum point so continuous crossover capabe of producing new offspring inside the candidate region to do further evoution as the generation moves on. Meanwhie, a new offspring can be produced whie carrying the information from both parents. The bending methods for this probem can be done by finding ways to combine variabe vaues from the two parents into new variabe vaues whie keeping the jobs number fixed during the crossover process. A singe offspring variabe vaue comes from a combination of the n- variabes of two corresponding parents variabe. Producing new offspring can be done through generating two different random vaue of β and combining the seected parents. The entire crossover procedure is shown as foows: C = [ β * ( P ) + ( β ) * ( P 2 )]; = 2, (2 2) c = n c (23) = 2 20

7 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 β = Random number on the interva [0, ] P = th variabe in the mother chromosome P2 = th variabe in the father chromosome C = th variabe in the new generated point n = Number of jobs In the continuous crossover, some gens are randomy seected to be combined whie for the proposed crossover operator, the combining process shoud be done for a the n- variabes and it can be seen as a main difference between ordinary continuous crossover and the proposed crossover operator. Figure 4 iustrates the proposed crossover operator for the considered probem. Crossover operator is considered as a main genetic operator in genetic agorithm so mutation operator is not executed in GA-. GA-2 for Job aocation probem: GA-2 attempts to aocate jobs to the assemby ines and find the best job sequence in order to minimize the objective functions. As the best order of jobs provide the optimum soution, it fas to permutation based genetic agorithm category. The chromosome is a string of ength N where k c ; =, represents the number of jobs assigns to the th assemby ine in the C th configuration of job aocation. Figure 5 represents a chromosome of tasks and the shows how they are assigned to the workstations. Fig. 4: Continuous cross over operator for GA- Fig. 5: Chromosome of jobs 2 Generay an appropriate fitness function cosey associates with mathematica objective function which is capabe of computing the cost for each chromosome quicky. Fitness function is used to evauate the generated chromosomes to measure the optimaity of soutions. Tota objective vaue is computed by summing the vaue of make-span time, process time difference and competion time difference. The proposed fitness function is given by: F = / max{cmax } + Te Tk (24) e= k= e+ Cmax = Competion time for th assemby ine T k = Tota process time of kth assemby ine = Number of assemby ines Those chromosomes that provide minimum makespan time and aso baance the ines are seected for mating operation. This process continues unti GA-2 finds the best job sequence and aocation for the corresponding chromosome of GA-. In the next step, the second chromosome of GA- is seected and the best attainabe cost is computed through GA-2. A the computed costs for the entire popuation members are transferred to GA- for sorting operation. Tournament seection: Tournament seection is a very popuar strategy that aims to imitate natura competition of specious (Michaewicz, 996). The tournament seection works in the way that two individuas are randomy seected from the mating poo. The individua with the highest fitness vaue is seected as the winner of the tournament and the seection process continues by seecting a new tournament group randomy unti a the individuas are seected. Finay the winner of each competition is copied to the worst chromosomes. Tournament seection is appied in both GAs as seecting mechanism for choosing the best individuas within popuation. Eitism is usuay used to prevent the oss of the current fittest member of the popuation due to crossover or mutation operators and keep the best individua from generation to generation (Haupt and Haupt, 997). Eitism is appied through genetic programming. Genetic parameter setting: Genetic Agorithm parameter setting aims to increase the agorithm performance by setting the genetic parameters by optima vaues. The initia popuation is composed of a set of individuas, which are generated by using random generator. The size of popuation for both GA- and 2

8 GA-2 are fixed during a generations. Crossover is considered as most important genetic operator which combines set of information from different chromosomes and generates new offspring which captures the both individuas information. Partiay Mapped Crossover (PMX) is empoyed as crossover operator in GA-2 agorithm which the cross over rate is set based on initia popuation size. Initia popuation size is directy associated with providing more diversity of potentia soution which is varied for different compexity of probem. The compexity of job aocation probem is increasing by n! order so an appropriate eve of popuation is required to provide more diversity of potentia soutions and discourages premature convergence to oca optimums. The popuation size for GA-2 is set to 80 with 50% of cross over rate which is used by many researchers and abe to find good soution in a reasonabe amount of time (Grefenstette, 986). Mutation operator aims to provide a means to prevent agorithm from rapid convergence or premature convergence and drive agorithm to search further feasibe probem space to escape from oca optimum. For this means swap mutation is eected as mutation operator. The Mutation probabiity is set to 0.02 in GA-2 agorithms which is a typica vaue for Genetic Agorithm (eu, et a. 994). Tota number of generation is used as a stopping criterion in GA-2 program to terminate the agorithm at 300 generations. Simuated anneaing-fine-tuning: Simuated anneaing is abe to dea with noisy search space and compex probems. In the anneaing process, the temperature of the moten meta decreases unti the crysta is frozen. If the cooing procedure is done quicky some structura irreguarities wi happen in the atomic structure. The agorithm starts with a sma random perturbation to the atomic structure. If this resuts in the ower energy sate, the agorithm is repeated by using new energy state. But if the higher energy state is achieved through the new atomic structure, the new state is accepted with certain probabiity which is depends on the history of the search (Winston, 2003). Simuated anneaing is ony used to fine-tune the soution obtained by inteigence based genetic agorithm to improve the quaity of soutions. This procedure heps to find the optimum soution if it was not found in previous step. It aso confirms the we performing of proposed search agorithm when no improvement is achieved during the fine-tuning agorithm. For each probem, the best job sequence which is obtained by inteigence based genetic agorithm is used as an initia point for simuated anneaing. A neighborhood search is used as Am. J. Engg. & Appied Sci., 3 (): 5-24, a main operator for exporing different soutions. Neighborhood search generates a new atomic structure by changing the candidate soution in order to visit more potentia soutions within the search space. In this case, two jobs are randomy swapped by generating two random keys (Naderi, et a. 2008). In order to avoid agorithm to reach to the oca optimum, some worse moves might be accepted based on current temperature. The exponentia cooing scheduing is used in this research as it beieved to be an appropriate cooing schedue for the SA (Wang and Zheng, 200). The initia experiment demonstrated us that the temperature over the range is proper for fine-tuning process and the stopping temperature is fixed at 0 whie cooing temperature is set to RESUTS AND DISCUSSION In order to check the efficiency of proposed procedure, different numbers of jobs are aocated to the ines which each considered as a new probem that shoud be soved by inteigence based genetic agorithm. There are three ines in which each consists of two workstations. The first probem starts with the first 0 jobs in the system and the probem compexity is rising as the number of jobs increasing unti reach to the maximum of 5. For each probem, upper bound and ower bound is computed by P and P2 to determine the range of variation for chromosomes of GA-. Tabe iustrates the required process time and the amount of workoad in workstations for every singe job. Tabe 2 incudes the initia setup time and change over time matrix for a jobs. Metaheuristic agorithms ony guaranty the oca optimaity so the best soution that provides minimum objective vaue is seected as a near optima soution. Different experiments are done based on different number of jobs and for each probem, the chromosome vaues range between the ower bound and the upper bound within the probem. Tabe : Job process time and workoad at workstation Work oad Job Process time W W

9 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 Tabe 2: Initia setup time and changeover time J J2 J3 J4 J5 J6 J7 J8 J9 J0 J J2 J3 J4 J5 Initia setup time J J J J J J J J J J J J J J J Tabe 3: Inteigent based genetic agorithm Seected configuration Probem No. of job Upper bound ower bound of job aocation Make-span Time difference Objective vaue 0 [8,, ] [4, 3, 3] [3, 4, 3] [9,, ] [4, 4, 3] [6, 2, 3] [0,, ] [4, 4, 4] [4, 3, 5] [,, ] [5, 5, 3] [4, 6, 3] [2,, ] [5, 5, 4] [6, 6, 2] [3,, ] [5, 5, 5] [5, 6, 4] Tabe 4: Job sequence for every singe ine No. of job ine ine 2 ine Tabe 5: Fine-tuning process by SA No. Seected configuration Time Objective Probem of job of job aocation Make-span difference vaue 0 [4, 3, 3] [6, 3, 2] [5, 4, 3] [6, 4, 3] [6, 6, 2] [6, 5, 4] Tabe 6: Fina resut for job sequence for every singe ine No. of job ine ine 2 ine Tabe 3 shows the resut obtained by inteigent based genetic agorithm in which the tota objective vaue is computed by summing the make-span time and time difference between the ines which is shown in Tabe 3. The corresponding job sequence for each probem is shown in Tabe 4. As can be seen from the resuts, there is no time difference between the ines in probem 6 and aso this vaue is reach to the minimum of 20 in probem 3, 4 and 5. The seected configuration of job 23 aocation for each probem ceary prove that there is no rues to determine the best configuration of job aocation as it directy based on jobs process time even though this vaue may dramaticay change with a itte changes in jobs time even with the same number of job. The soution obtained by inteigence based genetic agorithm is used as an initia point for fine-tuning process. The soution obtained from fine-tuning process is iustrated in Tabe 6. As can be seen from Tabe 6, no improvement is achieved by SA in minimizing the second objective (time differences between ines) in a probems. It ceary confirms that the soution obtained by inteigence based genetic agorithm was optimum as the tota objective vaue for probem -4 are fixed and no further improvements are gained by SA. Therefore the inteigence based genetic agorithm is straighty directed to the optimum soution in probem -4 in a objectives. Fine-tuning process heps to find better soutions in probem 3 and 6 in finding the better job sequences which resuts in improving the first objective function (overa make-span). Athough the time differences in both probem 3 and 6 are fixed, utiizing fine-tuning agorithm eads to a shorter make-span form 050 to 009 in probem 3 and 2274 to 2230 in probem 6. CONCUSION In this study, an inteigence based genetic agorithm is appied to tacke the compexity of

10 Am. J. Engg. & Appied Sci., 3 (): 5-24, 200 sequencing probem in parae mixed-mode assemby ine probems. For soving such probems by mathematica methods the proposed muti objective mixed-integer mode shoud be formuated for severa configuration of job aocation which is quite time consuming and inefficient. A simpe genetic agorithm aso faces difficuties due to massive search space so the proposed search technique is impemented to reduce the probem compexity and overcome the required massive search space. The soving procedure initiates by generating initia popuation for different configuration of job aocation. The cost evauation for the invoved chromosomes is done by GA-2 and then the popuation is sorted according to computed cost. GA-2 tries to aocate jobs to the assemby ines in order to minimize the muti objective functions. The simuated anneaing is appied to fine-tune the obtain soution in order to increase the quaity of soutions. The achieved resuts from SA proves that proposed agorithm capabe of finding the best sequence of aocated job in the most of probems. However, there are enormous opportunities for future work of this research by engaging more practica issues of materia handing systems in order to feed the workstations which are widey used in many industry units. Meanwhie some new parameters and constraints are required to represent the system properties. Other systematic oca search agorithms can be deveoped to reduce the probem compexity as we as increasing the soution quaity. REFERENCES Eiben, A.E. and J.E. Smith, Introduction to Evoutionary Computing. st Edn., Springer, ISBN: , pp: 299. Godberg, D.E., 989. Genetic Agorithms in Search, Optimization and Machine earning. Addison- Wesey ongman Pubishing Co., Inc., Boston, MA., USA., ISBN: , pp: 442. Grefenstette, J.J., 986. Optimization of contro parameters for genetic agorithms. IEEE Transactions Syst. Man Cybernet., 6: DOI: 0.09/TSMC Groover, M.P., 200. Automation, Production Systems and Computer-Integrated Manufacturing. 2dn Edn., Prentice Ha, ondon, NJ., ISBN: 0: , pp: 856. Haupt, R.. and S.E. Haupt, 997. Practica Genetic Agorithms. Wiey-Interscience, New York, ISBN: 0: , pp: 92. Johnson, S.M., 954. Optima two-and three-stage production schedues with setup times incuded. Nava Res. ogist. Q., : DOI: 0.002/nav eu, Y.Y.,.A. Matheson and.p. Rees, 994. Assemby ine baancing using genetic agorithms with heuristic-generated initia popuations and mutipe evauation criteria. Dec. Sci., 25: DOI: 0./j tb086.x in, S.W. and K.C. Ying, Appying a hybrid simuated anneaing and Tabu search approach to non-permutation fowshop scheduing probems. Int. J. Prod. Res., 47: DOI: 0.080/ Michaewicz, Z., 996. Genetic Agorithms + Data Structures = Evoution Programs. 3rd Edn., Springer, ISBN: 0: , pp: 387. Naderi, B., M. Zandieh, A. Khaeghi Ghoshe Baagh and V. Roshanaei, An improved simuated anneaing for hybrid fowshops with sequencedependent setup and transportation times to minimize tota competion time and tota tardiness. Expert Syst. With Appi., 36: DOI: 0.06/J.ESWA Pinedo, M.., Scheduing: Theory, Agorithms and Systems. Prentice Ha, Upper Sadde River, New Jersey, pp: 586. Skorin-Kapov, J. and A.J. Vakharia, 993. Scheduing a fow-ine manufacturing ce: A tabu search approach. Int. J. Prod.. Res., 3: Wang,. and D.Z. Zheng, 200. An effective hybrid optimization strategy for job-shop scheduing probems. Comput. Res., 28: DOI: 0.06/S (99) Winston, W.., Introduction to Mathematica Programming: Appications and Agorithms. Duxbury Resource Center, ISBN: