APPLICATION OF BPSO IN FLEXIBLE MANUFACTURING SYSTEM SCHEDULING

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 5, May 2017, pp , Article ID: IJMET_08_05_020 Available online at aeme.com/ijmet/issues.asp?jtype=ijmet&vtyp pe=8&itype=5 ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed APPLICATION OF BPSO IN FLEXIBLE MANUFACTURING SYSTEM SCHEDULING M.Nageshwar Rao Asst. Prof, KL University, A.P., India. D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K. Bhargav Department of Mechanical Engineering, K L University, A.P., India. ABSTRACT In the present work studies about the application of BPSO (Binary particle swarm optimization) for scheduling of Machines in the flexible manufacturing system. Soft computing methodology is used for scheduling the optimum machine sequencing based on the make span minimization as constraint. Overall performance of the selection of the machine sequence is achieved by lowering the computation time,on comparison with the traditional algorithm. Key words: BPSO, Soft computing, FMS, Scheduling, make span. Cite this Article: M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav Application of Bpso in Flexible Manufacturing System Scheduling. International Journal of Mechanical Engineering and Technology, 8(5), 2017, pp IType=5 1. INTRODUCTION Particle swarm optimization is a heuristic kind of iterative algorithm that is framed based in the natural instincts. Mostly derived from the bird s idea of navigation in folks and their social behavior. This algorithm visually simulate the uncertainty dace of the birds. In this algorithm each of the bird is translated into the vector in the quadrant space where it is governed by another vector for the movement of particle which is called as velocity vector. The main aim of this algorithm is to determine the velocity of the particle which is the weighted residuals and so which is based on the previous value. Each vector update its velocity based on the current velocity and the best position it has explored as it past instances and also based in the globall best position in the swarm. The PSO iterate itself until the minimum error is archived. In binary PSO, each particle is represented as its position in binary values which is of 0 or 1. There are many versions of binary PSO. The present paper is organized as follows: in section II we will consider continuous PSO algorithm and also binary PSO algorithms. Then we willl introduce its shortcomings editor@iaeme.com

2 M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav 2. LITERATURE REVIEW. The permutation flow shop sequencing problems with the minimizing the make span and the total flow time of the job has been made and have shown the total arguable result with the PSO for the 57 out of 90 best known bench mark problems [1]. The particle swarm optimization has been used to minimize the make span for the job grid scheduling and one experimental studied shave shown the proposed method has well fitted and efficient than presented in literature [2]. The discreet particular the binary particle swarm optimization has been used for the gird job scheduling and have shown the comparative brief summary of the existed methods [3].Unlike the traditional an new particle swarm optimization has been proposed by changing the velocity vector of the binary of the single PSO and have shown that the most of the all the benchmark problems have given the satisfied results [4]. The binary particle swarm optimization has been used for the scheduling of the demand side resources to schedule a varied interrupted loads for 16H and have shown the result that the possibility of handling of scheduling problem in manageable computation time[5]. The discrete version of the particle swarm optimization has been used for floor shop scheduling by developing the new definition of the velocities of the particles and have verified by the standard PSO and have shown that the newly defined computation algorithm has been competitive to the traditional PSO [6]. The new combinatorial particle swarm optimization has been used for the solving the multi-mode R-C project scheduling problems, have shown the competitive nature of the CPSO and have outperforms the simulated annealing algorithm, and have approached the traditional PSO in the optima found [7]. The hybrid improved binary particle swarm optimization has been used based on which the minimizing the annual supply reserve ratio deviation by taking the live case study by showing the fast better convergence characteristics[8]. 3. METHODOLOGY OF SCHEDULING Scheduling is a decision making process to determine when a job is to be started in a machine and when it is to be completed. A job may have to be processed in various different machines or process centers. Similarly a machine or process centre may have to take different jobs and complete them. The order in which jobs are being taken up in a machine or process center is called sequencing FMS Scheduling In an FMS life cycle there are different levels of decision problems for its design and operation. Among them scheduling is a critical function for the control and operation of any FMS. Scheduling in flexible manufacturing systems (FMSs) differs from that conventional job shop because each operation of a job may be performed by any one of several machines. FMS scheduling has been researched extensively over the past two decades. It has been shown that most FMS scheduling problems are NP hard. Scheduling in FMS is more complex than scheduling in classical machine shops. The additional complexity comes from the following two factors together with the need for real time operation. 1. In FMS scheduling, decisions that need to be made include not only sequencing of jobs on machines but also the routing of the jobs through the system. 2. Apart from the machines, other resources in the system, e.g. material-handling devices like AGVs and AS/RS must be considered. In solving the FMS scheduling problem, decisions on these three aspects must be made so as to achieve some scheduling objectives, like maximizing machine utilization, minimizing the penalty cost and minimizing the distance traveled by AS/RS machine. However, before editor@iaeme.com

3 Application of BPSO in Flexible Manufacturing System Scheduling the sequencing decision is made, it is impossible to precisely measure the performance of these three decisions. The sequencing decision, on the other hand, cannot be made without the specification of part routing at the same time or in advance. Therefore, all three aspects are closely related. These interconnections and the additional resource constraints make the scheduling problem in FMS more complex than those in conventional machine shops. Ideally, considering all three aspects of the scheduling decisions and the constraints of all the resources in the system concurrently should solve the FMS scheduling problem Performance measures in Scheduling problem The choice of a schedule will depends on the criterion or objective that the population manager withes to consider in his or her evaluation.we will now provide notation and definitions and discuss some criteria that area often employed in evaluating the performance of a flow shop schedule. Makespan : make span is interval of time from the start of processing until all jobs are completed as the starting time of the first can be assumed as zero. In detail it is the total time calculated from the start of first operation of the job to completion of last operation of the last job determines the make span of the schedule. It is a time for a group of jobs to be completed. Make span = max Ci Job lateness: It is the amount of time by which the completion time of job i exceeds its due date. It gives information of whether the job is completed ahead of, on, or behind the schedule. It is the difference between a late jobs due date and its completion time. Li = Ci Di Note: Lateness can be either positive or negative. Tardiness: A positive lateness represents a violation of the due date and is called tardiness (Ti). It is the amount of time by which the completion time exceeds its due date. Earliness: A negative lateness represents the completion of a job before its due date and is called earliness. Mean Tardiness:This criterion is useful when the objective function of the company includes a penalty per unit of time if a job completion is delayed a specified due date. n 1 Mean Tardiness = T i n i= 1 Maximum Tardiness: To compute maximum tardiness, the tardiness of each job is calculated. The job that has the largest tardiness of all the jobs determines T max {0, Li}. This criterion is useful when the penalty per day for tardiness increases with the amount of tardiness B.P.S.O Methodology PSO Algorithm which is based on the swarm intelligence (SI) concept was developed by Kennedy and Eberhart in 1995 after studying the social behavior of birds. According to this, the birds when they are in search of food determine their velocity not only based on their personal experience but also through the information gained through interaction with other members of the flock. In particle swarm terminology, each bird which flies through the solution space searching for the optimum solution is called a particle, which is a potential solution to the optimization problem and the available solutions in each iteration are called the swarm which is equivalent to the population in genetic algorithms (GA). The basic algorithm of PSO for any global optimization problem is as follows: editor@iaeme.com

4 M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav Initially a swarm S of particles each with a random position pi and velocity is initialized. Now the fitness of all particles in the initial swarm is calculated. From this step onwards the iterative procedure begins where every time the positions and velocities of all the particles are changed by using the following equations +1 = + + Eq.1 +1 = + +1 Here the first term in the velocity updating equation (5.1) represents the inertial velocity of the particle. Since C1 helps in self-exploration (or experience) of a particle, it can be treated as self-confidence coefficient of the particle. Similarly it is appropriate to treat C2 as swarm confidence, since it is this coefficient which contributes in moving the particle towards the global best direction by considering the motion of all the other particles in the swarm in the preceding program iterations. C1and C2 are sometimes also known as cognitive and social parameters respectively. Once the positions and velocities for the next instance are calculated, they will be checked whether they are in the prescribed limits or not. These limits for positions and velocities are [0, Pmax] and [-Vmax, Vmax] respectively. The next step is to calculate the fitness values of these particles which completes one generation or iteration. This procedure is summarized below step wise: id P id (t) V (t) Step 1: Initialize a population of particles with random positions and velocities on d dimensions in the search space. Step 2: Update the velocity of each particle, using equation (1). Step 3: Update the position of each particle, using equation (2). Step 4: the Mapping of the position of each particle into solution space and evaluation of fitness value according to the desired optimization fitness function. At the same time, update p bes t and g best position if necessary. Step 5: jump back to step 2 until a convergence assumption is met, usually a sufficiently good fitness Control Parameters The size of the swarm is one of the deciding factors of the quality of the result which may be varied from 10 to 50 or even more depending on the size of the problem. Inertia weight (ω) is an important parameter to be optimized for getting better results in PSO; a large inertia weight facilitates searching new areas while a small weight facilitates fine searching in the current search space. To strike a balance between global exploration and local exploitation a suitable selection of inertia weight is necessary. The inertia weight can be varied in two ways. In the first case its value is changed from 0.1 to 0.9 and every time its effect can be tested. The other way is to linearly decrease the inertia factor from a large value (ωmax) to a relatively small value (ωmin) through the course of the PSO run. By doing so the PSO tends to have more global search ability at the beginning of the run while having the more local search ability near the end of the run. In such case the following formula is used to calculate the value of ω: Eq.2 = Where, ω max = initial value of weighting coefficient, editor@iaeme.com

5 Application of BPSO in Flexible Manufacturing System Scheduling ω min = final value of weighting coefficient, iter max = maximum number of iterations or generations, iter = current iteration or generation number. The other important parameters of PSO are the values of C1 and C2 whose values can be varied between 0.1 and 0.5 in general andsometimes it is tested with values between 0.1 and 1.0. It is also observed in the literature that some of the researchers gave a value of 2.0 for both the parameters. Finally the limiting values for the position p i, d max. And velocity v i, dmax.of the particle are defined by the user 3.5. Methodology followed for implementing particle swarm optimization algorithm. The most important requirement for successful implementation of any evolutionary algorithm is proper encoding. Here, in this work every possible sequence of operations is considered as a particle, where each operation is represented by the dimension of the particle. In this case a two digit number is assigned to each dimension to represent it completely, for example 32 indicates the second operation in the third job. Hence a group of schedules randomly created is the initial swarm, the size of which is taken as twice the length of the particle i.e., total number of operations in that specific job set. For every particle in the initial swarm, position and velocity are assigned randomly. In this step every particle is first represented by a two digit random number between 0 and 1, each representing a dimension of the particle. The number of such random numbers is equal to the total number of dimensions of that particle (i.e., total number of operations in this case). For example, let us consider problem set 1, which has a total of 13 operations (table 1). By this process we get a particular sequence of operations which indicates a particle of the initial swarm and this procedure is repeated to generate the entire initial swarm. Once the swarm is generated, the fitness of each particle, which is makespan for the schedule, is calculated. Position and velocity are assigned to each particle by generating two digit random numbers again for each dimension of the particle. Position should be a positive integer and hence the corresponding random numbers are generated in between (0 and 1). Velocity should be set within the limits so that it will not overshoot the search space and hence the corresponding random numbers are generated in between (-1 and 1). It is assumed that these first position and velocity are the best position and the best velocity for that particle at each dimension and the particle is treated as locally the best particle. Similarly the particle with minimum make span among all the particles is treated as the globally best particle in that swarm. Now the velocity of each particle is updated first using equation (5.1) and then the position of that particle is updated by using equation (5.2). The particles with updated positions and velocities are evaluated again based on their make span and the locally best particle and globally best particle are identified. This procedure repeats till the termination criterion is satisfied. As the problem considered needs scheduling of material handling system along with that of machines, the heuristic developed for vehicle assignment which is explained in is used here. The heuristic checks which vehicle can reach the concerned machine of that operation at the earliest and allot the vehicle for a particular operation. The iterative procedure adopted in PSO results in the best sequence, which fulfils the make span minimization objective criteria. For implementation of Binary particle Swarm Optimization algorithm, we have considered Job set 3 and Layout editor@iaeme.com

6 M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav Job Set 3 Job 1 Job 2 Job 3 Job 4 Job 5 Job 6 M 1 M 3 M 2 M 4 M 1 M 2 M 3 M 4 M 1 M 2 M 3 M 4 M 2 M 3 M 4 M Here total 16 operations are processed in this job set, So 16 random numbers are generated from 0 to 1 in two digits. Following are the example random numbers generated by the system: Next step is to arrange the random numbers in an ascending order as follows Now random numbers are arranged with the job numbers sequentially as follows Now consider again the random numbers that are first generated, and the operation numbers are assigned to those random numbers as shown below According to the coding mechanism, the sequence of operations is as follows Generate 16*2 i.e. 32 sequence like this. Next step is to calculate the velocity and position values by using equations 4.1 and 4.2. Constant input control parameters that are used in this simulation are as follows: Inertial Factor ( ): 0.5 Cognit parameter, C1 (0.1-2): 0.6 Social Parameter, C2 (0.1-2): 0.4 Random Value1 (0-1): 0.3 Random Value2 (0-1): editor@iaeme.com

7 Application of BPSO in Flexible Manufacturing System Scheduling Figure 1 simulation of jobset 3 with makespan values. Figure 2 Control parameters window of a java application Binary Particle Swarm Optimization Algorithm is mostly iterative algorithm, so we developed a Java application for the easy calculation of makespan. Maximum 1000 iterations can be performed for a single job set Job set3 is simulated by using this java application. More the number of iterations, more accuracy of makespan is obtained. In the above figure graph shows the decrease in the makespan in the increase of the iteration numbers. At 184 th iteration the makespan value is reduced to 88 which is the least makespan of all the iterations editor@iaeme.com

8 M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav Figure 3 Makespan Vs Iterations. 4. RESULTS AND DISCUSSIONS STM-Sliding time window AGA Abdelmaguid genetic algorithm UGA-Ulusoy genetic algorithmpga-proposed genetic algorithm t- Travelling time p-processing time Table 4.1 Makespan values of jobset3 for t/p ratio >0.25 Prob. No STW AGA PGA DGTHA SS BPSO editor@iaeme.com

9 Application of BPSO in Flexible Manufacturing System Scheduling Table 4.1 Makespan values of jobset3 for t/p ratio >0.25 (continued) Prob. No STW AGA PGA DGTHA SS BPSO CONCLUSION In this project the FMS scheduling optimization is done by using BPSO Algorithm, the optimal sequences of Machines and AGVs are determined. The purpose of this study is to make AGV scheduling an integral part of the scheduling activity, actively participating in the specification of the off-line schedule, rather than just reacting to it. The iterative algorithm created anticipates the complete set of flow requirements for a given machine schedule and makes vehicle assignments accordingly, as opposed to a real-time dispatching scheme that uses no information other than the move request queue. The iterative algorithm promises improvement in scheduling especially in environments where cycle times are short and travel times are comparable, or where the layout and the process routes do not suit each other editor@iaeme.com

10 M.Nageshwar Rao and D.Hari Krishna, P.Triyaplus, P.Vivekananda, M.Chayukyana, K.Bhargav REFERENCES [1] Tasgetiren, M. F., Liang, Y. C., Sevkli, M., &Gencyilmaz, G. (2007). A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem. European journal of operational research, 177(3), [2] Izakian, H., Ladani, B. T., Zamanifar, K., & Abraham, A. (2009, March). A novel particle swarm optimization approach for grid job scheduling. In International Conference on Information Systems, Technology and Management (pp ). Springer Berlin Heidelberg. [3] Khanesar, M. A., Teshnehlab, M., &Shoorehdeli, M. A. (2007, June). A novel binary particle swarm optimization. In Control & Automation, MED'07. Mediterranean Conference on (pp. 1-6). IEEE. [4] Izakian, H., Ladani, B. T., Abraham, A., &Snasel, V. (2010). A discrete particle swarm optimization approach for grid job scheduling. International Journal of Innovative Computing, Information and Control, 6(9), [5] Pedrasa, M. A. A., Spooner, T. D., &MacGill, I. F. (2009). Scheduling of demand side resources using binary particle swarm optimization. IEEE Transactions on Power Systems, 24(3), [6] Liao, C. J., Tseng, C. T., &Luarn, P. (2007). A discrete version of particle swarm optimization for flowshop scheduling problems. Computers & Operations Research, 34(10), [7] Jarboui, B., Damak, N., Siarry, P., &Rebai, A. (2008). A combinatorial particle swarm optimization for solving multi-mode resource-constrained project scheduling problems. Applied Mathematics and Computation, 195(1), [8] Suresh, K., &Kumarappan, N. (2013). Hybrid improved binary particle swarm optimization approach for generation maintenance scheduling problem. Swarm and Evolutionary Computation, 9, editor@iaeme.com