Information about A Comparative Study of AI Techniques for Solving Hybrid Flow Shop (HFS)...

A Comparative Study of AI Techniques for

Solving Hybrid Flow Shop (HFS) Scheduling

Problem

Solving Hybrid Flow Shop (HFS) Scheduling

Problem

has the capability limitation any he could not single device and only one of the processing work at the same time . (Fig. 1) parallel machine HFS structure In the following identify scheduling problem : Perm | Cmax |Hfm. The meaningful of this character is : hybrid flow shop scheduling prblems HFSS situation together with all of Jobs that have equivalent succession and decreasing the total time to end all the jobs is the aim That must be resolved. Mathematical Formula for HFSS is given by the following: (Lee, Lei et al. 1997, Nowicki and Smutnicki 1998, Brah and Loo 1999, Kahraman, Engin et al. 2008, Ronconi and Henriques 2009) Character of HFS: J: Group of jobs To determine scheduled |J| = n: the number of the jobs. s: The Number of steps that will be process each job . |s|=s . j: Subscript letters represents jobsj. l: Subscript letters represents stepsl. i: Subscript letters represents machine i. lm : The numbers of the parallel machine stepl. B:means A much big number positive. jlS :Starting the time of the jobs j in stepl. Explain of the model is as follows: Constraint(1) Shows us(Q) that the time to complete last job (j) when the last step (s),(2) Indicates that it is unreasonable to work each step processor at step( l+1) before all job is accomplished at step (l), (3), (4) and (5) they are Processor in orders for all job (g) and ( f ) on machine (I) at step (l) . These Could not be allow to be processed set of jobs on machine at any time,(6) could not allow a jobs j to be processing on the most than one machine in any time, Constraints (7) and (8) States that the variables nonnegative and (0-1) Integer values.

A HFSS problem with (5-jobs×3-steps) where the steps have( 2, 3, and 3) machines Respectively is given in Fig. (2). Figure 2. Hybrid Flow Shop Scheduling Problem To solving HFSS problem, we gave three improvement heuristic searches, in this paper used Simulated Annealing (SA), Tabu Search (TS)and Genetic Algorithm (GA). We will apply this improve heuristic search to solving corresponding problem Cases to Direct comparison execution In the three search algorithms. this problems to be resolved contain of From the smallest problem to the biggest problems which are substantial NP- hard to be the systematically solve by applying this search, this problems can be resolved in multinomial calculation time. As of the experience consequence, Study will be three searches. The buildings in this paper are systematic are as follows In Chapter (II) descript of perfection heuristic programs searching, as one type of the heuristic programs searching, Will be reviewed. Particular of perfection the heuristic programs searching, which are SA, TS and GA will reviewed this in part III, IV and V relatively Then comes Experiment the result will presented in part VI and finished this paper in conclusion in part VII. Literature review on HFS scheduling problems. II. RELATED RESEARCH Scheduling problem, are classified into three problems of search algorithms, that consist of heuristic algorithm, Rounding algorithms and exact algorithms as in Figure. (3). Exact algorithm is a perfect listing search that searches all Possible solution in area. It will be give us this algorithms is the best solution. Exact algorithm has finite implementation With regard to the calculation of time to the problem of large-scale. bound and Branch is type of exact algorithm, Rounding algorithms Is one of the search algorithms which use mathematical drafting to Guidance the search to detection best Possible solution. Heuristic algorithm is a type of search algorithms which uses specific rule to search practical

solution in area to detection best possible solution. Figure (3) Compilation of search algorithm in building problems Heuristic searchs which consists precisely of 2 groups there are development the heuristic and construction heuristic. (Koulamas 1998, Ronconi 2004). Manufacture heuristic: is heuristic searchs Which usually begin from a blank scheduling solution sets, and at every iteration, will be added and one job in the solution of schedule set even every jobs are the scheduled. Development heuristic search: is heuristic search which usually begin from initial entire schedule, Randomly generate or with specific send rules and the schedule solution sets are edited in every iteration even arrive specific stop criteria. (SA), (TS) and (GA) are categorized as perfection heuristic searchs. The use of heuristic searches or approximation search Comes Behind this background is much less calculation time , until though this search can able just give better solution, we luck if it optimum. Although this research can just give a best solution, optimize if we lucky. Heuristic search and approximation is Effective for a wide range size of the problem, particularly for problems that are difficult NP-hard to resolve if the use of an algorithm exactly. III. GENETIC ALGORITHM (GA) GA: is type of the AI techniques used to solve the problems, first discovered by (( John Holland)). (GA) is a heuristic technique stochastic which start from a large number of initial solutions, and we call upon the population, and the new population is configured through the generation. Population is populated by individuals in the chromosome. And called on each element of the chromosome names gene. Each of these genes this representing job and the position of the genes representing the sequence of job scheduling. To create a new population, GA Works on the choice the better individual of the total current populace and using operator to Establish population new on the a generation new. GA has operator is: Crossover and Mutation. Through crossover,(GA) products the neighborhood to search a new possible solution. (Martin 2009, Zhou, Cheung et al. 2009) A. Selection In this process is the selection of the better individual together with a fitness function. n j j i i f f P 1 )( (9) B. ( Crossover) The Crossover is one of type operator (GA) to create new individuals to be to replenish the populace by the new generation. Parent is choose at random from the individual of the new generation are chosen through rate of crossover, here will come to the possibility of Will become a single individual one of the parents. There are several methods with regard to crossover, that are: Order Basis Crossover (OBX), Position Basis Crossover (PBX), One Point ((1PX)), Order Crossover (OX), Cycle Crossover Operator ((CX)), Partially Mapped Crossover (PMX), Linier Order Crossover (LOX), The Two Point Version 1 (2PX_V1), The Two Point Version (2.0) (2PX_V2), and Two Point Version (3.0) (2PX_V3.0). (Kellegöz, Toklu et al. 2008). C. ( Mutation) The aim of mutation is to make the search space is not located in local optima. It trying to search space that avoids local Optima, It is possible to give a result near the Optima Global. Mutation is

the process done optional on the chromosome, and this is why the possibility of a very small number of mutations, and there are two common kinds of mutations that are: 1) Inversion Inversion mutation is the method through which random mutation of a gene to another gene in chromosome as in Fig.(4). Fig.(4) Mutation Inversion 2) Pairwise Interchange Pairwise interchange is a method through which the exchange between the two neighboring genes as in Fig. (5). Figure 5: Mutation Pairwise GA Steps: STEPS (1): Generate initial population P(0) arbitrarily and set (i=0) . STEPS (2): REPEAT . a. Fitness evaluate of every individual and chose the fittest individual of the population: n j j f fi f f PP 1 )()( (10) b. Applied crossover accordance to rate of crossover. c. Applied mutation accordance to rate of mutation. d. Production offspring even if all population is full of. STEPS (3): An even stop criterion is convinced.In Fig.(6), structure of Genetic Algorithms is showed. in the structure, not everyone separated, the crossover process resulted , would be mutated. Just a few new individual will able mutated count on its rate of mutation . Fig.( 6 ) GA structure Are selected a maximum of 75% of the population of the next generation through using function fitness in the roulette wheel. Will fill the break of the population through the crossover, which is made from crossing random two individuals, depending a crossover rate, of the population of the past generated. The crossover operation will iteratively finished even individuals in the next generation amount to the population size. After that, mutation process will be completed to a few individuals in modern generation depending on rate of mutation. IV. SIMULATED ANNEALING (SA) Is one kind of the AI techniques used to solve problems, SA applied by Kirkpatrick (1982) to optimization problems, SA used to improvement heuristic search. Simulated annealing is further determine compared to Genetic Algorithm . Simulated Annealing randomly selects neighbors and then decide if it is better or not, SA in initial solution start from one, in every iteration, A new solution must be born in each iteration to advance the solution. Simulated Annealing some time

accepting worsening result in specific probability, called probability. by means of probability, if can avert, local optima while Exploration in the near neighbors. SA uses exchange operator to generate its neighbors, SA depends on the temperature (start, stop) and the number of iteration at each stage and change in the cost function. Must be sufficient temperature to continue to find the best solutions, does not require a very high temperature, because the opportunity to choose the best solution is the same opportunity if they are low, we need at each stage sufficient number of iteration so that we can find the best solution, stop depends on the specific number of iterations or low temperature. There are a number of interchange operators that of uses but there are two types most commonly used, which are Pairwise Interchange and SWAP. In GA, there are used two operators to fleeing from local optima replacement of generating neighborhood. In the starting, The Current, and Candidate have corresponding original solution. In every iteration, final solution that has been registry compared to the current solution, If the current solution is better , then the current solution It becomes is candidate solution, if else (final solution is better ), with a some probability, this worsening current solution Can still acceptable. This operation continues until stop condition is achieved. Algorithm for Simulated Annealing V. TABU SEARCH TS is one of the AI techniques used to solve problems, TS as in the SA randomly start and begins from one initial solution and generates the number of iterations to generate a new solution through its neighborhood show in Fig. (7). In TS, The acceptance moving to the all solutions in neighborhood is not Probability like SA, but determine, In TS is accepted worsening move. (Zhou, Cheung et al. 2009). Fig. (7)TS Flowchart

TS Contains the memory from which logs recent moves in the search area , Tabu move call it, and retained in list and it is called Tabu list as in Figure(8). That the task of the tabu list is to remember recent moves Undertaken, and avoid selecting similar steps. Fig.(8)Tabu List How to fix the parameter of tabu list size, tabu tuner, neighborhoods size, neighborhoods type and number of iteration. TS Like SA, it used Exchange operator to generate neighborhoods. and there are two types more use operators: it is Pairwise Interchange and SWAP. in every iteration, Tabu Search Generate many neighbors. call on this a Inner Step. In Figure. (9) for examples to used three from inner steps. Fig.(9) Example of inner step After doing a certain number of iterations, TS select the best solution from the current solution and mind is the main solution and not necessarily be better than the current solution. Must before generate the neighbors, TS moving to check the memory ( tabu list) ,After a number of iterations choose the best of these solutions and makes it the parent for the next generation. Tabu Search(TS) Algorithm: VI. EXPERIMENT RESULT Data from Tailard’s problem set was used for this experiment . They are made up of (12) problems set and every problem set constitute (10) problem Cases with every problem Cases, (14) solutions are for submission consisting of (10) Genetic Algorithm (GA) solutions, (2) Simulated Annealing (SA) solutions and (2) Tabu Search (TS) solutions. The (10) of ( GA) solutions come from( 10) individual crossover chosen to distinction the result because crossover are (GA), the source of new neighborhood or generated solutions. The different results obtained from the SA and TS are as a result of the neighborhood generation method from SWAP and pairwise interchange. The overall number of operating are (12) Problem sets( × ) (10) problems Cases on every problem sets (×) (14) various solutions approach equals 1680 of number of operating. Results of (10) problem sets were averaged and

presented, consisting of 14 solutions. Each of these problem sets, apart from the 14 solutions, it also contain averaged Cmax and computation time. Samples of best solutions from every problem set are taken as presented in TABLEII. The methods used in implementing the experiment and extracting the results were an improvement of the other methods earlier considered. The analysis indicated that TS was found to generate 6 results considered acceptable, while 3 results comes from the results of SA, and GA produced yet another 3 results. These results are as a result of SWAP neighborhood generation for TS and SA. However, the best results obtained from (GA) stems from PMX , OX and 2PX_V2 and by implementing the work with, 5 inner steps that generates neighborhoods for every iteration results of TS turn out to be the best. For the crossover rate of GA, 90% probability of gene is most likely to be parents that will generate new population. This makes GA to be a feasible solution space for optimal solution, as the probability tends to becomes narrower. We compared the computation time as indicated in table. II. In this experiment, though the computation time shows that (SA) his the minimum value of calculation time while the GA carries the maximum computation time and between these calculation time lies TS. Additionally, GA and TS, computation times are dependent on number of iteration and problem size respectively, while SA depends only on computation time. That is to say that GA computation time is a function of population size and TS computation time is of inner steps. that efficiency of TS algorithm to solve the problem is effective not only to solve computation time but also to solve HFS problems.

VII . CONCLUSION In this paper, we have three of artificial intelligence techniques which we have explained previously(GA,SA and TS), we applied these techniques on HFS scheduling problems ,Through comparing the effectiveness and efficiency of these algorithms we found the TS is the best algorithm to solve the HFSS problem is more effective and efficient calculate the time. VIII. References: Brah, S. A. and L. L. Loo (1999). "Heuristics for scheduling in a flow shop with multiple processors." European Journal of Operational Research 113(1): 113-122. Kahraman, C., et al. (2008). "An application of effective genetic algorithms for solving hybrid flow shop scheduling problems." International Journal of Computational Intelligence Systems 1(2): 134-147. Lee, C. Y., et al. (1997). "Current trends in deterministic scheduling." Annals of Operations Research 70: 1-41. Nowicki, E. and C. Smutnicki (1998). "The flow shop with parallel machines: A tabu search approach." European Journal of Operational Research 106(2): 226-253. Ronconi, D. P. and L. R. S. Henriques (2009). "Some heuristic algorithms for total tardiness minimization in a flowshop with blocking." Omega 37(2): 272-281. Al-Harkan, I. M. (1997). On merging sequencing and scheduling theory with genetic algorithms to solve stochastic job shops, University of Oklahoma. Branke, J. and D. C. Mattfeld (2005). "Anticipation and flexibility in dynamic scheduling." International Journal of Production Research 43(15): 3103-3129. Chou, F. D. (2009). "An experienced learning genetic algorithm to solve the single machine total weighted tardiness scheduling problem." Expert Systems with Applications 36(2): 3857-3865. Fernandez-Marquez, J. L. and J. L. Arcos (2009). An evaporation mechanism for dynamic and noisy multimodal optimization. Proceedings of the 11th Annual conference on Genetic and evolutionary computation, ACM. Goldberg, D. E. (1989). "Genetic algorithms in search, optimization, and machine learning." He, J. and X. Yao (2002). "From an individual to a population: An analysis of the first hitting time of population-based evolutionary algorithms." Evolutionary Computation, IEEE Transactions on 6(5): 495-511. Low, C. and Y. Yeh (2009). "Genetic algorithm- based heuristics for an open shop scheduling problem with setup, processing, and removal times separated." Robotics and Computer- Integrated Manufacturing 25(2): 314-322. Reinelt, G. (1994). The traveling salesman: computational solutions for TSP applications, Springer-Verlag. Russell, M. D., et al. (2003). Making the most of two heuristics: Breaking transposition ciphers with ants. Evolutionary Computation, 2003. CEC'03. The 2003 Congress on, IEEE. Zhu, T., et al. (2011). An adaptive strategy for updating the memory in evolutionary algorithms for dynamic optimization. Computational Intelligence in Dynamic and Uncertain Environments (CIDUE), 2011 IEEE Symposium on, IEEE. Kellegöz, T., et al. (2008). "Comparing efficiencies of genetic crossover operators for one machine total weighted tardiness problem." Applied Mathematics and Computation 199(2): 590-598.

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