Automated Guided Vehicles scheduling Optimization by Fuzzy Genetic Algorithm

Transcription

1 Automated Guided Vehicles scheduling Optimization by Fuzzy Genetic Algorithm M. K. A. Ariffin 1, M. Badakhshian 2, S. B. Sulaiman 3 A.A Faeiza 4 Department of Mechanical and Manufacturing Engineering, Faculty of Engineering Universiti Putra Malaysia (UPM) UPM, Serdang, Slangor, Darul Ehsan, , 2, 3 Malaysia khairol@eng.upm.edu.my 1, m.badakhshian@gmail.com 2, suddin@eng.upm.edu.my 3, faeiza@eng.upm.edu.my 4 Abstract: Recent decades, automation and flexibility are the two most important items in manufacturing systems that both are worked integrating into flexible manufacturing system (FMS). Automated guided vehicles (AGVs) are one of the material handling equipments in FMS. The scheduling of AGVs integrated with machines is an essential factor contributing to the efficiency of the FMS. Fuzzy logic controller (FLC) is proposed to control the behavior of genetic algorithm (GA) to solve the scheduling problem of AGVs. GA cannot achieve the global optimum and sticks in local optima and premature convergence may occur usually. This paper presents an FLC to control the crossover and mutation rate for controlling the GA in AGV scheduling problem. An FMS with fixed rout, six machines and two AGVs is considered as the test case and results compared to those derived from GA model for AGVs scheduling problem. Keywords: Fuzzy logic controller, Genetic Algorithm, Flexible manufacturing system and Automated guided vehicle. 1. Introduction A flexible manufacturing system (FMS) is a production system including set of some numerical controlled machine centers, load/unload station, and automated storage and retrieval system (AS/RS) which are connected through an AGV system. The most advantages of FMS through the flexibility, such as dealing with machine and tool breakdowns, changes in schedule, product mix, and alternative routes [1]. AGVs are an important part of many low to medium volume manufacturing operations, including FMSs. AGVs are battery-powered driverless vehicles that is controlled and addressed by computer and move along wire guidepaths (flowpath), or by magnetic or optic guidance. They are handled workpieces between workstations and AS/RS on a factory floor safer than competitive technologies; all vehicles are equipped with lights and horns to warn pedestrians of their presence [2]. The first large-scale manufacturing application of an AGV system occurred in 1974 at a Volvo plant in Kalmar, Sweden. Within little more than a decade thereafter, about 3,300 plants worldwide employed more than AGVs. The largest application in North America is at the truck assembly plant of General Motors (GM) in Oshawa, Canada, where AGVs transport truck engines, bodies, and chassis across the 2.7 million square feet plant. Ganesharajaha et al. [2] Review some of the most important example of applying the AGVs. They showed that AGVs are Applicable in a wide diversity of service, and manufacturing systems.**** 2. Related literature

2 FMS performance can be increased by better synchronization and scheduling of production machines and material handling equipments. Scheduling is defined by allocating the confined resources to tasks overtime and is a determination process that relatives to operations, time, cost and other company objectives. Scheduling of machines, other resources such as vehicles, personnel, tools etc. has been done with a certain objective, to be either minimized or maximized [3]. The scheduling process task is to ascertain the start/end times for the individual operations to optimize a specified performance measure. The minimization of makespan objective is the most frequently used because it is directly related to the efficient utilization of resources [4]. Ganesharajah et al. [2] merge various lines of research related to AGVs and considered problem arising in flow path design, fleet sizing, job and vehicle scheduling, dispatching and conflict free ruting. Chen and Ho [1] described multiobjective evolutionary optimization of FMS including machines, computers, robots and AGVs. Jawahar et al. [5] proposed an AGV scheduling integrated with production in FMS by their heuristic algorithm. They considered an FMS that is required to process various types of job loaded at discrete points of time at different processing stations. Tuan and Koster [6] comprehensive presented a review on design and control of AGVs. They addressed most key related to guide-path design, determining vehicle requirement, vehicle scheduling and other related options to AGV. Correa et al. [7] proposed a hybrid constraint programming and mixed integer programming approach for scheduling and routing of AGVs. They used constraint programming for scheduling and mixed integer programming for routing sub problems. Recent years utilizing heuristic methods for AGV scheduling are noteworthy by authors that most illustrious is GA. Ulusoy et al. [8] addressed a GA approach to the simultaneous scheduling machine and AGVs. Abdelmaguid et al. [4] developed hybrid GA/heuristic approach to the simultaneous scheduling of machines and AGVs. Jerald et al. [9] presented adaptive GA for simultaneous scheduling of parts and AGVs in an FMS environment. Reddy and Rao [3] designed a hybrid multi-objective GA for simultaneous scheduling of machine and AGVs in FMS. This study focuses on the scheduling of AGV integrated machine in FMS by FLC-based GA. The FMS environment is the same as introduced in [3]. It s inclusive a load/unload station, number of machine that known sufficient input/output buffer space is provided at each machine, and number of AGVs those are available at load/unload station which carry a single unit load at the time and move along shortest path. 3. FLC based GA for Scheduling In this section is explained the problem that must optimized in this paper and then is defined the FMS environment that AGVs work in it. 3.1 Problem definition Two types of trips are performed by AGVs. When materials are handled by vehicle called loaded trip and deadheading trip is the second one trip where the vehicle moves to pickup a load. Deadheading trip can be placed immediately after unloading and vehicle demand at different workstations is considered and the subsequent duty assignment is made. If any of AGVs are available assign the task to the earliest available vehicle. Earliest available time is computed when there is no available vehicle. Next earliest completed operation is identified if the vehicle is idle and no job is ready, and move the vehicle to pickup that job. In this paper vehicle scheduling is based on the operation sequencing to minimize the makespan. Waiting time is reduced in FLCbased GA vehicle scheduling methodology thus helps to decrease the production period time as makespan and the resource utilization and the throughput improving.

3 3.2 configuration and operating environment of FMS The sample FMS that AGVs scheduled in it is Reddy and Rao [3] that contains six machine centers, Load/unload (L/U) station, and two AGVs handle the material between six machine centers and L/U station. Fig. 1 shows a layout of this manufacturing system. L/U M 1 Fig.1 M 2 M 3 M 6 M 5 M 4 FMS layout Table 1 show the job set details, time of processing, and the operations sequencing per every job in this FMS environment. 4. FLC-based GA Method for Optimization GA operates on a population of potential solutions applying the principle of survival of the fittest to produce better and better approximations to a solution. GA search and find local optima through problem solving process to obtain the global optimum. When the GA can not achieve the global optimum and sticks in local optima premature convergence may occur. Fuzzy logic controllers (FLC) are known for their applicability on controllable systems with complicated mathematical model. The human expertise and knowledge would be useful to increase the capabilities of GA. This expertise generally is vague, incomplete, or ill-structured. FLC-based GA proposes to use an FLC whose inputs are any combination of GA performance measures or current control parameters and whose outputs are GA control parameters. FL and GA integration has been accomplished by two different approaches 1) the application of GA in optimization and search problem related fuzzy systems, and 2) the use of fuzzy tools or fuzzy logic-based techniques for modeling different GA components or adapting GA control parameters, respectively, with the goal of improving performance. Generally this type of integration called Fuzzy GA (FGA). [10] In this problem, fuzzy controllers control the operation of GA like crossover and mutation rate that the GA doesn t break to premature convergence. 4.1 AGVs scheduling algorithm During the scheduling, AGVs follow the steps those are presented below: 1- Schedule the operations according to the chromosome sequence. 2- Find which AGV will reach the L/U station or the machine with demand point early. 3- Move the AGV from the current point to request point for its next assignment. 4- Wait the AGV till the job is ready if there is no job ready. 5- Move the job to the machine at which is the next operation is scheduled. 6- If the machine is busy AGV drops the job at the machine buffer; job will be loaded after the machine becomes free. 7- Load the job on the machine if the machine was free. 8- Check all the operation is completed [3]. Table 1 Job set details 6 jobs each with 6 operations are to be processed on 6 machines Job along with the machine number (M) and processing time (PT) are given alternatively Job No. M PT M PT M PT M PT M PT M PT Job-based Genetic Algorithm

4 The most important things in jobbased GA initial population, job-based crossover operator and mutation operators. These operators should check and ignore the chromosomes that don t observe the operation sequencing in every job during the operation. In initial population must make chromosome considering the sequence of operation in each job. The population algorithm must ignore chromosome without operation sequencing. Because operation 6 of job 3 cannot be came about before operation 5 of job 3. In Fig. 2 is showed the correct and wrong Chromosome in operation sequencing job 3. The number 17 that presents the operation five of job three can not be after number 18 that present the operation six of job three. Correct chromosome: 13,1,7,19,8,9,25,26,14,15,27,16,28,2,3,31,20,10,4,21,17,11,5,22,29,30,23,32,33,34,18,6,24,35,12,36 Denied chromosome: 13,1,7,19,8,9,25,26,14,15,27,16,28,2,3,31,20,10,4,21,18,11,5,22,29,30,23,32,33,34,17,6,24,35,12,36 In fitness function makespan is evaluated in each generation based on the given GA operation sequence and the heuristic vehicle assignment method. Operation completion time = Oij = Tij + Pij j th operation i th job (traveling time + operation processing time) Job completion time Ci =??i=1??n??oij?? Makespan = Max (C1; C2; C3;... Cn ) Job-based crossover is used which never offends the precedence constraints. A job is selected randomly and the operations of the selected job are directly copied in the Fig. 2 Wrong and Correct Chromosome respective positions of their offspring. As they are directly copied the positions are not changed during the crossover process and thus the off springs generated will maintain the precedence relation (Fig. 3). 1: Randomly select one job from the given job set. 2: Mark the operations of the selected jobs on the parent strings. 3: Copy the operations of the selected jobs of parent 1 onto the matching positions of offspring 2 and vice versa. 4: Fill the unfulfilled positions of the offspring 2 by the operations of the unselected jobs from left to right according to their order of appearance in parent 2 and vice versa[3]. Parent Parent Offspring Offspring Fig.3 Crossover operation

5 Job-based mutation is used which never offends the precedence constraints too. Two operations of two jobs are selected for replacing mutually but must check considering operation sequencing in these two jobs. At first randomly select two operators from one of the given chromosome that they are in different job. And secondly change the position of two operators if in new position is between before and after operators otherwise the mutation doesn t occur. 4.3 Fuzzy logic Controller for GA The choice of parameters for GAs, such as crossover and mutation rates is a rather hard task, due to the enormous possibilities of variations in the modeling of the problem and fitness function. Traditional GAs base themselves upon the generation of several random factors in the creation of the crossover and mutation. Therefore, two executions with the same initial parameters of execution can produce significantly different results. The prime objective of using FLCs for GAs is to determine the important parameters of GAs. These parameters can be used during various generations of the GA, for a better performance of GA. The FLC receives the indices of GA periodically as its inputs, and Input Variables through its rule base decides about the GA parameters. The most important step in designing the FLC is to know the required outputs. In FGA methodology, various parameters of GA are considered to be controlled by the FLCs such as crossover and mutation rate, surviving percentage, and stop criteria [10]. In this paper the crossover and mutation rates are considered to be controlled by the proposed FLC. The candidate input variables are the ones which have a great significance for the chosen FLC outputs. The best value of each generation, the number of similar chromosomes in each generation, and the number of repeated chromosomes in last five generations which have the same best values. For each selected variable, either input or output, its domain is defined in three fuzzy linguistic values, {low, average, and high}. The trapezoid and triangular membership functions were used to model the values of the input variables. The output variables are represented by using Gaussian membership functions. The mamdani-type fuzzy rulebase is used in the proposed FLC. Output Variables Optimal Value Frequency of Best Value Duplicate Individuals Rate Mutation Rate Crossover Rate Good Low Low Low High Good Low Average Average High Good Low High High High Good Average Low High Average Good Average Average High Average Good Average High High Average Good High Low High Average Good High Average High Average Good High High High Low Average Low Low Low High Average Low Average Average High Average Low High High High Average Average Low Average High Average Average Average Average Average Average Average High High Average Average High Low Average Average Average High Average High Average Average High High High Low poor Low Low Low High poor Low Average Average High poor Low High High High poor Average Low Low High poor Average Average Average High poor Average High High High

6 poor High Low Average High poor High Average High High poor High High High High The 27 rules (Brito et al.) are defined in a way that decreases the crossover rate when the optimal characteristic of the current population is not so good which inherit by the offspring [11]. The full rule base is displayed in table 2. This is determined by the best value of current generation. Moreover the Table 2 Fuzzy Rule base-ga mutation rate needs to be increased in such cases. When the number of repeated similar chromosomes with best value is increasing and the best value is not recognized as the good one, a premature convergence may occurred. In such cases the fuzzy rule base tries to increase the mutation rate. 5. Result and discussion In this paper, the problem of simultaneous scheduling of machines and identical automated guided vehicles (AGVs) in flexible manufacturing systems is addressed by considering the minimization of the makespan objective. An FLC-based GA coding scheme is developed for the studied problem. From the testing of the proposed GA and the adopted operators, the best fitness or the optimal makespan by fuzzy operators (crossover, mutation) was achieved 246. Before optimization by this method the makespan was but after GA optimizing all the generations converge to 246. The crossover rate change from 0.87 to 0.5 based on the performance indices of the GA. Furthermore the mutation rate which is controlled by the FLC varies from 5 to 2 percent. Fig. 4 shows the best sequencing for AGV scheduling. In this figure as shown no. seven is the first gen in the last chromosome. It shows that the first AGV should bring the job number two to machine number two for operation number one. The operations are sequenced in one job. It is mentioned operation four of job three is came after operation three of job three in last chromosome. The last chromosome 7, 31, 32, 8, 33, 9, 34, 10, 35, 36, 11, 13, 12, 1, 14, 2, 15, 3, 16, 4, 5, 6, 17, 18, 25, 26, 19, 20, 21, 27, 28, 29, 30, 22, 23, 24 Fig.4 the best sequencing foragv scheduling References: [1] Jian-Hung Chen and Shinn-Ying Ho, Proceedings of the Genetic and Evolutionary Computation Conference, L. Spector et al., E&. San Francisco, CA: Morgan Kaufmann, 2001, vol.l,pp [2] Th.Ganesharajaha, N. G. Hallb and Ch. Sriskandarajah, Annals of Operations Research 76, pp , [3] B. S. P. Reddy and C. S. P. Rao, Int. J. Adv. Manuf. Technol., 31, pp , 2006 [4] T. F. Abdelmaguid, A. O. Nassef, B. A. Kamal and M. F. Hassan, International Journal of Production Research, 42, pp , [5] N. Jawahar, P. Aravindan, t, S. G. Ponnambalam and R. K. Suresh, Int. J. Advanced Manufacturing Technology, 14, pp , [6] Tuan Le-Anh and M.B.M. De Koster, European Journal of Operational Research, 171, pp. 1 23, [7] A. I. Corréa, A. Langevin, L. Rousseau, Computers & Operations Research, 34, pp , [8] Gtindtiz Ulusoyt, Funda Sivrikaya-erifo, Omit Bilg, Computers Operation Research, 24, no. 4, pp , [9] J. Jerald, P. Asokan, R. Saravanan and A. Delphin Carolina R, Int. J. Advanced

7 Manufacturing Technology 29, pp , [10] F. Herrera, M. Lozano and J. L. Verdegay, Fuzzy Sets and Systems, 92, ppt , [11] F. H. de Brito, A. N. Teixeira, O. N. Teixeira, and R. C. L. de Oliveira, Springer- Verlag Berlin Heidelberg 2006, L. Jiao et al. (Eds.): ICNC 2006, Part I, LNCS 4221, pp , 2006