ANT BASED MULTI ATTRIBUTE JOB SHOP SCHEDULING OF IDENTICAL MACHINES

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 8, Issue 12, December 2017, pp , Article ID: IJMET_08_12_058 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed ANT BASED MULTI ATTRIBUTE JOB SHOP SCHEDULING OF IDENTICAL MACHINES B. Sasikala Research Scholar (Part-Time Ph.D Category-B), Department of Computer Science, Research & Development Centre, Bharathiar University, Coimbatore, Tamilnadu, India Dr. V.P. Eswaramurthy Assistant Professor, Department of Computer Science, Government Arts and Science College, Namakkal, Tamilnadu, India ABSTRACT Several problems in various industrial environments are combinatorial. The problem of job shop scheduling has been approached using various methods but suffers to achieve the required performance. The problem so formulated is extremely difficult to solve, as it comprises several concurrent goals and several resources which must be allocated to lead to our goals, which are to maximize the utilization of individuals and/or machines and to minimize the time required to complete the entire process being scheduled. To overcome the issues present in the previous methods, the author presents a novel ant based approach which considers many factors like average waiting time, resource usage, makespan time, availability and so on. The method first generates a number of ants according to the number of jobs being provided. The number of ants is about the number of resources and for each ant the method identifies the resource available. Then for each ant, the method generates a job sequence and computes the makespan time, average waiting time of resource and jobs. Using the above factors the method estimates the multi attribute scheduling strength for each sequence. Based on the estimated scheduling weight of the sequence, a single sequence is selected for scheduling. The method performs iterative scheduling by computing the multi attribute scheduling strength. The method produces efficient results on job shop scheduling and reduces the overall makespan time. Key words: Ant Based Scheduling, Job Shop Scheduling, Multi Attribute Scheduling Strength, Identical Machines, AIMS Scheduling, Waiting Time. Cite this Article: B. Sasikala and Dr. V.P. Eswaramurthy Ant Based Multi Attribute Job Shop Scheduling of Identical Machines, International Journal of Mechanical Engineering and Technology 8(12), 2017, pp INTRODUCTION Real-world frameworks frequently include vulnerability and element changes, particularly in make-to request job shop environments. Scheduling in these situations is difficult because editor@iaeme.com

2 B. Sasikala and Dr. V.P. Eswaramurthy informed scheduling decisions wish to be made quickly based on variation in the shops [1]. The job-shop scheduling problem mostly concentrated in the course of the most recent quite a few years and it draws in the consideration of scientists and specialists similarly. The established JSP is normally characterized as: there are n jobs, each comprising a particular arrangement of operations which must be prepared by m machines or work stations on a given day and age as indicated by a given specialized priority arrange, a calendar should be made to limit a measure (or numerous measures) of execution [2]. Every job must go through every machine once and once as it was. Every job ought to be handled by the machines in a specific request and there are no priority requirements among various job operations [3]. Every machine can handle just a single job at once and it can't be intruded. Besides, the handling time is settled and known. The issue is to discover a schedule to limit the make traverse. Analytical solution strategies can rapidly lose their applicability as problem size increases and even quick methods for reasonably estimated shops may not be valuable in a dynamic genuine environment where changes in processes and machines are the order of the day [4]. For this reason, Operation Research(OR) practitioners resort to dispatching standards or heuristics to settle practical-sized instances in sensible time. On the other hand, based on the degree of vulnerability related to input parameters, scheduling issues can be arranged into deterministic and nondeterministic classes [5]. The deterministic scheduling models do not consider vulnerabilities, while this present real issues always, face unstable events such as machine failures, varieties in due dates and demands, and fluctuating preparing times, which can prompt to interruption for working procedures [6, 7]. Branch-and-Bound(BB) or Dynamic Programming(DP) is potential strategies for finding the correct ideal arrangements by dispensing with various candidate arrangements in light of certain prohibitive criteria. However, these procedures are not proficient and compelling in handling the vast size of issues.dp faces the space blast issue when the quantity of state factor grows [8,9,10]. Ant colony is the technique of visiting various locations by ant. An ant can move through different routes and in a road map, there may be a number of routes to reach the destination but each would produce different traversal time and each would produce different waiting time. By using ant colony an efficient scheduling of the jobs can be performed. The same can be adapted for the problem of job shop scheduling where the ants are the resources and the locations are the jobs. This corollary can be viewed in vice versa also. By using ant colony optimization technique the problem of job shop scheduling can be improved [11]. The organization of the paper is as, Literature review is given in Section 2, Problem definition and proposed method is given in Section 3, Experimental results and Performance analysis is in Section 4 and Conclusion is in Section LITERATURE REVIEW There are a number of approaches for job shop scheduling has been discussed. This section discusses some related methods for the problem of job shop scheduling. Solving job shop scheduling problem using an ant colony algorithm [11] initializing the pheromone trails based on an initial sequence. Moreover, the pheromone trail intensities are limited between lower and upper bounds which change dynamically. The performance quality of a solution constructed by an artificial ant is improved by a job-index-based local search procedure incorporated with a threshold probability of choosing a job to insert into the other editor@iaeme.com

3 Ant Based Multi Attribute Job Shop Scheduling of Identical Machines positions of the sequence. Once all ants in the colony have generated their solutions, the pheromone trails are modified by applying a global updating rule. Hegen Xiong et al [12] have explained a simulation-based analysis of dispatching rules for scheduling in a dynamic job shop with batch release taking into account the extended technical precedence constraint which was a term defined as the extension of conventional routing-based technical precedence constraint. With respect to tardiness-related measures, the relative performances of some widely-used dispatching rules were used. The effectiveness of the four dispatching rules, and also reveals that the relative performance of dispatching rules could be affected by some model parameters. For the standard job shop scheduling problem model, where there were no extended technical precedence constraints between jobs, as well as for the models taking into account the extended technical precedence constraint, it was shown that for minimizing the total tardiness and the percentage of tardy jobs, the four dispatching rules were very effective under relatively loose due date. With respect to tardiness-related objectives, the relative performance of the analyzed dispatching rules could be affected by changing not only the levels of the extended technical precedence constraint but also the due date tightness. Kameng Nip et al [13] have stated combinatorial optimization problems which combine the classic open shop or job shop scheduling problem and the shortest path problem. It selects a subset of jobs that constitute a feasible solution of the shortest path problem, and then execute the selected jobs on the shop machines to minimize the makespan, i.e., the last completion time of all the jobs. They prove that these problems were NP-hard even if there were two machines. If the number of machines was an input, they show that it was unlikely to find approximation algorithms with performance ratios better than 2 unless P = NP. They use an intuitive approximation algorithm when the number of machines was an input, and an improve approximation algorithm when the number of machines was fixed. In addition, they use a polynomial time approximation scheme for the open shop case when the number of machines was fixed. Large-scale assembly job shop scheduling problems with a bill of materials: models and algorithms [14] study an assembly job shop scheduling problem with tree-structured precedence constraints and jobs characterized by specific bills of materials. We propose a mathematical model to deal with a simplified version of the problem, as well as a fast and efficient constructive heuristic that is able to easily face real-world-sized instances. The production schedule takes into account the actual availability of materials in stock as well as the supply times and the capacity constraints with the goal to minimize the average delay with respect to the due dates associated with the customers orders. Computational results on data related to real-life instances show that the mathematical model is able to solve (not always to optimality) small-sized instances only. On the other hand, our heuristic approach is able to solve efficiently very large problems. Hybrid Genetic Algorithm with Multi-parents Crossover for Job Shop Scheduling Problem [15] proposes a hybrid genetic algorithm with multi-parents crossover for JSSP. The multi-parents crossover operator known as extended precedence preservative crossover (EPPX) is able to recombine more than two parents to generate a single new offspring distinguished from common crossover operators that recombine only two parents. This algorithm also embeds a schedule generation procedure to generate a full-active schedule that satisfies precedence constraints in order to reduce the search space. Once a schedule is obtained, a neighborhood search is applied to exploit the search space for better solutions and to enhance the GA. This hybrid genetic algorithm is simulated on a set of benchmarks from editor@iaeme.com

4 B. Sasikala and Dr. V.P. Eswaramurthy the literature and the results are compared with other approaches to ensure the sustainability of this algorithm in solving JSSP. Yoni Nazarathy et al [16] have stated a large volume job shop scheduling problems, in which a fixed number of machines, a bounded number of activities per job, and a large number of jobs were applied. In large volume job shops,it makes sense to solve a fluid problem and to schedule the jobs in such a way as to track the fluid solution. There had been several papers which used use approximate solutions which were asymptotically optimal as the volume increases. it was assumed that the problem consists of many identical copies of a fixed set of jobs. They use a very simple heuristic which could schedule such problems. They discuss asymptotic optimality of this heuristic, under a wide range of previously unexplored situations. A Hybrid Genetic Algorithm with a Knowledge-Based Operator for Solving the Job Shop Scheduling Problems [17] describes the development of a hybrid genetic algorithm for solving the non-preemptive job shop scheduling problems with the objective of minimizing makespan. In order to solve the presented problem more effectively, an operation-based representation was used to enable the construction of feasible schedules. In addition, a new knowledge-based operator was designed based on the problem s characteristics in order to use machines idle times to improve the solution quality, and it was developed in the context of function evaluation. A machine based precedence preserving order-based crossover was proposed to generate the offspring. Furthermore, a simulated annealing based neighborhood search technique was used to improve the local exploitation ability of the algorithm and to increase its population diversity. In order to prove the efficiency and effectiveness of the proposed algorithm, numerous benchmarked instances were collected from the Operations Research Library. 3. ANT BASED ITERATIVE MULTI ATTRIBUTE JOB SHOP SCHEDULING Figure 1 AIMS System Architecture editor@iaeme.com

5 Ant Based Multi Attribute Job Shop Scheduling of Identical Machines The ant based multi attribute job shop scheduling algorithm initiates a number of ants according to a number of jobs given. Then based on the initial sequence, the method generates a number of sequences and computes the average waiting time, resource waiting time, resource usage factor, and makespan time. Based on the above measures the method estimates the multi attribute scheduling strength. Finally, based on the scheduling strength, the method selects a single sequence. At each iteration, the method produces the sequences and schedules them accordingly. This section briefs the scheduling approach in a detailed manner. Figure 1 shows the architecture of the AIMS scheduling and their stages involved. The proposed method generates the initial sequence of jobs to be executed and estimates the multi attribute scheduling strength value. Based on estimated value, a single optimal sequence is selected and executed. Then with the remaining jobs, the method once again generates the sequence in an iterative manner and estimates MASS value to choose a single sequence 3.1. Iterative Sequence Generation At this stage, first the list of jobs being submitted is identified and the resources required are identified. Then the method identifies the list of resources and the number of resources available is identified. Third, the jobs with the resource are populated in a random manner to produce the initial sequence. For each sequence generated, the method generates the subsequent sequences to be used for scheduling. Algorithm 1: Input : job set Js, resource set Rs. Output : sequence set Ss Start Read job set Js. Read resource set Rs. According to the number of resources available generate initial sequences. Initial sequence set Iss = //initial sequence generated For each sequence s Identify remaining jobs Rj = Generate other sequences Iss = //combination of all other sequences End Stop The above discussed iterative sequence generation algorithm1 generates the sequences initially according to the number of resources available and for each job, a single sequence as first is generated. For the remaining jobs, the sequences will be generated in an iterative manner Multi Attribute Scheduling Strength Estimation The multi attribute scheduling strength is the measure which represents the strength of scheduling algorithm in achieving the scheduling parameters considered. In this approach, the method considers the makespan time, overall waiting time, overall resource utilization, editor@iaeme.com

6 B. Sasikala and Dr. V.P. Eswaramurthy overall resource waiting time. Using all these parameters the method computes the multi attribute scheduling strength for the sequence given. Algorithm 2: Input : sequence S, resources R Output : MASS Start Read sequence S. Identify list of jobs Js = Compute average waiting time Awtime = //sum of all waiting time of jobs / number of jobs Compute overall makespan time Mt. Mt = ( ) //sum of all waiting time and processing time of jobs Compute overall resource waiting time Rwt. Rwt = //sum of all idle time of resources Stop Compute resource utilization factor Ruf = Compute MASS = The above discussed algorithm2 computes the waiting time of jobs, waiting time of resources, resource utilization and makes pan time of the jobs. Using all these factors the method estimates the multi attributes scheduling strength for the given sequence AIMS Scheduling The ant based multi attribute scheduling algorithm generates iterative job sequence at each stage. For each sequence generated the method estimate the multi attribute scheduling strength and based on the scheduling strength the method selects a single sequence for each sequence generated earlier. This will be performed at the finishing of each job by the ant or when the ant visits the job. Algorithm 3: Input : job set Js, resource set Rs. Output : Null Start Read job set Js Read resource set Rs. Initialize ants as As = Generate iterative sequences Iss = Iterative-sequence-Generation. For each sequence S End Compute MASS = editor@iaeme.com

7 Ant Based Multi Attribute Job Shop Scheduling of Identical Machines Stop. Choose sequences according to number of resources. Sequence set ss = For each sequence Sk from ss While(Js(Unvisited)>0) Generate subsequence iterative sequence Estimate Mass value Select sequence with higher MASS Assign to Ant. End End The ant based iterative multi attribute scheduling algorithm3 generates the sequences in an iterative manner at the finishing of the given job. The ant itself would generate the sequence and compute the MASS value. Based on the value estimated the method selects a single job which the ant should visit. 4. EXPERIMENTAL RESULTS AND PERFORMANCE ANALYSIS The Methodology is implemented in the stage of MATLAB 2015a with the frame job design is i5 processors with 4GB RAM which is utilized for makespan time minimization handle in various experiments. The performance of the approach has been evaluated on different measures. The method has been measured for its scheduling performance and large scale support. For the evaluation, a different number of jobs with machines has been considered. The details of the simulation scenario have been presented in Table 1. Let us consider there exist 7 jobs in the job set and 3 resources available. The details of the jobs and their processing time are given below: Table 1 Jobs and processing time. Job Number Processing Time According to iterative ant based multi attribute job shop scheduling the method generates a number of sequences as follows: 4.1. Analysis on Inventory Based Scheduling The inventory based approach considers the availability of resources or machines. First, the method schedules the jobs on available machines according to their time constraint. Then with the available machines, the method schedules them editor@iaeme.com

8 B. Sasikala and Dr. V.P. Eswaramurthy Table 2 Scheduling of Inventory based scheduling. Jobs Processing Time Machines Allotted Completion Time The Table 2, shows the details of inventory based scheduling which is performed based on the inventory approach. The inventory based approach produces the completion time of 19 seconds Analysis on Ant Based Iterative Multi Attribute Scheduling The proposed multi attribute scheduling algorithm generates different sequences and for each of them, the completion time is estimated. Based on the completion time a single one is scheduled. This is performed iteratively to improve the performance of the scheduling. Table 3 List of sequences generated. Iterative sequence Execution time Other patterns Processing time Remaining jobs 2,3,5,6 Again, sequence 3,5, Remaining Job NA 5 Execution time 10 The Table 3, shows the list of sequences being generated based on the ant based iterative job shop scheduling algorithm. The Table 4, shows the list of jobs and their allotted machines. Table 4 Jobs and allotted machines. Job J Number of machines used According to AIMS algorithm for a small scale scheduling with a 7 3 problem. No of sequences generated is Np Np=N + (N 2 n ) +1 (1) editor@iaeme.com

9 Large scale Support Performance % Ant Based Multi Attribute Job Shop Scheduling of Identical Machines Here, N for a number of machines. The total completion time C t of job J i is the total time it takes to complete the job and the last operation of the job J i. The total completion time C t is computed as follows: C t = t (2) According to Equation(2), the total completion time is the sum of all completion time of jobs from the job set. The average completion time AC t is computed as from equation (2), which has been reduced for better scheduling. AC t = ( i)/n (3) Job J Table 5 Average completion time of each job scheduled from Table 2. Number of machines used Processing time Total completion time Average completion time 8.57 According to the above scheduling sequence, the method computes the multi attribute scheduling strength. Based on the measure estimated, the method selects a single sequence by the ants and performs scheduling. The proposed method has produced only 8.57 as the completion time. Large Scale Support Imperialist Inventary Based EPPX Knowledge Based AIMS Figure 2 Problem support comparison. Figure 2 shows a comprehensive comparison in terms of adaptability between the different methods of scheduling large scale problem. The inventory, knowledge based and GA-Based methods can be adapted for small and large scale problem up to certain limit only. Among all the method randomized pattern method has been found to be effective even in scheduling large sets of jobs. When it exceeds more than 100 jobs the scheduling efficiency editor@iaeme.com

10 Scheduling Performance % B. Sasikala and Dr. V.P. Eswaramurthy and performance will be reduced. But in the case of the proposed method, it produces effective scheduling. Also, the baseline method and GA-Based methods are designed to schedule jobs where the number of jobs and machines should be in a bounded range, whereas the proposed randomized pattern mining method has a dynamic nature in the number of jobs and machines with multi objective optimization. 100 Scheduling Performance Imperialist competitive Inventary Based EPPX Knowledge Based AIMS Figure 3 Comparison on scheduling performance Figure 3 shows the comparison of scheduling performance and shows that the proposed AIMS method has produced higher scheduling performance than others. 5. CONCLUSIONS In this paper, an efficient ant based iterative multi attribute job shop scheduling has been discussed. The method generates a number of sequences according to a number of resources available. At each stage, the method generates the sequences with remaining jobs in combinatory. For each sequence generated, the method estimates the multi attribute scheduling strength. Based on the scheduling strength estimated the method selects a single sequence at each stage and allocates the machine to the jobs. The method produces efficient results on job shop scheduling and reduces the time complexity as well. REFERENCES [1] A. Azadeh, N. Hosseini, S. Abdolhossein Zadeh and F. Jalalvand, "A hybrid computer simulation-adaptive neuro-fuzzy inference system algorithm for optimization of dispatching rule selection in job shop scheduling problems under uncertainty", The International Journal of Advanced Manufacturing Technology, vol. 79, no. 1-4, pp , 2015 [2] R. Mellado, C. Cubillos and D. Cabrera, "A constructive heuristic for solving the Job- Shop Scheduling Problem", IEEE Latin America Transactions, vol. 14, no. 6, pp , 2016 [3] H. S. Keesari and R. V. Rao, "Optimization of job shop scheduling problems using teaching-learning-based optimization algorithm", OPSEARCH, vol. 51, no. 4, pp ,2013 [4] Lvjiang Yin, Xinyu Li, Liang Gao, Chao Lu and Zhao Zhang, "A novel mathematical model and multi-objective method for the low-carbon flexible job shop scheduling problem", Sustainable Computing: Informatics and Systems, editor@iaeme.com

11 Ant Based Multi Attribute Job Shop Scheduling of Identical Machines [5] Sadegh Mirshekarian and Dusan N.Sormaz, "Correlation of job-shop scheduling problem features with scheduling efficiency", Expert Systems with Applications, vol. 62, pp , 2016 [6] Liping Zhang, Liang Gao and Xinyu Li, "A hybrid intelligent algorithm and rescheduling technique for job shop scheduling problems with disruptions", The International Journal of Advanced Manufacturing Technology, vol. 65, no. 5-8, pp , 2012 [7] Mohamed Kurdi, "An effective new island model genetic algorithm for job shop scheduling problem", Computers & Operations Research, vol. 67, pp , 2016 [8] Leila Asadzadeh, "A parallel artificial bee colony algorithm for the job shop scheduling problem with a dynamic migration strategy", Computers & Industrial Engineering, vol. 102, pp ,2016. [9] Su Nguyen, Mengjie Zhang,Mark Johnston and Kay Chen Tan, "Automatic Programming via Iterated Local Search for Dynamic Job Shop Scheduling", IEEE Transactions on Cybernetics, vol. 45, no. 1, pp. 1-14, [10] Omid Gholami and Yuri N. Sotskov, "A fast heuristic algorithm for solving parallelmachine job-shop scheduling problems", The International Journal of Advanced Manufacturing Technology, vol. 70, no. 1-4, pp , [11] Habibeh Nazif, Solving Job Shop Scheduling Problem Using An Ant Colony Algorithm, Journal of Asian Scientific Research, [12] Hegen Xiong, Huali Fan, Guozhang Jiang and Gongfa Li, "A simulation-based study of dispatching rules in a dynamic job shop scheduling problem with batch release and extended technical precedence constraints", European Journal of Operational Research, vol. 257, no. 1, pp , [13] Kameng Nip, Zhenbo Wang and Wenxun Xing, "A study on several combination problems of classic shop scheduling and shortest path", Theoretical Computer Science, vol. 654, pp , [14] Gianpaolo Ghiani, Antonio Grieco, Antonio Guerrieri, Large-scale assembly job shop scheduling problems with bill of materials: models and algorithms, Wseas Transactions On Business And Economics, Volume 12, [15] Noor Hasnah Moin, Ong Chung Sin, and Mohd Omar, Hybrid Genetic Algorithm with Multiparents Crossover for Job Shop Scheduling Problems, Hindawi, Mathematical Problems in Engineering Volume [16] Yoni. Nazarathy and Gideon. Weiss, "A fluid approach to large volume job shop scheduling", Journal of Scheduling, vol. 13, no. 5, pp , [17] Hamed Piroozfard, Kuan Yew Wong, and Adnan Hassan, A Hybrid Genetic Algorithm with a Knowledge-Based Operator for Solving the Job Shop Scheduling Problems, Hindawi, Journal of Optimization Volume [18] R. Vidhyasri and R. Sivagamasundari, A Review on Factors Influencing Construction Project Scheduling. International Journal of Civil Engineering and Technology, 8(3), 2017, pp [19] Hymavathi Madivada, C.S.P. Rao, A Review On Non Traditional Algorithms For Job Shop Scheduling. International Journal of Production Technology and Management (IJPTM), 3(1), 2012, pp editor@iaeme.com