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- 1. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012 Comparison of Memetic Algorithm and PSO in Optimizing Multi Job Shop Scheduling M. Nandhini#1, S.Kanmani*2 # Research and Development Centre, Bharathiar University,Coimbatore-46 Tamil Nadu, India -14. 1 mnandhini.pu@gmail.com * Professor, Department of Information Technology, Pondicherry Engineering College, Puducherry, India -14. 2 kanmani@pec.eduAbstract—This paper proposes a memetic algorithm tooptimize multi objective multi job shop scheduling problems. It Genetic algorithms(GA), Simulated annealing(SA), Tabucomprises of customized genetic algorithm and local search of search(TS), Artificial neural networks(ANN), Greedysteepest ascent hill climbing algorithm. In genetic algorithm, the randomized adaptive search procedures(GRASP), Thresholdcustomization is done on genetic operators so that new selection, algorithms, Scatter, Variable neighborhood search(VNS),crossover and mutation operators have been proposed. The Cooperative search systems are some of the meta heuristicsexperimental study has done on benchmark multi job shop applied for optimization of combinatorial problem over 20 toscheduling problems and its versatility is proved by comparing 30 years (Schaerf S A, 1999). GA helps in diversifying theits performance with the results of simple genetic algorithm and search in order to get global optima and local searchparticle swarm optimization . techniques help in intensifying the search. This motivated us to form a hybrid model called as memetic algorithm (Olivia Index Terms— Combinatorial optimization, geneticalgorithm, particle swarm optimization, local search, multi job and Ben(2004) by combining GA with local search to get theshop scheduling, optimal solution. exertion of both. In the past years, evolution of the population in GA took I. INTRODUCTION place with the vast introduction of GA operators particularly on selection, crossover and mutation [3-7] and variety of Scheduling deals with the timing and coordination of representation of chromosomes [8-11] on variousactivities which are competing for common resources. applications like traveling salesman problem, multi job shopMJSSP is one of the most eminent machine scheduling scheduling, timetabling etc.problems in manufacturing systems, operation management, Although the existing algorithms in the literature canand optimization technology. increase the convergence rate and search capability of the The goal of MJSSP is to allocate machines to complete simple genetic algorithm to some extent, the crossover andjobs over time, subject to the constraint that each machine mutation operators used in these algorithms have notcan handle at most one job at a time. The complexity of sufficiently made to use the characteristics of the problemMJSSP increases with its number of constraints and size of structure.search space. Most of genetic operators only change the form of Scheduling problems like timetabling, job scheduling encoding and are difficult to integrate the merit of the parentetc., are the process of generating the schedule with multiple individuals. Sufficient use of information in the problemobjectives, follows multi objective combinatorial structure and the inspiration of soft constraints satisfactionoptimization or MOCO problem which decide the optimality factor, motivated us to propose Since exact approaches are inadequate and requires too domain specific reproduction operators; Combinatorialmuch computation time on large real world scheduling Partially Matched crossover(CPMX), mutation with adaptiveproblems, heuristics and meta heuristics are commonly used strategy and grade selection operator to generate the optimalin practice. Meta-heuristics usually combines some heuristic solution with minimum execution time.approaches and direct them towards solutions of better To balance the exploration and exploitation abilities,quality than those found by local search heuristics. local search (SAHC) is applied simultaneously with Meta-heuristics, using mainly two principles: local search customized GA architecture. This hybrid combination hasand population search. Local search is the name for an been tried over multi job shop scheduling (MJSSP) and itsapproach in which a solution is repeatedly replaced by versatility was proved by comparing its performance withanother solution that belongs to a well-defined neighborhood simple GA and PSO.of the first solution. In Population search methods, a The organization of the rest of the paper is as follows. The discussion on related works is given in Section 2. In Section diversified exploitation of the population of solution is 3, the problem definition of MJSSP with its constraints andperformed in each generation, resulting new generation with chromosome representation are mentioned. In Section 4,better optimal solutions. proposed methodology with design of GA operators followed 256 All Rights Reserved © 2012 IJARCET
- 2. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012by description of particle swarm optimization (PSO) in processing on that machine without interruption.Section 5. The data set and discussion on experimental results The JSSP consists of n jobs and m machines. Each joband comparison with other algorithms are done in Section 6 must go through m machines to complete its work. It isand 7. Finally, Section 8 concludes this work. considered that one job consists of m operations. Each operation uses one of m machines to complete one job’s work II. LITERATURE REVIEW for a fixed time interval. Once one operation is processed on Over two decades, a number of investigations are carried a given machine, it cannot be interrupted before it finishes theout in the evolution strategies. The striking point of using GA job’s work. In general, one job being processed on one threfers to the way how to select a combination of appropriate machine is considered as one operation noted as Oji (means jGA operators in selection, crossover , mutation probability job being processed on i machine, 1 ≤ j ≤ n, 1 ≤ i ≤ m) thand so forth. Some of the related works carried out using GA (Garey et.al., 1976 , Lawler et.al.,1993). Each machine canwith some local search for solving MJSSP are given below. process only one operation during the time interval. Ping-Teng Chang and Yu-Ting Lo (2001) modelled the The objective of MJSSP is to find an appropriatemultiple objective functions containing both multiple operation permutation for all jobs that can minimize thequantitative (time and production) and multiple qualitative makespan i.e., the maximum completion time of the finalobjectives in their integrated approach to model the JSSP, operation in the schedule of n×m operations with minimumalong with a GA/TS mixture solution approach. waiting time of jobs and machines. Kamrul Hasan S. M. et. al., (2007) proposed a hybrid The problem can be made to understand with its knowngenetic algorithm (HGA) that includes a heuristic job constraints (mandatory (Ci) & optional(Si)) / assumptions(Ai)ordering with a GA. as listed below. Christian Beirwirth (1995) proposed a new crossover C1: No machine should process more than one job at a timeoperator preserving the initial scheme structure as C2: No job should be processed by more than one machineGeneralization of OX (GOX) to solve MJSSP. The new at a timerepresentation of permutation with repetition and GOX C3:The order in which a job visits different machines issupport the cooperative aspect of genetic search for predetermined by technological constraintsscheduling problems. C4:Different jobs can run on different machines Adibi M A et al.(2010) developed dynamic job shop simultaneouslyscheduling that consists of variable neighborhood search C5:At the moment T, any two operations of the same job(VNS), a trained artificial neural network (ANN). ANN cannot be processed at the same timeupdates parameters of VNS at any rescheduling. A1: Processing time on each machine is known Takeshi Yamada and Ryohei Nakano (1996) presented S1: Idle time of machines may be reducedmulti-step crossover operators fusion (MSXF) with a S2: Waiting time of jobs may be reducedneighborhood search algorithm for JSS. MSXF searches for agood solution in the problem space by concentrating itsattention on the area between the parents. GA/MSXF could Mathematical Modeling of Constraints:find near-optimal solutions. Rui Zhang (2011) presented a PSO algorithm based on Entities used in mathematical representation ofLocal Perturbations for the JSSP. In his work, a local search constraints are given below.procedure based on processing time perturbations is designed J (j1, j2, j3) :Jobsand embedded into the framework of PSO for MSSP model. M (m1, m2, m3) :Machines In this paper, we attempt to introduce a new customized O (01, 02, 03) :Sequence of operations for a jobGA algorithm which has the strength of improving TS :Processing time of an operationoptimality obtained through satisfaction of multi soft Cmax :Makespanconstraints where crossover and mutation operators are M[j][ts] ->m : machine name with job j at time tsdesigned according to the problem structure. To improve the J[m][ts] -> j : job name on machine m at time tsoutcome of GA operators, proposed to apply SAHC local Mac[j][o][ts] ->m: machine name with operation o of jobsearch. j at time ts Also, the optimization mechanism of the traditional PSOis analyzed and a general optimization model based on swarm Capacity Constraintsintelligence is proposed to solve MJSSP. C1: No machine may process more than one job at a time. It is showed that this customized GA with local search m1 M , j1, j 2 J , ts TScould give better optimal solution than simple GA and PSO. ifM [ j1][ts ] m1, M [ j 2][ts ] m1This proposed algorithm is described in the following C2: No job may be processed by more than one machine at asection. time. m1, m2 M , j J , ts TS III. MULTI JOB SHOP SCHEDULING ifJ [ m1][ts ] j , J [ m2][ts ] j The job shop scheduling problem (JSSP) can be describedas follows: given n jobs, each composed of m operations that C3: The order in which a job visits different machines ismust be processed on m machines. Each operation uses one predetermined by technological constraints.of the m machines for a fixed duration. Each machine canprocess at most one operation at a time and once an operationinitiates processing on a given machine it must complete 257 All Rights Reserved © 2012 IJARCET
- 3. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012 j J , constraints S1 and S2 in the proposed objective functions to m,1, m 2...mm M , o1, o 2,..om O, get wealthy chromosomes and is proposed as follows. j[o1][ts ] m1, j[o 2][ts ] m 2,.... Minimize Z = Min (Makespan+ Jobs Waiting Time+ j[on][ts ] mm | o1 o 2 ..om; Machines Waiting Time) Where, Job No. i : 1..m ; Machine No. j: 1..nC4: Different jobs can run on different machines 2) Selection: Selection is the process of choosing parents simultaneously. from the generated population to undergo genetic operations like mutation or crossover. j1, j 2 J , m1, m2 M , ts TS , ifj1 j 2thenM [ j1][ts ] m1, M [ j 2][ts ] m2 a) Grade Selection : The problem of local searchPrecedence Constraints algorithms in finding optimal solution isC5: At the moment T, any two operations of the same job terminating in local optimal solution. The cannot be processed at the same time. global optimality is made possible by ts TS , j J , o1, o2 j , introducing variety in the population. In GA, m1, m2 M , the feature of individuals is exploited by the ifMac [j][o1][ts] m1 then Mac[j][o2][ts] m2 recombination operators. This trails theSoft Constraints individuals to undergo problem specificS1: Idle time of machines may be reduced. recombination operation. It is the striking m M , idleTime(m) Min{t} point of proposing this selection operator.S2: Waiting time of jobs may be reduced. This takes chromosomes randomly from j J , waitTime( j ) Min{t} combination of groups decided based on fitness value such as worst, worst; worst,Chromosome Representation better; worst, best; better, better; better, best; In our work, each state is represented as an array of and best, best and mating those chromosomesstructures. Each structure consists of job name and its result in salient features. Hence, random withoperation as members. In this representation, the guided selection is done.chromosome consists of n*m genes. Each job will appear mtimes exactly. By scanning the chromosome from left to b) Procedure of Grade Selection: Each group isright, the k-th occurrence of a job number refers to the k-th formed with the chromosomes of similaroperation in the technological sequence of this job. This nature. To form the groups, the standardmethod followed with heuristics which can always gain the deviation for the individuals in the mating poolfeasible scheduling solution. is found using the formula, Job Op. Job Op. Job Op. … … No. No. No. No. No. No. Where, Where Job No. i: 1..n; Operation No. j: 1..m; xi - Cost of the ith individual N - Number of individuals in the mating pool IV. PROPOSED MEMETIC ALGORITHM To select the individuals for mating, the first To design a robust steady state GA, domain specific parent is randomly selected from one groupoperators for selection, crossover and mutation are and the other one is selected randomly fromintroduced. The GA operators probability also decided any other group other than the groupexperimentally. containing first parent. After selecting both the parents, they are removed from the mating A. Design of proposed operators: pool. The right choices of GA operators help in getting the 3) Crossover:optimal solution. This motivates us to propose domain To encourage the exploration of search spacespecific GA operators like grade selection , crossover crossover is applied on individuals. The proposed(Combinatorial Partially Matched (CPMX)) and mutation domain specific operators are,with adaptive strategy. To analyze the performance of these CPMX: It revises partially matched crossover (PMX)customized operators, they have been combined to form (Sivaanandham S N and Deepa S N , 2008) tocustomized GA architecture. To have faster convergence and exchange more genes by finding the permutation ofto improve the quality of individuals, Steepest Ascent Hill partially matched set. To avoid the uncertainty in theClimbing(SAHC) local search algorithm is combined with resulted individuals due to the context sensitivity ofthis combination and resulting to a new memetic algorithm these problems, this guided crossing is proposed. Theand the proposed methodology is given in Fig.3. The procedure of this crossover operator is given in Fig.1.descriptions about the proposed operators are as follows. 1) Objective Function: Procedure for CPMX. The fitness value (objective function) decides the Find the partial matching set(PMS) in twostrength of the chromosome. In MOCO problem, the chromosomessatisfaction of soft constraints decides the optimality factor. / Length of the PMS to be decided earlierThis aspires us to include the satisfaction level of soft Find the possible combinations of PMS 258 All Rights Reserved © 2012 IJARCET
- 4. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012 in Table.1. The parameters probabilities which gave better performance from various experiments are taken. Repeat Do the exchange in genes between a combination of Table.1 GA parameters PMS of two chromosome Parameter Probability Count the number of exchanges done on genes Population 1000 Until All combination of PMS of two chromosomes are Elitism .01 over Crossover .08 Take the resultant chromosomes formed with maximum Mutation .03 exchanges of genes in PMS Check the feasibility of resultant offspring If offspring solution is infeasible V. PARTICLE SWARM OPTIMIZATION Repair the solutions Particle swarm optimization (PSO) is one of the else metaheuristics algorithms. The concept of particle swarm has Apply SAHC become very popular these days as an efficient search and End if optimization technique. PSO does not require any gradient Fig. 1. Procedure for Proposed CPMX. information of the function to be optimized, but uses only primitive mathematical operators and is conceptually very 4) Mutation: simple. In general the change in genes is done on random basis. In PSO[16], there is a population called a swarm, and From the past researches, it is inferred that there is no every individual in the swarm is called a particle which guarantee of improvement in the solution by these represents a solution to the problem. All of particles have random changes. To achieve this, removing the violation fitness values which are evaluated by the fitness function to of soft constraints is attempted through mutation. This is be optimized, and have velocities which direct the flying of achieved by tuning the genes and hence proposed and the particles. The particle flies in the D-dimensional problem named as gene tuning. To identify the soft constraint to be space with a velocity which is dynamically adjusted satisfied, the following strategy on mutation has been according to the flying experiences of its own and its proposed and its procedure is given in Fig.2. colleagues. The basic Principle of Particle swarm move towards the best position in search space, remembering each Mutation with adaptive : Selecting the soft constraint particle’s best known position (pbest) and global (swarm’s) strategy resulting to minimum fitness best known position (gbest). score by gene tuning 1) General Particle Swarm Optimization Algorithm: Algorithm begins with a set of solutions as a Initial Population called swarm of particles and searches for optima by updating generations. For each particle in the swarm, velocity and position is calculated with their constraints to obtain feasible solutions. In every iteration, each particle is updated by following two "best" values. The first one is the best solution (fitness) it has achieved so far. This value is called pbest. Another "best" value that is tracked by the particle swarm optimizer is the best value, obtained so far by any particle in the population. This best value is a global best and called gbest. The new generation of solutions thus formed is most likely to be better than the previous ones. This process of forming new generation of solutions is continued until a best fitness value is obtained. Fig.2 Procedure for Adaptive strategy Mutation 2) Particle Swarm Optimization Algorithm for MJSSP: B. Local Search (Steepest Ascent Hill Climbing) The Multi Job Shop Scheduling Problem is implemented using Particle Swarm Optimization Algorithm by theWe use a very effective local search consisting of a stochastic following steps:process in three phases: i) Generate random population of N particles using The first phase to improve an infeasible solution Random Constructive heuristic process (timetable/jobs schedule) so that it becomes feasible ii) Evaluate makespan for each particle in the swarm (Repair Function) iii) For each particle in the swarm The second phase to increase the quality of a feasible a. Calculate pbest and gbest solution by reducing the number of soft constraint b. Update particle velocity and position violated (Mutation) and iv) Use the new generated swarm for the further run of The third phase is to improve the quality of the feasible the algorithm solution by interchanging the genes(SAHC) v) Repeat the steps (ii) to (iv) until stop criterion is metThe above discussed GA operators and SAHC are combinedto form a memetic approach with the probabilities specified 259 All Rights Reserved © 2012 IJARCET
- 5. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012 a) pbest Evaluation This position should be scheduled using constructive The particle’s best known position achieved so far in their heuristics process. In the above figure, the position 4respective iteration is said to be pbest. It is obtained by corresponds to job 2 first operation and the same position 4 iscomparing the previous pbest value with the fitness of the repeated, so their next operation is scheduled. Position 5 iscurrent particle. If it is better the pbest is changed with the repeated twice and job 2 operations are completed. So, thenew better fitness. Modifying solution procedure is applied and unscheduled least job operation is scheduled. Likewise, the schedule is b) gbest Evaluation obtained for the above positions. The global best known position in swarm achieved so farin each iteration is said to be gbest. It is obtained bycomparing the previous gbest value with the minimum fitness These steps are repeated for further generations, to find theobtained in current iteration. If it is better the gbest is optimum value for MJSSP.changed with the new better fitness. VI. DATA SET c) Velocity Updation In this work, 15 instances (LA1-LA10, LA16-LA20) with In each iteration, after finding the two best values, the various sizes for MJSSP from bench mark problems ofparticle updates the velocity with the following equation (a). OR-Library contributed by Lawrence( 1984) (Beasley J E ,1990) . have been taken as data set to test our new proposed algorithms. The works taken for comparison to prove thev[] = v[] + c1 * rand() * (pbest[] - present[]) + c2 * rand() * versatility of this proposed algorithm are Simple GA and(gbest[] - present[]) --- (a) PSO. The equation (a) helps the particle move in samedirection to achieve optimum. The velocity equation hasthree parts. The first part represents the inertia of previousvelocity, forces the particle to move in same direction. The VII. RESULTS AND DISCUSSIONsecond part is the ―cognition‖ part, which represents the In order to evaluate the reliability of proposed operators inprivate thinking by itself and forces the particle to go back to defining MA algorithms, the quality of solution is measuredthe previous best position. The third part is the ―social‖ part, with respect to the high optimal value found. To analyze thewhich represents the cooperation among the particles, forces results, the best optimal values found for various instances ofthe particle to move to the best previous position of its MJSSP taken from [Lawrence(1984)] OR library forneighbors. The maximum velocity vmax is said to number of population size 1000 with different sizes(Small, Mediumjobs. If the velocity exceeds vmax, then it is assigned to vmax. and Large)are compared and is shown in Table.2. As the evolution progresses, more and more good d) Position Updation candidates exist in the next generation and therefore, it can The position vector represents jobs’ arrangement on all narrow the search space so that fast convergence can bemachines. The maximum position pmax is said to nxm (no. of achieved.jobs * no. of operations). If the position exceeds pmax, then it A. Performance of Simple GA:is assigned to pmax. The results of a particle’s position may The operators used in GA are roulette wheel selection,have a meaningless job number as a real value such as 3.125. partially matched crossover and random mutation. For noSo, the real optimum values are round off to its nearest instances, the optimal values found by simple GA are betterinteger number. The computation results of the following than the best known values found.equation (b), present[] = persent[] + v[] ------------------------ (b) B. Performance of Proposed Memetic Algorithm and PSOwill generate repetitive code (job number), i.e. one job is From the Table.2, it is observed that,Simple GA does notprocessed on the same machine repeatedly. It violates the beat the best known values for any of the instancesconstraint conditions in MJSSP and produce banned PSO beats the best known values for 2 instances ,solutions. Banned solutions can be converted to legal LA03,LA10.solutions by modification. The process of modifying Memetic Algorithm beats the best known values for 6solutions is proposed as follows: instances , LA03,LA06,LA07,LA10, LA17 and LA20 Check a particle and record repetitive job numbers on From the results, it is obvious that proposed memetic every machine. algorithm is giving optimal values higher than best known Check absent job numbers on every machine of a particle. values found for 6 instances(LA03,LA06,LA07,LA10, LA17 Sort absent job numbers on every machine (of a particle) and LA20) and for other instances giving optimal values according to increment order of their processes. same as the best known values. In the case of PSO, only for 2 instances, it is giving results better than the best known Substitute absent job numbers for repetitive codes on values but not better than memetic algorithm. That is , PSO is every machine of a particle from low dimension to high not giving better results than memetic algorithm for no one dimension accordingly. instances.For example, the following is the positions obtained after With these discussions, it is concluded that proposed andapplying to the formula. customized memetic is doing better than existing bio inspired GA and nature inspired algorithm. Time Complexity: 260 All Rights Reserved © 2012 IJARCET
- 6. ISSN: 2278 – 1323 International Journal of Advanced Research in Computer Engineering & Technology Volume 1, Issue 5, July 2012 From the Table.2, it is observed that , memetic algorithmis taking lesser CPU time than simple GA and PSO. In somecases, PSO takes more execution time than simple GA.Hence, the converging speed of population is increased in theproposed algorithm. This is the effort of compensating [14] Christian Bierwirth, ― A generalized permutation approach to job shopcomputational complexity of the proposed operators with its scheduling with genetic algorithm‖, OR Spectrum, Vol .17, No 2-3, pp.87-92,1995.domain specific nature. [15] M.A.Adibi,M. Zandieh,and M.Amiri, ― Multiobjective Scheduling of Hence, a customized algorithm has been designed to Dynamic Job Shop Using Variable Neighborhood Search‖, Expertsolve multi constrained combinatorial problem with multi Systems with Applications,Vol.37,No.1, pp.282-287, 2010.objectives. [16] Rui Zhang, ―A Particle Swarm Optimization Algorithm based on Local Perturbations for the Job Shop Scheduling Problem‖, International Journal of Advancements in Computing Technology, Vol.3, No.4, May VIII. CONCLUSION 2011. [17] J.E.Garey,D.S.Johnson, and R.Sethi, ―The complexity of flowshop and The proposed memetic algorithms with customized GA jobshop scheduling‖,Mathematics of Operations Research, Vol.1,2,and SAHC producing more promising results Also, its pp.117–129, 1976.robustness is proved by obtaining better performance for all [18] E.L.Lawler, J.K.Lenstra, A.H.G.Rinnooy Kan, andproblem instances than algorithms taken from the literature. D.B.Shmoys,―Sequencing and scheduling: Algorithms and complexity‖, Handbooks in Operations Research and ManagementSince, the operators have been designed in order to reduce the Science,Vol.4, pp.445-552,1993.complexity of adjusting resources according to the [19] S.N.Sivanandham, and S.N. Deepa, ―Introduction to Geneticconstraints; these models are suitable for optimizing soft Algorithm‖. New York: Springer Berlin Heidelberg,2008.constrained combinatorial problems with multi objectives. [20] J.E.Beasley, ―OR-library: Distributing test problems by electronic mail‖, Journal of the Operational Research Society, Vol.41,No.11, pp.1069–1072,1990. REFERENCES S. Kanmani received her B.E and M.E in Computer Science and Engineering from[1] S. A. Schaerf ,―A Survey of automated timetabling‖, Artificial Bharathiar University, Coimbatore and Ph.D Intelligence Review, Vol.13,pp. 87- 127,1999. from Anna University, Chennai.[2] Olivia Rossi-Doria and Ben Paechter, ― A memetic algorithm for University Course Timetabling‖, in Proceedings of Combinatorial She has been the faculty of department of Optimization(CO’2004), School of Computing, Napier University, Computer Science and Engineering, Scotland, 2004. Pondicherry Engineering College from 1992.[3] D. Datta, K.Deb, and C.M. Fonseca, ― Multi-objective evolutionary Her research interests are in Software algorithm for university class timetabling problem‖, Series of Studies Engineering, Software Testing and Object in Computational Intelligence, Berlin: Springer, Vol. 49, pp.197-236, Oriented Systems. 2007. She is a member of Computer Society of India,[4] K.Royachka, and M.Karova, ―High-performance optimization of ISTE and institute of engineers India.. genetic algorithms‖, in IEEE International Spring Seminar on Electronics Technology, 2006, pp.395-400. M. Nandhini received her B.Sc (Mathematics)[5] Shigenobu Kobayashi, Isao Ono, and sayuki Yamamura,―An efficient and M.C.A from Bharathidasan University, genetic algorithm for job shop scheduling problems‖, ICGA,1995, Trichirappalli. M.Phil in Computer Science pp.506-511. form Alagappa University, Karaikudi.[6] Takeshi Yamada, and Ryohei Nakano,―A fusion of crossover and local She is the faculty of department of Computer search‖, in IEEE International Conference on Industrial Science, Pondicherry University, Puducherry. Technology,1996,pp.426-430. She is doing her research in Artificial[7] T.Yamada and R.Nakano, Chapter 7: Job Shop Scheduling, In Genetic Intelligence domain for finding the efficient algorithms in engineering systems, The Institution of Electrical Engineers, London, UK,1997. scheduling for Combinatorial Problems using[8] D.E.Goldberg, ―Genetic Algorithms in Search, Optimization and hybrid approach. She is a member of ACEEE, Machine Learning‖. USA: Addison-Wesley, Boston, MS,1989. ICASIT .[9] K.M.Lee,T. Yamakawa and K.M.Lee,― A genetic algorithm for general machine scheduling problems‖, in International Conference on Knowledge- Based Electronic System, 1998,pp.60-66.[10] J.G. Qi,G.R.Burns, and D.K.Harrison,― The application of parallel multi population genetic algorithms to dynamic job-shop scheduling‖,International Journal of Advanced Manufacturing Technology,Vol.16, pp.609-615, 2001.[11] T.Yamada, Studies on metaheuristics for job shop and flow shop scheduling Problems, Japan: Kyoto University, 2003.[12] Ping-Teng Chang, and Yu-Ting Lo ,―Modeling of Jobshop Scheduling with Multiple Quantitative and Qualitative Objectives and a GA/TS Mixture approach‖, Int. J. Computer Integrated Manufacturing, Vol.14,No.4,pp.367-384, 2001.[13] S.M.Kamrul Hasan,M.Rauhul Sarker, and David Cornforth,― Hybrid genetic algorithm for solving job-shop scheduling problem‖, in IEEE International Conference on Computer and Information Science,2007, pp. 519-524. 261 All Rights Reserved © 2012 IJARCET

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