Student at Computer science, Mathematics Department, Faculty of Science, Helwan University, Egypt 2

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1 Volume 5, Issue 10, October-2015 ISSN: X International Journal of Advanced Research in Computer Science and Software Engineering Research Paper Available online at: Study on Job Scheduling Problem for Flexible Manufacturing System based on Ant Colony System 1 Asmaa Kamal, 2 Iman Badr, 3 A. A Darwish 1 Student at Computer science, Mathematics Department, Faculty of Science, Helwan University, Egypt 2 Lecturer of Computer science, Mathematics Department, Faculty of Science, Helwan University, Egypt 3 Professor of mathematics, Mathematics Department, Faculty of Science, Helwan University, Egypt Abstract In most real-world environments, Flexible Manufacturing System (FMS) has attracted the attention of researchers in these recent years. FMS s scheduling is an important problem in production planning which directly affects both cost and time of the production. Scheduling of FMS includes determining the optimal input sequence of job parts and an optimal allocation of those jobs on suitable machines. Job Scheduling Problem (JSP) is regard as a combinatorial optimization problem therefore it impossible to get all possible optimal solutions in a reasonable time. In this paper, The JSP for FMSs will be represented using the Ant Colony System (ACS) optimization technique to minimize the overall completion time for a set of specified tasks (Makespan). Finally, the impact of incoming new job to the exiting schedule, the factors that characterized it will be analyzed and the computational experiments have been executed based on the JSP data benchmarks to apply the ACS algorithm for a JSP. Keywords Flexible Manufacturing Systems (FMSs), Job Scheduling Problem (JSP), Incoming Job, Makespan, Ant Colony System (ACS) I. INTRODUCTION Generally FMS s refer to the system s realization to changing demand patterns as well it has capability to recover from equipment crashes and breakdowns. In other hand FMSs are characterized by a highly dynamic environment causing or necessitating changes to the planned allocations, the timely allocation of resources to the planned jobs is referred to Scheduling. FMS comprises of multiple computer numerically controlled (CNC) machines, linked with an automated handling material, transfers system and controlled by a central computer. The material handling and transportation system is responsible for making material and processed parts available to the required machines and consists basically of automatic guided vehicles (AGV) which are controlled by computer programs. Each CNC machine is a multi-tasking machine, the operations for one job in FMS can be performed on one or more machines, so the FMS s scheduling is considered a computationally complicated problem. FMS Scheduling is described as an extension to the traditional job shop scheduling problem (JSSP) [1]. The flexibility of the FMS refers to the maximum number of machines that have capability of processing each of the operations of jobs. Scheduling problem is regarded as a dynamic problem when there are continuous arrivals of incoming new jobs and a stochastic problem when considering uncertain events e.g. machine breakdowns and various processing times considered.when arriving a new job at time t, the solution of operations already started before t is given and a new schedule is constructed, consisting of an accumulation of uncompleted operations to be starting after time t, in addition to all the operations from coming new job. Therefore, in a dynamic JSP, each incoming new job makes change in the setting of the existing scheduling problem. There are three factors that characterize a JSP [i] The arrival time of a new job [ii] the sequence of machines that the job has to be processed in and [iii] the processing time distribution over machines. The objective is to find a best schedule i.e. get an allocation of the operations to time intervals on the machines which has the minimum duration required completing all jobs so JSP. The standard model of a JSP is described as (J/M/G/C max ) where J, M, G and C max stand for the number of jobs, the number of machines, the precedence rules and the minimum of makespan, respectively. Meanwhile the nature has inspired several meta-heuristics; among these is Ant Colony System (ACS) that applied to solve different discrete optimization problems by simulating the nature for solving those problems like the scheduling problem of FMSs. The ACS algorithm is regarded as a distributed algorithm which is used to solve combinatorial optimization problems. Its model is depended on the foraging action of real ants that find an approximately shortest path to the source of food via revealing of the density of pheromone (chemical substance) precipitate on the route as they walk. The structure for this paper is as follows: in section 2, the related works on some approaches for dynamic scheduling and some of recent optimization techniques that solve JSP. The description of a JSP is given in Section 3, then ACS is defined in Section 4. Section 5 is to describe the model of JSP by ACS and a case study with computational experiments is provided in Section 6. Finally, conclusions and future work are presented in Section 7. II. RELATED WORK Flexible manufacturing systems were studied in two coordinate, theoretically and practically by many researchers and many theoretical works have been reported recently to optimize the solution of scheduling problems of FMS, machine 2015, IJARCSSE All Rights Reserved Page 6

2 flexibility in dynamic scheduling of manufacturing systems which is composed of a material handling system and flexible machines, have been considered by S.Cenk et al. [2]. The scheduling of AGVs is also considered during the scheduling process. Li Nie et al. [3] concerned with proposing a scheduling and controlling mechanism based on agents that responses to the dynamic events in FMS like jobs arrive over time and machines breakdown through the collaboration between the agents. Ant colony optimization (ACO) algorithm is represented by an agent based model to merge process planning and shop floor scheduling by C.W. Leung et al. [4]. A three stage hybrid approach called JSFMA for solving the JSSP developed by K.Somayeh et al. [5] considering a manner similar to Shuffled Frog Leaping algorithm, in addition to solving the problem based on a memetic algorithm. R.S.Nakandhrakumar et al. [6] present how the adaptive search algorithms namely Tabu search is applied to solve JSSP problem, dispatching rules are used to obtain an initial solution and find more new solutions in a neighborhood depended on the jobs critical paths. A Hybrid Suffled Frog-leaping Algorithm (HSFLA) used for solving the several purpose flexible job shop scheduling problem is introduced by L.Junqing et al.[7] considering the total workload of all machines, as well the workload of the critical machine. S.G. Ponnambalam [8] focuses on scheduling job shops with respect to improving machine utilization or reducing lead time for manufacturing industry. I.Badr et al. [9] introduced Genetic Algorithms (GA) integrated with an agent-based scheduling model to cope with the shortcoming of agents and achieve required flexibility with efficiency. Mohd et al. [10] introduces the Artificial Immune System (AIS) approach for treating the schedule problem of FMS, based on the antigenic clustering features inherent at AIS. W. Xiang et al. [11] focuse on using an agent coordination mechanism inspired by both foraging and division of labor of ant colony in a MAS to solve a dynamic manufacturing scheduling problem, A.Motaghediet al. [12] study the flexible job-shop scheduling problem and proposed a new hybrid genetic algorithm to obtain a large set of optimal solutions in a reasonable run- time. Z.Jun et al. [13] presents an examination into the use of an Ant Colony System (ACS) for optimizing the JSP. III. PROBLEM DESCRIPTION When receiving an order for a number n of jobs defined as J= {j 1,j 2,.j n }, it has to determine how to allocate them to the appropriated group of machines and create the corresponding production schedule. Each group has number of machines and can produce all product types with different efficiency defined as M= {m 1,m 2,,m m }. Each job can be routed through m machines in a pre-defined order, processing of a job on a machine is called an operation, each operation can be processed on one or more suitable machine with different processing time. The operation can denoted by O ij and the set of operations can be formulated aso={o ij i [1, n], j [1, m]}. For an operation O ij of job i on machine m, the operation processing time can denoted by P ij and(p ij >0), C ij ( O ij O) is the completion time for operation, and the total completion time for a set of operation is C max. Thus, the objective of the problem is to minimizes C max =max(c ij O ij O). Constraints of the JSP are explained as the following: Once process can begin at any point in time, the required machine is available. Each job must pass through a sequence of operations that is predefined, where operations cannot begin until the completion of its predecessor (i.e. processing O ij cannot begin to be processed until O ij _1 has completed). Each operation must be processed completely on one or more machine. The solution approach applied in this paper is a graph-based approach, represents JSP as G = (N, D, C) where N is the set of nodes which represent the operations, N=O U {O 0 } U {O T+1 } ; {O 0 } and {O T+1 } are the special dummy operations for start and ending nodes, T is the overall number of operations that T=n m,d is a set of directed lines which connect operations approved to the same job and C is a set of undirected lines which connect operations working on a same machine. The edge is associated with the processing time p ij with each operations O ij O. IV. ANT COLONY SYSTEMS The ant colony feeding behavior is very interesting and very organized described in Fig. 1: (a) ants want to search food, so they begin from their nest and arrive at the decision making point where they must decide which path to go on, (b) there are more one path and ants have no information about who s the best path to choice, so they can choose the path just randomly, (c) the ants that choose the shortest way in the middle get the food more quickly than those who choose the other paths and while movement, ants can deposit some pheromone on their path, (d) finally,pheromone accumulates with a highest rate in the middle path, and then next ants will choose this path. The probability the ant coming later to choose the path is proportional to the quantities of pheromone on the path, deposited by other previous ants [13]. Ant System algorithm was initially introduced by Dorigo et al. [14] as a purpose metaheuristics approach for combinatorial optimization problems. ACS is a newalgorithm that has been introduced to improve the performance of this algorithm was presented in Dorigo and Gambardellan [15]. In the ACS algorithms, ant s behaviors are simulated by a virtual agent which capable of exploration a limited seeking and obtaining information about the environment surrounded, in addition to that ants have a stored memory called (tabu list) that can store visited elements from their current path. The artificial ant k walks from one node to another and construct step by step convergent solution to be saved at the tabu memory can store information about the sequence of nodes or the route taken with time t until a solution is constructed. Once ants get a good solution, they locate their path by putting quantity of pheromone substance on their edges of the path, then ants at the following iteration are gravitates towards the pheromone pre-position to follow the previous traversed best paths. For the optimization problem, a graphical representationmust first be constructed to apply the proposed ACS algorithm. 2015, IJARCSSE All Rights Reserved Page 7

3 Fig. 1(a) (d) The ant colony feeding behavior There are two types of related information which guide the motion of the ant and the values of both has been modified at each iteration by ants. One of them is the measuring of the heuristics predilection for moving ant from point i to point j called Heuristic information (η i,j ), as well during the implementation of the algorithm and this information don t change.the other one is the measuring of the approbation learned for point i to point j motion called pheromone trails (τ i,j ) information, as well during the implementation of the algorithm and this information has been modified depending on the solutions yield to share the experience obtained by these artificial ants. At begging of the meta-heuristic, initializing quantity of pheromone along each edge to be a positive real value, is done and the initial locations of ants are randomly chosen. Based on ending the initialization phase, the solution will constructed independently by each artificial ant. Each ant decision during its tour is based on the quantity of pheromone (τ i,j ) that presented along the graph edge E ij, and distance heuristic (η i,j )along the graph edge. The probability of transition to move from point i to point j for each ant k at time t is described as formula (1): P k (i,j)= [τ(i,j )] [η (i,j )] [τ(i,l)] if jallowed k [η (i,l)] lallowedk Where: p k i, j : represents the probability for ant k to choose node j after node i, allowedk = [N-tabu k] s.t N is the set of available edges at decision point i and tabu k is the tabu list of the ant k, α : is a parameter defined by the user to control the effect of τ i,j. β: is a parameter defined by the user to control the effect of η i,j. Let τ i,j on the edge (i,j) at time t, theneach ant at time t chooses the next node where it will be at time t + n. For an iterationof the ACS algorithm, x moves carried out by x ants in the interval (t, t + n), then every n iterations of the algorithm each ant has completed a tour. At this point the trail intensity is updated according to formula (2): τ i,j (t + n) = ρ. τ i,j (t) + τ i,j (2) Where ρ is a coefficient and 1 ρ represents the rate of evaporation of pheromone trail through time t and time t + n, that because of old pheromone should not have much effect on the future decisions of the ants, and itdecreases over time. The important property of evaporate the pheromone is that it prevents early assemblage to a sub-optimal solution, so ACS has been capable of forgetting bad solutions. Total quantity of pheromone laid by the x ants get by formula (3): x τ i,j = 0 Otherwise k 1 τ k i,j (3) Where τ i,j is the quantity per unit of length of trail substance laid on the edge E ij by the ant k between time t and t + n, it is inversely proportional to cost of the solution (makespan length), shown in formula (4) : ) 1( τ i,j = q / L k if the ant k travels along E ij (4) 0 otherwise Where q is a constant positive real value (0 q 1)and L k is a tour length of ant k. After the ant has completed its tour, its tabu list is emptied and become free again to choose its path. 2015, IJARCSSE All Rights Reserved Page 8

4 V. ACO FOR JSP The approach of the artificial ants algorithm applied to the FMS scheduling is discussed in this section. From the study of ACS model described above, we can transform it to solve the JSP. Given an m JSP, the modified ACS is described that each point (node) regarded as an operation of a job on a machine. Due to flexibility of the system more than one possible node for the operation of the same job may be appeared. After two dummy nodes are added to the set N of nodes, ants are all allocated in node0 (operation O 0 ) and whose goal is in node n m+1 (operation O N+1 ). Ant k cannot move to get a feasible route for a JSP before it has been provided with three lists: (1) tabu k List includes the nodes that are visited by ant k, (2) A K list stores the present accessible nodes that still to be visited by the ant K, (3) W k list stores the next operations that the ant K can visit based on the order constraint of jobs and the states of the machines (busy or free). For the linearity of ant s tour, machine constraints do not be considered here. For simple example, suppose thato i = {1,2,3,..,i} of job J, this operations can be done on machine m = {2, 3, 1,,m }, when ant k moves from O 1 to O 2, O 1 is deleted and O 2 is added to the set of next operations W k if the machine 3 is free. Gnarly, given n number of jobs then W k = {O i1 i [1,n]}, the process is iterated until A k = { }. Finally, the sequence of the nodes visited by the ant stored in the tabu list identifies the solution proposed by ant k. For the JSP, the technical orders of operations and their processing times cane be represented in a technical matrix T M and a processing time matrix P t respectively, each row of T M represents the order of machines where all the operations of one job can visit while each row of P t represents the processing times that those operations will take on their machines. For more explain matrices T M and P t define the job shop scheduling problem in Fig. 2. The first row represents the first job contains three operations [O 11, O 12, O 13 ] and will be processed on machines [m2, m3,m1] in sequence, and the three operations need processing times [t(o 11 ), t(o 12 ), t(o 13 ) ]respectively. In order to apply the ACS algorithm in JSP, graphical representation of the optimization problem can be constructed as Fig. 3, which represents number of nodes representing all the operations, O 12 to O 1i for the first job, O 21 too 2i and for the second job, etc., two dummy nodes O 0 and O f for the start and end of routing for overall operations. They are connected by directional edges that indicate the precedence constraints given in the technical matrix T m. The bidirectional edges indicate that no ordering constraints found among those operations. In addition Tis placed on the upper of operation represents its processing time, Fig. 2. The technical matrix T m and the processing matrix P t for a JSP Fig. 3. A graphical representation for a n-job, m-machine problem Each edge of the disjunctive graph is associated with a pair of values (τ ij, η ij ) that τ ij represent the intensity of the pheromone trail on the edge E ij and η ij represent the heuristic distance between the two nodes (i,j) it connects. The value of η ij is the traveling time for the operation so it can be easily get from matrix P t. The value for τ ij can be found in the pheromone matrix which records the values of pheromone for all the edges connecting every two nodes and then it is updated by the ants which found the best solutions. This updating of the pheromone matrix have a computing effort because of the size of the pheromone matrix (nxm+1) 2 where nand mare number of jobs and number of machines, respectively. A certain quantity of pheromone is dropped at an ant move. Two kinds of pheromone update plan are introduced (1) local updating rule: A step by step online pheromone trails update can be performed when moving an ant 2015, IJARCSSE All Rights Reserved Page 9

5 from node i to node j. (2) the global updating rule: The amount of pheromone on the edge is modified again by applying this update once all ants have arrived to their goal. The ACO pseudo-code is described as Step1 Initialization 1.1: Set Initial parameters for the ACO (α, β, ρ, q) 1.2: Each ant is located on initial node with empty memory. 1.3: Set initial pheromone trials value τ=τ 0 for each edge. Step 2 Iteration 2.1: start from dummy node (node 0) where a colony of ants is initially positioned. 2.2: If terminal condition is reached then go to step : Else; place each ant on a starting node. 2.4: if all the ants arrived then apply the global pheromone updating rule and go to step : Else; schedule has been constructed for each ant k that each ant repeatedly applies a stochastic greedy rule (transition rule) to choose the next processing operation, until a complete solution is built by all ants. 2.6: Appling local pheromone updating rule then go to step : Terminate the algorithm, recording the optimal solution of the schedule problem. VI. CASE STUDY A. Test Environment Given an instance for two jobs and three machine that illustrates the simple job shop schedule where each operation of each job can be assigned to only one machine described as 2/m/G/C max JSP with a machine technological matrix T m and a processing time matrix P t then the optimal schedule is C max =6.5, can be given in Fig. 4 : Fig. 4. T m, P t and an optimal schedule for 2x3 JSP To analysis the dynamic scheduling problem, three factors that characterize a JSP are described as the following: 1. The effects of the arrival time Assuming that there is a new job arrived at two different time t 1 =1 and t 2 =2.5, when coming new job at t=1 then the first available time for machines {m1, m2, m3} are from {2, 1, 2.5} respectively, and {O 12,O 13,O 22,O 23 } are the set of unexecuted operations in addition to the new job operations {O 31,O 32,O 33 }, but operations O 11 and O 21 are not included because they are already being processed when the new job arrived. Similarly at t=2.5, the first available time for machines {m1, m2, m3} are from {2.5,5,2.5} respectively, and { O 13,O 22,O 23 } are the set of unexecuted operations in addition to the new job operations {O 31,O 32,O 33 }, table 1 shown the two problems. To get optimal solution of two different problem, assume that the machine technological matrix for the new job T m =[2,3,1] with processing time P t =[1,1,1], then the new optimal schedule after a new job arrived at t=1 and t=2.5 can be given in Fig. 5(a)-(b). 2. The effects of the technical order The new problem is also affected by the technical order of the new job, that when the T m of the new job arrived at t=2.5 is changed to T m = [3, 1, 2] with same processing time Pt = [1, 1, 1], then the minimal makespan Cmax could be improved from C max = 8.5 to C max =6.5, Fig. 6. Table 1. The comparison of two problems at two different time Time Re-schedule operations The first available time for machines {m1, m2,m3} New job at t=1 { O 12,O 13,O 22,O 23 {2,1,2.5} 2015, IJARCSSE All Rights Reserved Page 10

6 ,O 31,O 32,O 33 } New job at { O 13,O 22,O 23,O 31,O 32,O 33 } {2.5,5,2.5} t=2.5 (a) New optimal schedule with C max =6.5 when the new (b) New optimal schedule with C max =8.5 when the new job comes at t= 1 unit time job comes at t=2.5 unit time Fig. 5. New optimal schedules after the same job arrived at different times 3. The effects of the distribution of processing times Similarly, C max could be improved from C max = 8.5 to C max = 8 (Fig. 7), if the processing time for the new job is redistributed from {1,1,1} to {1.5,0.5,1} while the overall processing time, the technical order and the arrival time remain unchanged. Fig. 6. New optimal schedule with C max =6.5 after the order of operations is change Fig. 7. New optimal schedule with C max =8 after the processing time of operations is re-distributed ACS for job scheduling problems The 2/3/G/C max JSP can be graphed in Fig. 8, the idea of ACS algorithm is to initiate a set of ants repetitively, which move in a common environment (the graph) comprised of all operations in a JSP. Each ant moves one by one through all of those node operations and forms a route, that can be constructed as scheduling and the length of route represents one of the values of performance measurement like makespan, the goal of every ant moving is to choose the shortest route. During ant moving, ant leaves behind on the edge some amount of pheromone, which cause change on the general environment. Fig. 8. A graphical representation for of a 2 3 JSP Ant K can choose the next operation based on rule in formula (5) [17]: Pij(k) = [τ(i,j )] [1/d(i,j )] [τ(i,l)] if jallowed k (5) [1/d(i,l)] lallowedk Where R is the index of iteration number, the distance d here is sum of traveling time among the current machine to the next machine and the operation processing time in this next machine. The pheromone matrix has represented the environment, that updated at each iteration in formula 6 and 7 [17] : 2015, IJARCSSE All Rights Reserved Page 11

7 τ i,j (R+ 1) = (1-ρ). τ i,j (R) + τ i,j (R+ 1)(6) and τ ij (R+1)= q / L k if the ant k travels along E i j (7) 0 otherwise For the previous 2/3/G/C max JSP, the pheromone matrix is explained in Fig. 9 represented nodes (operations) one to seven, that records the intensity of pheromone values for all the edges which connecting every two operation nodes. First row of the matrix shows the pheromone values of the graph edges that start from first node 0 to the other seven nodes, while ant moves from node 0 to node one, ant put behind on the edge quantity of pheromone be τ 01 =0.1 and similarly τ 04 = 0.1 that because node 0 can arrive node one and node four only, others formatted to be zeroes. Similarly second row shows the pheromones of the edges starting from node one to other seven nodes, while ant moves from node one to node two, ant put behind on the edge quantity of pheromone be τ 12 = 0.13 and similarly τ 14 = 0.16, τ 15 = 0.16, τ 16 = 0.17 because node one can only reach node two,four, five and sex, others formatted to be zeroes. Fig. 9.A 2 x 3 JSP pheromone matrix At each re-scheduling moment, a JSP has to be updated before the ACS algorithm can be executed through updating its pheromone matrix, which involves updating of nodes and pheromone values. The updating of the pheromone matrix Divided into two parts: deleting nodes that represent carried out or in processing operations and adding nodes representing all operations of the incoming new job, Fig. 10(a)-(c). The cells related to node 1 and the cells related to node 4 are shaded in table (a) of Fig.11 and need to be deleted. In table (b) three shaded new nodes representing three operations of the incoming new job are added to the pheromone matrix, initiated with appropriate values. Finally table(c) generates the new pheromone matrix with the nodes that re-numbered based on the updated order. ACS parameters Setting parameters of ACS is very important, when setting β = 0 that means only the pheromone information being used while setting α = 0 that means only the heuristic information being used, initial pheromone trials value τ0 must be not equal zero and the number of ants in each generation was X = n m. The values of the optimal parameter depend on the problem to solve, and it is difficult to find all proposal parameters setting for all problems. Parameters α = 1, β = 1, ρ =0.5, q=1 and τ 0 =0.5 developed to solve several JSP benchmarks, It is interesting that β = 0 is a better choice for many given problems in our test. The matlabe software for the proposed ACS algorithm is used to test different instance for JSP bench- mark problems. (a) Deleting all cells related to nodes 1, 4 (b)adding three new nodes 8,9,10 (c) The new update pheromone matrix Fig.10. Updating pheromone matrix 2015, IJARCSSE All Rights Reserved Page 12

8 B. The computational experiments Hurink et al. adapted some instances for classical JSSPs [19] and improve this instance data to suit the flexible job schedule problem,we can test our ACS algorithm on one of this improved instance data called edata refers to few operations may be assigned to more than one machine [20]. Table 2 Presents lower bounds (LB) and best known upper bounds (UB) for the minimization of the makespan, JSP instances that have been run by the ILOG Constraint Programming (CP) and the best known upper bounds from the literature have been improved by these new CP solution [20]. The instances mt06, mt10, and mt20 are originally instances of Fisher and Thompson [21]. The instance mt03 is sdata refers to one operation may be assigned to one machine, it regarded as a classical job shop scheduling problem instance. la01, la07 and la40 are some of instances generated by Lawrence [22]. Furthermore some instances abz05, abz06 by Adams et al. [23 ] and orb01, orb02 by D. Applegate, W. Cook [24] are provided for adaptations of the JSP instances. Table 2.The best results of some problems applying ACS for JSP Instance Size of problem Best known C max ACS C max (nxm) LB UB CP MT03 3X MT06 6X MT10 10X MT20 20X ORB01 10X ORB02 10X ABZ05 10X ABZ06 10X LA01 10X LA07 15X LA10 15X Fig. 11 show that, the makespan values obtained by ACS is near to the optimization best known values at some of instance which are (MT03,MT06,MT10,ORB01,ORB02,ABZ05, ABZ06, LA01) and not obtained the values in other which are (MT20, LA07,LA10). The results explains that whenever the number of jobs increased, the more complexity to find the best solution and the higher makespan. Fig. 11. Comparison of best makespan for instances between benchmark values and ACS VII. CONCLUSIONS AND FUTURE WORK Scheduling problem of Flexible manufacturing system is a highly dynamic problem that can be solved by many optimization techniques like Genetic algorithm, Frog-leaping Algorithm, Ant Colony Optimization, Tabu Search, etc. In this paper, Ant Colony System approach is applied to JSP problem to obtain best makespan; it is a metaheuristics that has the possibility to obtain efficiently solutions for scheduling problems. Re-scheduling operations appeared when new job arrived to the shop, the arrival time of this new job, the sequence of machines that it has to be processed in and the processing time distribution over machines are effective on the total completion time for all operations (makespan), as well as updating ant pheromone matrix, which involves updating of nodes and pheromone values. For the JSP, ACS performance depends on the values of parameters and the number of the ants. The computational experiments based on some instance of known benchmark have shown that the ACS is an effective technique for the JSP and it can find a near optimal solution. For future work exploration, pheromone updating of ACS can be improved to enhance the performance of the proposed algorithm. The ACSA can be combined with anther algorithms like genetic algorithm, frog, also it can use the recant optimization mathematical trends like Max-Plus algebra technique. 2015, IJARCSSE All Rights Reserved Page 13

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