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  1. 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – INTERNATIONAL JOURNAL OF ELECTRONICS AND 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December, 2013, pp. 93-106 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com IJECET ©IAEME A GENETIC ALGORITHM APPLICATIONS FOR MULTI-OBJECTIVE ADVANCED PLANNING AND SCHEDULING PROBLEMS - A REVIEW Prof. D. L. Bhombe1, Mr. N. B. Bhawarkar2 1 (Department of Electronics & Telecommunication, SSGMCE Shegaon/ SGB Amravati University, India,) 2 (Department of Electronics & Telecommunication, SSGMCE Shegaon/ SGB Amravati University, India,) ABSTRACT This paper gives a review for applications of Genetic algorithm for multi-objective advanced planning and scheduling problem. At the start, different needs for Multi-objective advanced planning and scheduling problem is discussed for various applications. Secondly, the brief history of Genetic algorithm (GA) with its detail structural flow, Problems optimization using Multi-objective GA for multi-objective scheduling model and advanced planning model is seen. Then different applications of GA approaches needed for Multi-objective scheduling and advanced planning problems in different areas are summarized. Keywords: Genetic Algorithm, Multi-Objective GA, Advanced Planning, Hybrid GA, Moga, Adaptive GA, GA with Tabu Search. 1. INTRODUCTION Advanced planning and scheduling (APS) is one of the best solutions for better supply chain and planning collaboration [1]. The scheduling problems composed of manufacturing problems having large inventories, difficulties in supply chain costs and promised delivery. It may cause larger lead times, non availability at promise due dates, and increasing mixed span. Most existing literature considers minimizing makespan for balancing workloads as one important objective in scheduling. But in real production more than one objective have to be solved such as minimization of penalty for tardiness in due date, simultaneously considering precedence constraints, machine selection, and flexible operation [2], etc. Advanced planning reduces total makespan, penalty for tardiness in due dates [3]. The advanced planning with scheduling i.e. APS for multi-objective problems can be achieved by the use 93
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME of Genetic algorithm. Genetic algorithm (GA) is one of the generic population based meta-heuristic optimization algorithms and the best one for finding a satisfactory solution in an acceptable time for Advanced planning and scheduling problems [4] [5]. GA is the most popular type of evolutionary algorithm [6]. In this review, we discuss first about GA and how it is used to find the optimize solution for problems in section 2. The model of advanced planning and scheduling problems is discussed in section 3. And the main focus is for different applications of GA used in different areas such as Hybrid GA for composite problems in manufacturing process, A multistage operation-based genetic algorithm (moGA) for flexible Job shop scheduling (FJSP), An adaptive genetic algorithm for advanced planning in Manufacturing Supply Chain (MSC), A genetic algorithm with Tabu Search for scheduling several machines routed for particular jobs is explained in further sections. 2. GENETIC ALGORITHM A Genetic Algorithm (GA) is a concept which is developed by Holland with his collegues in 1960s and 1970s [7]. It deals with the nature concept of survival of the fittest i.e. weak and unfit species within environment do not remain continued with future species. But the stronger species which can adopt the nature and remain survive undergoes the future generation via reproduction. The general form of GA was described by Goldberg (1989) and it differs from conventional algorithms. The GA concept uses a best solution vector i.e. x є X is called as an individual or a chromosome. The features of chromosomes are controlled by discrete units called genes. It requires some set of individual or chromosomes as an initial set of random solutions called populations [8] [9]. To find fitness solution, the process of successive iteration on every individual is called generation. At start any two individual is required to undergo through iteration process which are called parents, and the new generation produced after iteration of parent individual is called offspring chromosomes. The general structural of Genetic algorithm is shown in fig.1 Where, P(t) and C(t) are considered to be parents and offspring in current generation t. Fig.1: structure of genetic algorithm (GA) 94
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME The GA in general application follows the flow shown in above structure by considering the parameters given below: 2.1 Encoding: It is representation of individuals in binary form [10]. Generally two approach of representation is used. The first approach is bit string representation which is used in many GA applications [10]. But this representation does not work efficiently during the task having complex optimization. Hence the second approach i.e. real number representation [11] is used because of the advantages such as better adapted to complex optimization tasks, higher speeds of search and easy to develop for hybridized approach. 2.2 Crossover: Crossover is a main genetic operator which selects two individuals at a time to generate an offspring by combining features of both individuals. A simple way to choose is a random cut-point as shown in Fig.2 Fig.2: Example of one-cut point crossover operation Fig.3: Example of mutation operator 2.3 Mutation: Mutation mostly utilizes the background operator to produce spontaneous random changes in various chromosomes. A simple way to achieve this is to altering one or more genes as given in figure 3. 2.4 Selection: The best individual is selected according to their fitness value for reproduction. A different number of selection procedures are used such as proportional selection, tournament selection and rank based selection [12] 3. PROBLEMS OPTIMIZATION USING MULTI-OBJECTIVE GA Several objectives when achieved through the GA approach then it is called as multiobjective GA (MOGA). Several ideas have been proposed to solve bi-objective and tri-objective problems [13]. The multi-objective GA is preferred to achieve multi-objective advanced planning and scheduling. 3.1 Multi-objective scheduling model The scheduling model consists of multiple scheduling problems such as minimization of completion time, make span for several orders, total transportation time from one machine to another including lateness and tardiness, minimization of cost, total workload, etc. Here every problem is depends upon each other. These multiple objectives can be achieved using a GA approach so named as MOGA [14]. The MOGA objective function for multi-objective scheduling problem is given by: 95
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME f(x) = W1.f1(x) + W2.f2(x) + W3.f3(x)+ W4.f4(x) + ………+ Wn.fn(x) where, f1(x) – Completion time, f2(x) – make span, f4(x) – total tardiness & fn(x) – total cost (1) f3(x) – transportation time, and W1 , W2, W3, …. Wn are the weights of corresponding objectives that satisfy the conditions Wi ≥ 0 ; i- 1,2,…n & W1+ W2+-----+ Wn = 1 Using Pareto Optimal solutions, the objectives can be achieved by considering the following parameters and performance criteria[15]. Starting time of ith operation for order k i.e. Unit processing time of operation on machine m Lot size of order k Unit load size of order k from operation to operation Precedence constraint. Setup time from operation to operation Unit shipping time between machine m to machine n Decision variables: = = = f1(x) = f2(x) = f3(x) = f4(x) = Completion time of operation make span for order k, = = max { + } (2) I (3) Total transportation time from machine m to machine n, = ). Workload of machine m, (4) = f5(x) = Total setup time of machine m, f6(x) = Total machine idle time, (5) = = (6) - 96 - - (7)
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME 3.2 Advanced planning model The advanced planning i.e. APS problem is viewed in literature [16]. The APS problem for multi-plant also get optimized using mathematical model. It deals with the main objective of minimizing make span with simultaneously considering precedence constraints, machine selection, and flexible operational sequence. The APS problem in manufacturing supply chain was studied by Moon etal [17]. By considering the above parameters, few APS modeling formulation is given below. 1. Machine cannot simultaneously process more than one operation if, { -( + )} 0 (k,i), (l,j), m (8) 2. The intermediate transportation instances between machines are ensured if, { { - -( + )} ( + 0 )} 0 i, j, k, m, n (9) i, j, k, m, n (10) Both above constrained must be satisfied so that the operations can run on one machine without any interrupt. 3. The capacity restriction is given by, , m 4. The assurance about the precedence restrictions are not violated if, 5. For flexible operation sequence, (13) (k,i) 6. For flexible machine selection, = 0, k, I & =1, + k, i. & =1 = 0, (11) = 0, i, j, k (12) m (14) (k,i), (l,j), (k,i) Am , 4. HYBRID GENETIC ALGORITHM FOR JOB SHOP SCHEDULING PROBLEMS The advance planning and scheduling problems with delivery co-ordination involves three decisions: Order sequence, order to machine assignment and order to batch assignment. Some application where orders are processed by either one from several machines and the delivery is also by using single transportation with co-ordination among production stage and transportation stage [18]. To achieve the best system performance with proper co-ordination among machines and for minimization of Advanced planning and scheduling problems, a regular Genetic Algorithm(GA) and an efficient approach based on Hybrid of GA with parallel scheduling procedure (PSP) is used[19], this technique is called Hybrid Genetic Algorithm (HGA). The HGA finds the best result within shorter time than normal GA [20]. The Hybrid GA is developed to solve the composite problems of manufacturing (production) scheduling problem and or transportation routing problems. First approach is to make sequence of operations which includes an encoding using improved random keys developed for this part. And the second approach is to assign resources for each operation. 97
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME 4.1 Sequencing operation: The approach is based on the random keys vector which represents the priority list for performing operations. For example a vector given for sequence as (O1,O2,O3) = (0,2,1) represents a sequence of operations as O1 O3 O2. All these sequence vectors are called “permutations”. (a) Random space (b) Sequence space Figure 4: Sequencing operation for given vector. 4.2 Selecting Resources: The approach of combining resources assignment for each operation from two parents generates better combination of selected resources. So a dynamic programming can be applied simply if a tentative scheduling is a scalar value. A simple GA based on dynamic programming approach is applied to this part with the use of uniform crossover to generate candidates of resource assignment. Thus a Hybrid GA is used to formulate the advanced planning and composite scheduling [21]. Considering the example to schedule the three jobs having four machines with processing time given below: Table1. Job requirements of Example M1 J1 M2 M3 M4 3 4 1 3 8 2 1 O13 3 5 4 7 O21 4 1 1 4 O22 2 3 9 3 O23 9 1 2 2 O31 8 6 3 5 O32 J3 1 O12 J2 O11 4 5 8 1 The best schedule for the above problem will be as given in table: 98
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME Table2. Operation index Table3. Scheduling plan Machine Operation performed J1 M2 M1 M4 M1 O23,O21 J2 M4 M3 M1 M2 O11, O32 J3 M3 M2 M3 O31 M4 5. O22, O21 O13 A MULTISTAGE OPERATION-BASED GENETIC ALGORITHM (MOGA) FOR INTEGRATED DATA STRUCTURE AND SCHEDULING APPROACH A traditional genetic algorithm (GA) [22] is more complex with more CPU time for finding solutions. Hence a multistage operation-based GA approach has been proposed. The moGA is used for designing chromosome to improve the effectiveness for Optimizing Advanced Planning and scheduling in Flexible Manufacturing System. It deals with objective of optimal resource selection for assignments, operation sequence and allocation of variable transfer batches to minimize the total make-span by considering the transportation time. This approach is proposed to make the chromosomes simpler with improved efficiency after using the new representation. Most literatures for moGA deals for shop scheduling problem which concentrates on flexible Job Shop Scheduling (JSP) cases where the transportation problem is considered [23] [24 ] [25]. The JSP concerns minimization of total makespan with determination of set of jobs on a set of machine. For flexible Job shop scheduling (FJSP), at least one machine may be capable of performing more than one type of operation [26]. This flexibility is of two types: Total flexibility where all machines are available to achieve all operations and Partial flexibility where part of available machines achieves some operations [22]. The FJSP can be solved efficiently with better result using moGA compared with other approaches. The objectives of minimizing the makespan, total workloads of the machines and maximum workloads of the machines can be achieved by moGA which including k-stages of total number of operations for all jobs with m-state representing total number of machines [27]. These objectives are achieved by using following fuzzy operators. (a) The minimization of makespan: min = (15) (b) The minimization of workload: min = (16) (c) The minimization of total workload: min = (17) The moGA approach for F-JSP is shown in fig.5 below which represents 3 jobs operated on 4 machines. Two other nodes are added as starting node and terminal node. Hence the problem can be formulated as an 8-stage, 4-state problem [27]. 99
  8. 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME The feasible schedule can be obtained as: Fig.5: Example for Multistage Operation-based Representation (mO-R). ID : 1 2 3 V = 4 5 6 1 4 1 7 8 2 2 4 3 4 If we consider the same example with two more operations to perform having the transportation problems as given in table 1. The best schedule will be as shown in figure 6. Table 4. Manufacturing plan using moGA Machine Operation Performed M1 O22, M2 O21, M3 M4 O14, O25 O15 O13 O12 , O11 M5 O24 O23 Fig.6 Grant chart for the best solution 100
  9. 9. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME 6. ADAPTIVE GENETIC ALGORITHM FOR ADVANCED PLANNING IN MSC The adaptive genetic algorithm is mostly used for advanced planning model (APS) which is the important need for process and scheduling problem in manufacturing supply chain (MSC) [28]. The big industries with global manufacturing supply chain needs APS model. Also transportation associated with manufacturing process becomes an important issue. The normal GA developed to obtain good solution requires the identification of the correct settings of genetic parameters (such as population size, crossover and mutation rates). For global MSC, it is a very complex task. Hence to solve such complex mixed integer programming model, a new Adaptive Genetic algorithm (AGA) approach with new adaptive scheme is proposed. The AGA adaptively regulates the GA operators by an adaptive scheme and it also maintains the balance between exploitation and exploration [29] to prevent the premature convergence and to produce the optimal solution. AGA for advanced planning problem consists of three main parts. 6.1 Describing feasible solution (Chromosome coding): It states how to represent the feasible solution which considers all different possible constraints for a given problem. Generally a two dimensional coding concept is used, this coding significantly affect the generation of effective solution of a problem [17] [30]. 6.2 Determine fitness function: The measure of optimality of chromosomes used to obtain the probability that the chromosome will appear in the next generation is called the Fitness value. The for two weights and can integrated fitness functions for fitness objective functions and be given by: eval (f) = / + / 6.3 Selection: The genetic operator chooses best chromosomes from the population space to pass to the next generation. This probability of selection of chromosomes for next generation is given by: = Consider the following example for two different plants having three machines each to perform number of operations for different orders from customers. Table 5. Transition time between machines M1 M2 M3 M4 M1 5 6 M2 5 0 7 M3 Plant 1 0 6 7 0 Available capacity 1000 1000 M5 M6 M4 5 6 M5 5 0 7 M6 Plant 2 0 6 7 0 2000 2000 2000 2000 Available capacity 101
  10. 10. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME Table 6. Processing Time for Operations in Alternative Machines Order 1 Order 2 Order 3 Order 4 Operation 3 4 7 7 - M2 - - M3 - M4 6 7 8 9 10 11 12 13 14 15 16 17 6 - 3 8 - 10 6 15 - - - - - 5 6 - 9 5 - - - 5 - 6 - 5 - 5 - - 5 - - - 12 5 - - - - 6 - 6 - - 5 6 - - 8 - 9 - 10 - 6 - 6 - 4 3 - M5 - - 8 - - 6 - 8 - 6 - 5 - 9 - - 4 M6 Plant 2 2 M1 Plant 1 1 5 - - - 5 - - 8 - 7 - 5 - 8 - - 5 - The best schedule using Adaptive GA will be as given in table 7. Plant d Table 7. Best schedule Machine Operation performed M1 M2 O21 O42 O44 O31 O13 O43 O11 O12 O34 M5 O33 O35 M6 7. O45 M4 Plant 2 O23 M3 Plant 1 O22 O41 O32 O14 GENETIC ALGORITHM WITH TABU SEARCH (GATS) FOR JOB SHOP SCHEDULING The multistage-operation based G.A. (MOGA) has solved the scheduling problem for flexible Job-Shop scheduling. But achieving scheduling on m-machines for n jobs and having prescribed machine route for particular job is a very complex process. Hence to solve this problem a new approach is given having integrated GA and Tabu search i.e. GATS [31]. The GATS is having main approach to minimizing the makespan, processing time and the number of iterations with better result [32]. The job shop scheduling problem is already discussed in section5. A GATS process can be achieved by applying first a simple G.A. approach and then a Tabu Search approach. GA approach: This approach is shown in fig.7 and is having its main principle to produce best chromosomes by crossover and mutation operation [33]. 102
  11. 11. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME Fig.7: A Standard Genetic Algorithm Tabu-Search (TS) Approach: This approach is used after GA approach and it is nothing but a meta-heuristic approach used to achieve solutions on combinatorial optimization problems [34]. The flow of TS search is shown in fig.8. Fig.8: A standard Tabu Search algorithm The TS approach basically consists of Tabu list, aspiration criteria, stopping criteria with proposed algorithm [35]. Tabu list (TL): It is the list of trial solutions in order of their generation. The addition of new element is added to the ‘bottom’ of list and the element came first on the list is dropped from the ‘top’. The length of TL is assigned initially based on the size of problem and it may vary (i.e. increase or decrease) during construction of the solution to achieve better search of optimal solution. Aspiration Criteria (AC): This is a second essential element of TS algorithm used when the move under consideration has been found to the associated with each entry in TL. This criterion considers the move when a result in a solution for required objective value is better than the one which present in TL. Stopping Criteria (SC): This criterion describes that when to stop the Tabu Search. It is based on the different scheme used such as, (i) Stop after a fixed number of iterations. (ii) Stop after some number of iterations without an improvement in the objective function value. (iii) Stop when the objective function reaches a pre-specified threshold value. 103
  12. 12. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME If we apply the GATS instead of simple HGA and GA then we get the best optimum result as shown in following figure 9 and 10. Fig9. Average makespan values using different crossover strategie 8. Fig.10. Average relative error values using different crossover strategies CONCLUSION Even the scheduling model and advanced planning model is having much more optimization problems for different areas and applications, but the Genetic algorithm have created a optimal solution for these various problems. Thus, this paper provides a literature review for different applications of Genetic Algorithm in multi-objective scheduling and advanced planning problems. Here the multi-objective scheduling and advanced planning is explained in different areas with different forms of Genetic Algorithms. From this survey we can observe that the Adaptive GA is more preferable for Broad industries where more complex operations are there with large number of parameters effecting the final scheduling. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] C. Moon, J. S. Kim, M. Gen, “Advanced planning and scheduling based on precedence and resource constraints for e-plant chains,” International Journal of Production Research, vol. 42, no. 15, pp. 2941– 2954, 2004. C. Moon, Y. Seo, “Evolutionary algorithm for advanced process planning and scheduling in a multiplant,” Computers & Industrial Engineering, vol. 48, no. 2, pp. 311–325, 2005. C. Moon, Y. Seo, Y. Yun, M. Gen, “Adaptive genetic algorithm for advanced planning in manufacturing supply chain,” Journal of Intelligent Manufacturing, vol. 17, no. 4, pp. 509– 522, 2006. KJ. Chen, P. Ji, “Development of a genetic algorithm for scheduling products with a multilevel structure,” International Journal of Advanced Manufacturing Technology, vol. 33, no. 8, pp. 1229–1236, 2007. Mitsuo Gen, Lin Lin “Multi-objective Genetic Algorithm for Scheduling Problems in Manufacturing Systems,” Industrial Engineering & Management Systems Vol 11, No 4, pp.310-330, 2012 Imran Ali Chaudhry “A Genetic Algorithm Approach for Process Planning and Scheduling in Job Shop Environment,” Proceedings of the World Congress on Engineering, Vol III, 2012 Holland, J., Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, 1975. Mitchell, M., An introduction to genetic algorithms, The MIT Press, 1996. 104
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  14. 14. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 6, November - December (2013), © IAEME [29] X. Zhang, HS. Yan, “Integrated optimization of production planning and scheduling for a kind of jobshop,” International Journal of Advanced Manufacturing Technology, vol. 26, no. 7-8, pp. 876– 886, 2005. [30] R. Baker, G. D. Scudder, “Sequencing with earliness and tardiness penalties: A review,” Operation Research vol. 38, no. 1, pp. 22–36, 1990. [31] Amico, D and M.M. Trubian, 1993. Applying tabu search to the job-shop scheduling problem. Annals Oper. Res., 41: 231-252. DOI:10.1007/BF02023076 [32] Barnes, J.W. and J.B. Chambers, 1995. Solving the job shop scheduling problem using tabu search. IIE Transactions, 27, 257-263. [33] Cheng, R., M. Gen and Y. Tsujimura, 1996. A tutorial survey of job-shop scheduling problems using genetic algorithms—I. representation. Comput. Industrial Eng., 30: 983-997. DOI: 10.1016/0360- 8352(96)00047-2. [34] Thamilselvan, R. and P. Balasubramanie, “Integration of Genetic Algorithm with Tabu Search for Job Shop Scheduling with Unordered Subsequence Exchange Crossover,” Journal of Computer Science 8 (5): 681-693, 2012. [35] Calderia, J.P., F. Melicio and A. Rosa, 2004. Using a hybrid evolutionary-taboo algorithm to solve job shop problem. Proceedings of the ACM Symposium Applied Computing, Mar. 14-17, ACM, Nicosia, Cyprus, pp: 1446-1451. DOI: 10.1145/967900.968189. [36] Issam Nouaouri, Gilles Goncalves and Daniel Jolly, “A Hybrid Tabu Search for a Vehicle Routing Problem with Double Time Windows for the Depot and Multiple use of Vehicles: Case of Fuel Delivery”, International Journal of Industrial Engineering Research and Development (IJIERD), Volume 2, Issue 1, 2011, pp. 91 - 105, ISSN Online: 0976 - 6979, ISSN Print: 0976 – 6987. [37] Hymavathi Madivada and C.S.P. Rao, “An Invasive Weed Optimization (IWO) Approach for Multi-Objective Job Shop Scheduling Problems (JSSPs)”, International Journal of Mechanical Engineering & Technology (IJMET), Volume 3, Issue 3, 2012, pp. 627 - 637, ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359. [38] Kulbhushan Verma, Manpreet Kaur and Palvee, “Comparative Analysis of Various Types of Genetic Algorithms to Resolve TSP”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 4, Issue 5, 2013, pp. 111 - 116, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472. [39] Hymavathi Madivada and C.S.P. Rao, “A Review on Non Traditional Algorithms for Job Shop Scheduling”, International Journal of Production Technology and Management (IJPTM), Volume 3, Issue 1, 2012, pp. 61 - 77, ISSN Print: 0976- 6383, ISSN Online: 0976 – 6391. 106