International Journal of Production Technology and Management TECHNOLOGY–AND   INTERNATIONAL JOURNAL OF PRODUCTION (IJPTM)...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) ...
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  1. 1. International Journal of Production Technology and Management TECHNOLOGY–AND INTERNATIONAL JOURNAL OF PRODUCTION (IJPTM), ISSN 0976 6383 (Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME MANAGEMENT (IJPTM)ISSN 0976- 6383 (Print)ISSN 0976 - 6391 (Online)Volume 3, Issue 1, January-December (2012), pp. 61-77 IJPTM© IAEME: www.iaeme.com/ijptm.aspJournal Impact Factor (2012): 1.5910 (Calculated by GISI)www.jifactor.com ©IAEME A REVIEW ON NON TRADITIONAL ALGORITHMS FOR JOB SHOP SCHEDULING Hymavathi Madivada1, C.S.P. Rao2 1 (Research Scholar, Department of Mechanical Engineering, National Institute of Technology – Warangal, Warangal – 506004, India, hyma.madivada07@gmail.com) 2 (Professor, Department of Mechanical Engineering, National Institute of Technology – Warangal, Warangal – 506004, India, csp_rao@rediffmail.com, csp_rao63@yahoo.com) ABSTRACT A great deal of research has been focused on solving the job-shop problem, over the last fifty years, resulting in a wide variety of approaches. Recently, much effort has been concentrated on hybrid methods to solve job shop scheduling problem. JSSP is stated as a NP Hard problem [36, 37] so that as a single technique cannot solve this stubborn problem. As a result much effort has recently been concentrated on techniques that combine the specific methods and a meta-strategy which guides the search out of local optima. These approaches currently provide the best results. Such hybrid techniques are known as iterated local search algorithms or meta-heuristics. In this paper we seek to assess the work done in the job-shop domain by providing a review of many of the techniques used. The impact of the major contributions is indicated by applying these techniques to a set of standard benchmark problems. It is established that methods such as Tabu Search, Genetic Algorithms, Simulated Annealing should be considered complementary rather than competitive. In addition this work suggests guide-lines on features that should be incorporated to create a good job shop scheduling system. Finally the possible direction for future work is highlighted so that current barriers within job shop scheduling problem may be surmounted as we approach the 21st Century. Key Words: Job shop, scheduling, review, exact, approximation algorithms. 1. INTRODUCTION Research in scheduling theory has evolved over the past fifty years and has been the subject of much significant literature with techniques ranging from unrefined dispatching rules to highly sophisticate parallel branch and bound algorithms and bottleneck based heuristics. Not surprisingly, approaches have been formulated from a diverse spectrum of researchers ranging from management scientists to production workers. However with the advent of new methodologies, such as neural networks and evolutionary computation, 61
  2. 2. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEMEresearchers from fields such as biology, genetics and neurophysiology have also become regular contributors toscheduling theory emphasizing the multidisciplinary nature of this field. One of the most popular models in scheduling theory is that of the job-shop, as it is considered to be agood representation of the general domain and has earned a reputation for being notoriously difficult to solve. Itis probably the most studied and well developed model in deterministic scheduling theory, serving as acomparative test-bed for different solution techniques, old and new and as it is also strongly motivated bypractical requirements it is clearly worth understanding. Jain and Meeran (1999) provided a concise overview of JSPs over the last few decades and highlightedthe main techniques. The JSP is the most difficult class of combinational optimization. Garey, Johnson, andSethi (1976) demonstrated that JSPs are non-deterministic polynomial-time hard (NP-hard); hence we cannotfind an exact solution in a reasonable computation time. The single objective JSP has attracted wide researchattention. Most studies of single-objective JSPs result in a schedule to minimize the time required to completeall jobs, i.e., to minimize the makespan. Many approximate methods have been developed to overcome thelimitations of exact enumeration techniques. These approximate approaches include simulated annealing (SA)(Lourenço, 1995), tabu search (Nowicki & Smutnicki, 1996; Pezzella & Merelli, 2000; Sun, Batta, & Lin, 1995)and genetic algorithms (GA) (Bean, 1994; Gonçalves, Mendes, & Resende, 2005; Kobayashi, Ono, &Yamamura, 1995; Wang & Zheng, 2001). However, real world production systems require simultaneousachievement of multiple objective requirements. This means that the academic concentration of objectives in theJSP must been extended from single to multiple. Recent related JSP research with multiple objectives issummarized as below. Ponnambalam, Ramkumar, and Jawahar (2001) has offered a multi-objective GA toderive optimal machine-wise priority dispatching rules for resolving job-shop problems with objective functionsthat consider minimization of makespan, total tardiness, and total machine idle time. Ponnambalam’s multi-objective genetic algorithm (MOGA) has been tested with various published benchmarks, and is capable ofproviding optimal or near-optimal solutions. A Pareto front provides a set of best solutions to determine thetradeoffs between the various objects, and good parameter settings and appropriate representations can enhancethe behavior of an evolution algorithm. Esquivel, Ferrero, and Gallard (2002) studied the influence of distinctparameter combinations as well as different chromosome representations.Initial results showed that:(i) larger numbers of generations favour the building of a Pareto front because the search process does notstagnate, even though it may be rather slow,(ii) Multi-recombination helps to speed the search and to find a larger set size when seeking the Pareto optimalset, and(iii) operation-based representation is better than priority-list and job-based representation selected for contrastunder recombination methods.The Pareto archived simulated annealing (PASA) method, a meta-heuristic procedure based on the SAalgorithm, was developed by Suresh and Mohanasndaram (2006) to find non-dominated solution sets for the JSPwith the objectives of minimizing the makespan and the mean flow time of jobs. The superior performance ofthe PASA can be attributed to the mechanism it uses to accept the candidate solution. Candido, Khator, andBarcia (1998) addressed JSPs with numbers of more realistic constraints, such as jobs with several subassemblylevels, alternative processing plans for parts and alternative resources of operations, and the requirement formultiple resources to process an operation. The robust procedure worked well in all problem instances andproved to be a promising tool for solving more realistic JSPs. Lei and Wu (2006) first designed a crowding-measure-based multi-objective evolutionary algorithm (CMOEA) makes use of the crowding-measure to adjustthe external population and assign different fitness for individuals. Compared to the strength Pareto evolutionaryalgorithm, CMOEA performs well in job-shop scheduling with two objectives including minimization ofmakespan and total tardiness.2. OBJECTIVES OF SCHEDULING The scheduling is made to meet specific objectives. The objectives are decided upon the situation,market demands, company demands and the customer’s satisfaction. There are two types for the schedulingobjectives: (i) Minimizing the makespan (ii) Due date based cost minimizationThe objectives considered under the minimizing the makespan are, (a) Minimize machine idle time (b) Minimize the in process inventory costs (c) Finish each job as soon as possible 62
  3. 3. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME (d) Finish the last job as soon as possibleThe objectives considered under the due date based cost minimization are, (a) Minimize the cost due to not meeting the due dates (b) Minimize the maximum lateness of any job (c) Minimize the total tardiness (d) Minimize the number of late jobs Fig 1: Different algorithms for JSSP 63
  4. 4. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME3. SCHEDULING TECHNIQUES There are number of optimization and approximation techniques are used forscheduling of job shop scheduling problem. The techniques are generally, (i) Traditional Techniques • Traditional Techniques are also called as Optimization Techniques. These techniques are slow and guarantee of global convergence as long as problems are small. Mathematical programming (Linear Programming, Integer programming, Goal Programming, Dynamic Programming, Transportation, Network, Branch-and- Bound, Cutting Plane / Column Generation Method, Mixed Integer Linear programming, Surrogate Duality), Enumerate Procedure Decomposition (Lagrangian Relaxation) and Efficient Methods. (ii) Non Traditional Techniques • Non Traditional Techniques are also called as Approximation Methods. These methods are very fast but they do not guarantee for optimal solutions. Constructive Methods(priority dispatch rules, composite dispatching rules), Insertion Algorithms (Bottleneck based heuristics, Shifting Bottleneck Procedure(SBP)), Evolutionary Programs(Genetic Algorithm, Particle Swarm Optimization), Local Search Techniques(Ants Colony Optimization, Simulated Annealing, adaptive Search, Tabu Search, problem Space Methods like Problem & Heuristic Space and GRASP), Iterative Methods((Artificial Intelligence Techniques(Constraint Satisfacton (CSPs)),(Expert Systems), (Artificial Neural Network(Hopfield Networks and Back-Error propagation(BEP))), Heuristics Procedure, Beam-Search, and Hybrid Techniques.3.1. Literature Review on JSSP Scheduling Many researchers have been focusing on scheduling during the last few decades. Anumber of approaches have been developed and employed for solving various problems ofJob Shop Scheduling considering various objectives. The following sections discuss theliterature available in scheduling using various traditional and non-traditional optimizationtechniques.3.1. Review on Job Shop Scheduling using Non Traditional Optimization Techniques Table:1 Methodologies to solve the Job Shop scheduling Problem:S.no Method Author 1 Author 2Approximation Fisher and Rinnooy Kan(1988) Blazewicz et al.(1996)Algorithms (I) Constructive Methods(1) Jackson(1955) Smith(1956)Priority Dispatch Rules Giffer and Thomson(1960) Fisher and Thompson(1963) Crowston et al.(1963) Jeremiah et al.(1964) Gere(1966) Moore(1968) Panwalkar and Iskander(1977) Blackstone et al.(1982) Lawrence(1984) Haupt(1989) Chang et al.(1966) Sabuncuoglu and Bayiz(1997) 64
  5. 5. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME(2) Werner and Winkler(1995)Insertion Algorithms(i) Bottleneck based Alvehus(1997) heuristics(ii) Shifting Adams et al.(1988) Applegate and Cook(1991) Bottleneck Dauzere-Peres and lasserre (1993) Balas et al.(1995) Procedure(SBP) Balas and Vazacopoulos(1998) Holtsclaw and Uzsoy(1996) Demirkol et al.(1997) (II) Iterative Methods(1) Artificial intelligence Glover and Greenberg(1989)(i) Constrained Eerschler et al.(1976) Fox(1987) Satisfaction(CSPs) Sadeh(1991) Caseau and Laburthe(1994,95) Nuijten and Aarts(1994,96) Harvey(1995) Harvey and Ginsberg(1995) Sadeh et al.(1995) Baptiste and Le Pape(1995) Baptiste et al.(1995) Pesch and Tetzlaff(1996) Sadeh and Fox(1996) Cheng and Smith(1997) Nuijten and Le Pape(1998)(2) Neural Networks Wang and Brunn(1995) Jain and Meerun(1998)(i) Hopfield Networks Foo and Takefuji(1988a-c) Zhou et al.(1990,91) Van Hulle(1991) Lo and Bravian(1993) Willems and Rooda(1994) Satake et al.(1990,91) Foo et al.(1994,1995) Sabuncuoglu and Gurgun(1996)(ii) Back Error Dagli et al.(1991) Watanabe et al.(1993) Propagation(BEP) Cedimoglu(1993) Sim et al.(1994) Kim et al.(1995) Dagli & Sittisathanchai(1995)(3) Expert Systems Alexander(1987) Kusiak and Chen(1988) Biegel and wink(1989) Charalambous and Hindi(1991) Shakhlevich et al.(1996) Sotskov(1996) (III) Local Search Evans(1987) Vaessens(1995) Methods Vaessens et al.(1995,96) Arts and Lenstra(1997) Mattfeld et al.(2000) (1) Problem Space Methods(i) Problem & Storer et al.(1992,95) Heuristic Space(ii) GRASP Resende(1997)(2)Genetic Local Search Aarts et al.(1991,94) Pesch(1993) Della Croce et al.(1994) Dorndorf and Pesch(1995) Mattfeld(1996) Yamada and Nakano(1995b,1996b,c) Imen Essafi, Yazid Mati, Stéphane Dauzère-Pérès(2008)(3)Ant Optimization Colorni et al.(1995,96) Colorni, M. Dorigo et V. Maniezzo(1991) S. Goss, S. Aron, J.-L. Deneubourg et J.-M. Pasteels(4)Reinsertion Methods Werner and Winker(1995)(1)Threshold Algorithm Aarts et al(1991,94) Threshold 65
  6. 6. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME(i) Improvement Aarts et al(1991,94) Storer et al.(1992)(ii) Simulated Annealing Matsuo et al.(1988) Yan Laarhoven et al.(1988,92) Aarts et al(1991,94) Yamada et al.(1994) Sadeh and Nakakuki(1996) Yamada and Nakano(1995a,1996a) Kolonko (2001)(2)Threshold Acceptance Aarts et al.(1991,1994)(i) Large step Lourenco (1993,1995) Lourenco & Zwijnenburg(1996) Optimization Brucker et al.(1996a,1997a)(3)Tabu Search Taillard(1989,1994) Dell’Amico and Trubian(1993) Barnes and Chambers(1995) Sun et al.(1995) Nowioki and Smutnioki(96) Ton Eikelder et al.(1997) Thomson(1997) Alain Hertz(1996) Marino Widmer(1996) (IV) Evolutionary Algorithms(1) Genetic Algorithm Davis(1985) Falkenauer and Bouffouix(1991) Nakano and Yamada(1991) Tamaki and Nishikawa(1992) Yamada and Nakano(1992) Davidor et al.(1993) Ross et al.(1993) Mattfeld et al.(1994) Della Croce et al.(1995) Kobayashi et al.(1996) Norman and Bean(1995) Bierwirth(1995) Bierwirth et al.(1996) Cheng et al.(1996) Shi(1996)(2) Particle Swarm Tsung-Lieh Lin, Shi-Jinn Chen, Ray-Shine Run, Rong-Jian Chen,Optimization Horng, Tzong-Wann Kao, Jui-Lin Lai, I-Hong Kuo Yuan-Hsin Xinyu Shao, Peigen Li, Liang Gao(2009) Guohui Zhang(2009) Xingsheng Gu(2008) Qun Niu, Bin Jiao, (2008) Cheng-Yu Hsu(2006) D.Y. Sha(2006) Deming Lei(2008) Zhiming Wu(2005) Weijun Xia(2005) Hsing-Hung Lin(2009) D.Y. Sha (2009) Ren-qian ZHANG, Guo-ping XIA(2007) Kun FAN (2007) Davide Anghinolfi (2009) Massimo Paolucci(2009) G. Baharian Khoshkhou(2009) M. Rabbani, M. Aramoon Bajestani(2009)(3)Memetic Algorithm Jin-hui Yang, Liang Sun(2009) Yun Qian(2009) Heow Pueh Lee(2009) Yan-chun Liang(2009) Lacomme, Nikolay Tchernev Anthony Caumond, Philippe (2008) Nima Safaei, Farrokh Sassani Reza Tavakkoli-Moghaddam(2009) Mohsen Sadegh Amalnik Jalil Layegh, Fariborz Jolai, (2009)(5)Immune Algorithm A. Bagheri, M. Zandieh(2009) I. Mahdavi, M. Yazdani(2009)(6)Hybrid Algorithms(i) Hybrid PSO Dongyun Wang (2008) Liping Liu(2008) Peng-Yeng Yin, Shiuh-Sheng Yu, Pei-Pei Wang, Yi-Te Wang(2007) Dušan Teodorović(2008)(ii) Hybrid GA Jie Gao, Mitsuo Gen(2007) Linyan Sun, Xiaohui Zhao(2007) Hong Zhou, Waiman Cheung Lawrence C. Leung(2009) 66
  7. 7. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME4. OPTIMIZATION AND APPROXIMATION TECHNIQUES Various tools have been used in the field of Job Shop Scheduling. The methods used for JSPare generally divided into two broad categories: traditional approaches and nontraditional approaches.The traditional approaches are divided into two categories: (i) Theoretical research dealing with optimization procedures (ii) Experimental research dealing with dispatching rulesThe nontraditional approaches are used recently are robust for the JSP scheduling problems, as theproblems are NP-hard. This section analyzes some traditional and nontraditional approaches that havebeen implemented on JSP Scheduling.4.1. Non – Traditional Techniques4.1.1. Genetic AlgorithmGenetic Algorithms have been widely studied, experimented and applied in many fields ofengineering. GA is stochastic search procedure for combinatorial optimization problemsbased on the mechanism of natural selection and natural genetics [71]. These use the idea ofsurvival of the fittest by progressively accepting better solutions to the problems. The elementand mechanism of genetic algorithm are representation, population, evaluation, selection,operator and parameter. The algorithm starts with a randomly generated initial set ofpopulation called chromosomes that represent the solution of problem. These are evaluatedfor the fitness function and the selected according to their fitness value. Many selectionprocedures are based on the fitness value of the individuals of current generation. Thisselection alone cannot introduce any new individuals into population in the need of searchlarge space. The operators such as crossover and mutation are works on it.GA coding scheme As GA works on coding of parameters, the feasible job sequences ( the parameter ofthe considered problems) are coded in two different ways. (i) Pheno style coding (ii) Binary codingGenetic OperationsReproduction Rank order selection method is used for reproduction. The individuals in thepopulation are ranked according to fitness, and the expected value of individual depends onits rank rather than on its absolute fitness. Ranking avoids giving the largest share ofoffspring to a small group of highly fit individuals, and thus reduces the selection pressurewhen the fitness variance is high, thus keeping up selection pressure when the fitnessvariance is low. Each individual in the population is ranked in increasing order of fitnessfrom 1 to N. The expected value of each individual ‘i’ in the population at time ‘t’ is given by (Max-Min)(Rank(i,t)-1) Expected value (i,t) = Min + -------------------------------- N-1 Where, N= Population Size, Min.=0.4 and Max.=0.6After calculating the expected value of each rank, reproduction is performed using MonteCarlo simulation by employing random numbers.Cross overThe strings in the mating pool formed after reproductions are used in the crossover operation.The possibility of cross over is used for this work. With phenol type coding scheme, twostrings are selected at random and crossed at random site. Since the mating pool containsstrings at random, we pick of pairs of strings from the top of the list. When two strings are 67
  8. 8. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEMEchosen for crossover, first a coin is flipped with a probability Pc=0.6 to check whether acrossover is desired or not. If outcome of the coin flipping is true, the crossover is performed;otherwise the strings are directly placed in the intermediate population for subsequent geneticoperation. Crossover site is chosen by creating a random number between 1 and 20. For exampleif the random number is 10, the strings are crossed after 10th position. The current sequenceafter 10th position the first string in that pair, is rearranged according to the next string.Similarly the sequence after the 10th position of the 2nd string in that pair is rearrangedaccording to the first sequence.(E.g.) pair of strings before crossover: Crossover = 10th position5 4 6 9 10 15 19 20 1 17 / 7 3 11 13 18 2 8 12 14 161 20 15 9 19 6 10 5 4 6 / 3 11 2 14 12 16 7 8 18 13Pair of strings after crossover:5 4 6 9 10 15 19 20 1 17 / 3 11 2 14 12 16 7 8 18 131 20 15 9 19 6 10 5 4 6 / 7 3 11 13 18 2 8 12 14 16Mutation The possibility of mutation is determined by a probability from 0.01 to 0.1. In thiswork, bit wise mutation is used. With the phenol type scheme, two sites are selected bygenerating two numbers of random numbers between 1 1nd 20. If random numbers generatedare 8 and 15, then the corresponding job numbers in these positions are exchanged and thenew sequence is obtained.(E.g.) string before mutation:5 4 6 9 10 15 19 20 1 17 7 3 11 13 18 2 8 12 14 16String after mutation:5 4 6 9 10 15 2 20 1 17 7 3 11 13 18 19 8 12 14 16Algorithm:Step 1: Generate random population of n chromosomes(suitable solution for problem)Step 2: Evaluate the fitness f(x) of each chromosome x in the population.Step 3: Create a new population by repeating following steps until the new population iscompleteStep 4: Select two parent chromosomes from a population according to their fitness (thebetter fitness, the bigger chance to be selected)Step 5: With a crossover probability crossover the parents to form a new offspring(children).If no crossover was performed, offspring is an exact copy of parents.Step 6: with a mutation probability mutate new offspring at each locus(position inchromosome)Step 7: place new offspring in a new populationStep 8: use new generated population for a further run of algorithm.Step 9: if the end condition is satisfied, stop, and returns the best solution in currentpopulation and Go to step 2.4.1.2. Particle Swarm Optimization One of the latest evolutionary techniques for unconstrained continuous optimization isparticle swarm optimization (PSO) proposed by Kennedy and Eberhart (1995), inspired bysocial behavior of bird flocking or fish schooling. PSO learned from these scenarios are used to solve the optimization problems. InPSO, each single solution is a “bird” in the search space.[37],[38],& [39]. We call it“particle”. All of particles have fitness values, which are evaluated by the fitness function tobe optimized, and have velocities, which direct the flying of the particles. The particles are 68
  9. 9. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME“flown” through the problem space by following the current optimum particles.PSO isinitialized with a group of random particles (solutions) and then searches for optima byupdating generations. In each iteration, each particle is updated by following two “best”values. The first one is the best solution (fitness) it has achieved so far. (The fitness value isalso stored.) this value is called ‘pbest’. Another “best” value that is tracked by the particleswarm optimizer is the best value, obtained so far by any particle in the population. This bestvalue is a global best and called ‘gbest’.Algorithm :Step 1: initialize a population on n particles randomly.Step 2: Calculate fitness value for each particle. If the fitness value is better than the bestfitness value (pbest) in history. Set current value as the new pbest.Step 3: Choose particle with the best fitness value of all the particles as the gbest.Step 4: for each particle, calculate particle velocity according to the equationV[]=c1*rand()*(pbest[]-present[])+c2*rand()*(gbest[]-present[])Where present[]=present[]+v[]V[] is the particle velocity, present[] is the current particle(solution),rand() is random functions in the range [0,1].c1,c2 are learning factors=0.5.step 5: particle velocities on each dimension are clamped to a maximum velocity Vmax. If thesum of acceleration would cause the velocity on that dimension to exceed Vmax (specified byuser), the velocity on the dimension is limited to Vmax.Step 6: Terminate if maximum of iterations is reached. Else, goto Step2The original PSO was designed for a continuous solution space. In original PSO we can’tmodify the position representation, particle velocity, and particle movement. Then anotherheuristic is made to modify the above parameters, called Hybrid PSO. So they work betterwith combinational optimization problems. This Hybrid PSO was designed for a discretesolution space.4.1.3. Ant Colony OptimizationThe ant system is a new kind of co-operative search algorithm inspired by the behaviour ofcolonies of real ants. The blind ants are able to find astonishing good solutions to shortestpath problems between food sources and their home colony [72]to[80]. The medium used tocommunicate information among individuals regarding paths, and decide where to go, wasthe pheromone trails. A moving ant lays some pheromone on the path they move, thusmarking the path by the substance. While an isolated ant moves essentially at random, it canencounter a previously laid trail and device with high probability to follow it, and alsoreinforcing the trail with its own pheromone. The collective that emerges in a form ofautocatalytic behaviour where the more the ants following a trail, the more attractive that trailbecomes for being followed.The path of ants There is a path along which ants are walking from nest to the food source and viceversa. If a sudden obstacle appears and the path is cut off, the choice is influenced by theintensity of the pheromone trails left by proceeding ants. On the shorter path morepheromone is laid down.The below figure shows the behaviour of ants when faced with an obstacle in its search path. 69
  10. 10. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME Figure: path traced by ants without and with obstacle AN FS O B S FS AN T A C L EAnts Colony algorithm can be applied for the continuous function optimization problems.Here, the domain has to be divided into a specific number of R randomly distributed regions.These regions are indeed the trail solutions and act as local stations for the ants to move andexplore. The fitness of these regions are first evaluated and stored on the basis of fitness.Totally a population of ants explores these regions; the updating of the region is done locallyand globally with the local search and global search mechanism respectively. The distributionof local and global ants is illustrated in the below figure.Algorithm:Step 1: fix the evaporation rate and no. of runs.Step 2: while (number of runs is less than required).Step 3: Initialize pheromone values.Step 4: Call random no. generation function.Step 5: Generate group of ants with difference paths(sequences).Step 6: Call the function for calculating COF.Step 7: Sort the COF values in ascending order.Step 8: For best routes update pheromone level.Step 9: Repeat 4,5,6,7&8 till obtaining required no. of runs.Step 10: Print the best routes and the COF values.Step 11: Change evaporation rate and no. of runs for next trail. 4.1.4. Simulated Annealing Algorithm The simulated annealing algorithm resembles the cooling process of molten metalsthrough annealing. At high temperature, the atoms in the molten metal can move freely withrespect to each another. But, as the temperature is reduced, the movement of the atoms getsreduced. The atoms start to get ordered and finally form crystals having the minimumpossible energy. However, the formation of the crystal depends on the cooling rate. If thetemperature is reduced at a fast rate, the crystalline state may not be achieved at all; insteadthe system may end up in a polycrystalline state, which may have a higher energy state than 70
  11. 11. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEMEthe crystalline state. Therefore, to achieve the absolute minimum state, the temperature needsto be reduced at a slow rate. The process of slow cooling is known as annealing inmetallurgical parlance. SA simulates this process of slow cooling of molten to achieve theminimum function value in a minimization problem. The cooling phenomenon is simulatedby controlling a temperature – like parameter introduced with the concept of the Boltzmannprobability distribution. [83]to [87].Algorithm:Step 1: Choose an initial point X^(o), a termination criterion ∈. Set T as a sufficiently high value number of iterations to be performed at a particular temperature n, and set t=0.Step 2: Calculate the neighbouring point X^(t+1) = N(x^(t)). Usually, a random point in the neighbourhood is created.Step 3: If ∆E= E(x^(t+1))-E(x^(t))<0, set t=t+1; Else create a random number (r) in the range (0,1). If r≤exp(∆E/T), set t=t+1; Else go to Step 2.Step 4: if (x^(t+1)-x^(t))< ∈ and T is small, Terminate. Else go to Step 2.4.1.5. Memetic algorithm Memetic algorithm is a combination of a population based global search and theheuristic local search made by each of the individual. Memetic algorithms (MA) areevolutionary algorithms where, two non-traditional techniques are combined to form analgorithm. Combining global optimization approaches has in fact been recognized as apowerful algorithmic paradigm for evolutionary computing, as it consists of a separate localsearch process to refine individuals. In particular the relative advantage of MA over EA isquite consistent on complex search spaces. Each algorithm is designed to obtain globaloptimum solution. The output of the first iteration of the algorithm is obtained and is given tothe second algorithm in the same iteration. Memetic algorithm is a population basedapproach. The flowchart of the Memetic algorithm illustrated in below figure.Algorithm:Step 1: Initialize the population randomly. Set iteration k=0Step 2: Implement algorithm 1 in the populationStep 3: Implement algorithm 2 on the population obtained from step 2Step 4: Calculate the fitness and find the best solution.Step 5: If termination criteria is not achieved, increment k=k+1 and go to step 2.4.1.6. Tabu search The basic idea of Tabu search (Glover 1989, 1990) is to explore the search space ofall feasible scheduling solutions by a sequence of moves. A move from one schedule toanother schedule is made by evaluating all candidates and choosing the best available, justlike gradient-based techniques. Some moves are classified as tabu (i.e., they are forbidden)because they either trap the search at a local optimum, or they lead to cycling (repeating partof the search). These moves are put onto something called the Tabu List, which is built upfrom the history of moves used during the search. These tabu moves force exploration of thesearch space until the old solution area (e.g., local optimum) is left behind. Another keyelement is that of freeing the search by a short term memory function that provides “strategicforgetting”.Tabu search methods have been evolving to more advanced frameworks that includes longerterm memory mechanisms. These advanced frameworks are sometimes referred as AdaptiveMemory Programming (AMP, Glover 1996). Tabu search methods have been applied 71
  12. 12. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEMEsuccessfully to scheduling problems and as solvers of mixed integer programming problems.Nowicki and Smutnicki (Glover 1996) implemented tabu search methods for job shop andflow shop scheduling problems. Vaessens (Glover 1996) showed that tabu search methods (inspecific job shop scheduling cases) are superior over other approaches such as simulatedannealing, genetic algorithms, and neural networks.CONCLUSION Since job shop scheduling problems fall into the class of NP-complete problems, theyare among the most difficult to formulate and solve. Operations Research analysts andengineers have been pursuing solutions to these problems for more than 35 years, withvarying degrees of success. While they are difficult to solve, job shop scheduling problems are among the mostimportant because they impact the ability of manufacturers to meet customer demands andmake a profit. They also impact the ability of autonomous systems to optimize theiroperations, the deployment of intelligent systems, and the optimizations of communicationssystems. For this reason, operations research analysts and engineers will continue this pursuitwell into the next coming centuries.Limitations of traditional techniques:In the traditional approaches the following limitations are observed: • Most traditional techniques that give optimal solutions apply only to problems of very small size. • These techniques require excessive computation time and are not practical for use on a daily basis. • The traditional techniques are not efficient in handling multiple objectives. • The convergence to an optimal solution depends on the chosen initial random solution. • These techniques start with a single point and are not efficient when practical search space is too large. • The results tend to stick with local optima and follow a deterministic rule. • Most scheduling problems are NP-hard, and this degrades the performance of traditional operations research techniques and also modelling the method is a difficult task. • In branch and bound, the number of decision nodes are numerous depending upon the problem size and thus requiring large computations. • The performance of heuristic is suitable as long as the operating characteristics and objectives of the system remain the same.These limitations urge the researchers to implement nontraditional optimization techniques inthe domain.Merits of Non Traditional TechniquesThe following strengths of the non- traditional techniques are observed over the traditionaltechniques. • The nontraditional techniques yield a global optimal solution • The techniques use a population of points during search. • Initial populations are generated randomly which enable to explore the search space. • The techniques efficiently explore the new combinations with available knowledge to find a new generation. • The objective functions are used rather than their derivatives. 72
  13. 13. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEMEREFERENCES [1] Guohui Zhang, Xinyu Shao, Peigen Li, Liang Gao “An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem” Computers & Industrial Engineering, Volume 56, Issue 4, May 2009, Pages 1309-1318 [2] Runwei Cheng, Mitsuo Gen, Yasuhiro Tsujimura “A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: hybrid genetic search strategies” Computers & Industrial Engineering, Volume 36, Issue 2, April 1999, Pages 343-364 [3] Dirk C. Mattfeld, Christian Bierwirth “An efficient genetic algorithm for job shop scheduling with tardiness objectives” European Journal of Operational Research, Volume 155, Issue 3, 16 June 2004, Pages 616-630 [4] Lars Mönch, Rene Schabacker, Detlef Pabst, John W. Fowler “Genetic algorithm- based subproblem solution procedures for a modified shifting bottleneck heuristic for complex job shops” European Journal of Operational Research, Volume 177, Issue 3, 16 March 2007, Pages 2100-2118 [5] Jason Chao-Hsien Pan, Han-Chiang Huang “A hybrid genetic algorithm for no-wait job shop scheduling problems” Expert Systems with Applications, Volume 36, Issue 3, Part 2, April 2009, Pages 5800-5806 [6] Ferdinando Pezzella, Emanuela Merelli “A tabu search method guided by shifting bottleneck for the job shop scheduling problem” European Journal of Operational Research, Volume 120, Issue 2, 16 January 2000, Pages 297-310 [7] Bo tjan Murovec, Peter uhel “A repairing technique for the local search of the job-shop problem” European Journal of Operational Research, Volume 153, Issue 1, 16 February 2004, Pages 220-238 [8] Johann Hurink, Sigrid Knust “Tabu search algorithms for job-shop problems with a single transport robot” European Journal of Operational Research, Volume 162, Issue 1, 1 April 2005, Pages 99-111 [9] Jagadish Jampani, Scott J. Mason “A Column Generation Heuristic for Complex Job Shop Multiple Orders per Job Scheduling” Computers & Industrial Engineering, In Press, Accepted Manuscript, Available online 24 September 2009 [10] Helena Ramalhinho Lourenço “Job-shop scheduling: Computational study of local search and large-step optimization methods”European Journal of Operational Research, Volume 83, Issue 2, 8 June 1995, Pages 347-364 [11] Betul Yagmahan, Mehmet Mutlu Yenisey “A multi-objective ant colony system algorithm for flow shop scheduling problem”Expert Systems with Applications, In Press, Corrected Proof, Available online 11 July 2009 [12] S.Q. Liu, H.L. Ong, K.M. Ng “A fast tabu search algorithm for the group shop scheduling problem”Advances in Engineering Software, Volume 36, Issue 8, August 2005, Pages 533-539 [13] Ju-Seog Song, Tae-Eog Lee “A tabu search procedure for periodic job shop scheduling” Computers & Industrial Engineering, Volume 30, Issue 3, July 1996, Pages 433-447 [14] Jean-Paul Watson, J. Christopher Beck, Adele E. Howe, L. Darrell Whitley “Problem difficulty for tabu search in job-shop scheduling”Artificial Intelligence, Volume 143, Issue 2, February 2003, Pages 189-217 73
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  15. 15. International Journal of Production Technology and Management (IJPTM), ISSN 0976 – 6383(Print), ISSN 0976 – 6391 (Online) Volume 3, Issue 1, January- December (2012), © IAEME Computation, Volume 205, Issue 1, 1 November 2008, Pages 148-158 Qun Niu, Bin Jiao, Xingsheng Gu [30] A hybrid particle swarm optimization for job shop scheduling problem Computers & Industrial Engineering, Volume 51, Issue 4, December 2006, Pages 791-808 D.Y. Sha, Cheng-Yu Hsu [31] An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems Computers & Industrial Engineering, Volume 48, Issue 2, March 2005, Pages 409-425 Weijun Xia, Zhiming Wu [32] A multi-objective PSO for job-shop scheduling problems Expert Systems with Applications, In Press, Corrected Proof, Available online 4 July 2009 D.Y. Sha, Hsing-Hung Lin [33] Solving a Class of Job-Shop Scheduling Problem based on Improved BPSO Algorithm Systems Engineering - Theory & Practice, Volume 27, Issue 11, November 2007, Pages 111-117 Kun FAN, Ren-qian ZHANG, Guo-ping XIA [34] A new discrete particle swarm optimization approach for the single- machine total weighted tardiness scheduling problem with sequence-dependent setup times European Journal of Operational Research, Volume 193, Issue 1, 16 February 2009, Pages 73-85 Davide Anghinolfi, Massimo Paolucci [35] Clonal Selection Based Memetic Algorithm for Job Shop Scheduling Problems Journal of Bionic Engineering, Volume 5, Issue 2, June 2008, Pages 111- 119 Jin-hui Yang, Liang Sun, Heow Pueh Lee, Yun Qian, Yan-chun Liang [36] Hybrid particle swarm optimization for solving resource-constrained FMS Progress in Natural Science, Volume 18, Issue 9, 10 September 2008, Pages 1179-1183 Dongyun Wang, Liping Liu [37] A hybrid of genetic algorithm and bottleneck shifting for multiobjective flexible job shop scheduling problems Computers & Industrial Engineering, Volume 53, Issue 1, August 2007, Pages 149-162 Jie Gao, Mitsuo Gen, Linyan Sun, Xiaohui Zhao [38] An artificial immune algorithm for the flexible job-shop scheduling problem Future Generation Computer Systems, In Press, Accepted Manuscript, Available online 15 October 2009 A. Bagheri, M. Zandieh, I. Mahdavi, M. Yazdani [39] Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm European Journal of Operational Research, Volume 194, Issue 3, 1 May 2009, Pages 637-649 Hong Zhou, Waiman Cheung, Lawrence C. Leung [40] A multi-objective particle swarm optimization for project selection problem Expert Systems with Applications, Volume 37, Issue 1, January 2010, Pages 315-321 M. Rabbani, M. Aramoon Bajestani, G. Baharian Khoshkhou [41] Task allocation for maximizing reliability of a distributed system using hybrid particle swarm optimization Journal of Systems and Software, Volume 80, Issue 5, May 2007, Pages 724-735 Peng-Yeng Yin, Shiuh-Sheng Yu, Pei-Pei Wang, Yi-Te Wang [42] Particle swarm optimization: A study of particle displacement for solving continuous and combinatorial optimization problems International Journal of Production Economics, Volume 121, Issue 1, September 2009, Pages 57-67 Sylverin Kemmoé Tchomté, Michel Gourgand [43] Swarm intelligence systems for transportation engineering: Principles and applications Transportation Research Part C: Emerging Technologies, Volume 16, Issue 6, December 2008, Pages 651-667 Dušan Teodorović 75
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