Machine Loading in Flexible Manufacturing System: A Swarm Optimization Approach

Transcription

1 Machine Loading in Flexible Manufacuring Sysem: A Swarm Opimizaion Approach Sandhyarani Biswas Naional Insiue of Technology sandhya_biswas@yahoo.co.in S.S.Mahapara Naional Insiue of Technology mahaparass2003@yahoo.com Loading is one of he vial issues in flexible manufacuring sysem (FMS) producion planning which deals wih assignmen of he necessary operaions and ools among various machines in an opimal manner. Such a problem is combinaorial in naure and found o be NP-complee. In his paper, an aemp has been made o address such problems using muaion in paricle swarm opimizaion (PSO) o avoid premaure convergence wih he objecive of minimizaion of sysem unbalance. Promising resuls have been obained when he soluion is compared wih exising echniques for en sandard problems available in lieraure represening hree differen FMS scenarios. Keywords: Flexible Manufacuring Sysem,Machine Loading Problem, Paricle Swarm Opimizaion, Muaion; Sysem Unbalance. Inroducion Today s dynamic producion environmen is characerized by a large volume of uncerainy such as rapid marke changes, increased produc variey, compeiive prices and shor produc life cycles. Therefore, i is of prime imporance o inroduce flexible manufacuring sysems (FMSs) so ha hese uncerainies can be handled in an effecive manner. FMS is characerized as an inegraed, compuer-conrolled complex arrangemen of auomaed maerial handling devices and compuer numerically conrolled (CNC) machine ools ha can simulaneously process medium-sized volumes of a variey of par ypes (Secke, 983). The highly inegraed FMS offers he opporuniy o combine he efficiency of ransfer line and he flexibiliy of a job shop o bes sui he bach producion of mid volume and mid variey of producs. However, flexibiliy has a cos, and he capial invesmen susained by firms o acquire such sysems is generally very high. Therefore, paricular aenion mus be paid o proper planning of FMS during is developmen phase in order o evaluae he performance of he sysem and jusify he invesmen incurred. Prior o producion, careful operaional planning is essenial o esablish how well he sysem ineracs wih he operaions over ime. Hence, successful operaion of FMS requires more inense planning as compared o any convenional producion sysem. The decisions relaed o FMS operaions can be broadly divided ino pre-release and pos-release decisions. Pre-release decisions include he FMS operaional planning problem ha deals wih he pre-arrangemen of jobs and ools before he processing begins whereas pos-release decisions deal wih he scheduling problems. Pre-release decisions viz., machine grouping, par ype selecion, producion raio deerminaion, resource allocaion and loading problems mus be solved while seing up of a FMS. Amongs pre-release decisions, machine loading is considered as one of he mos vial producion planning problem because performance of FMS largely depends on i. Loading problem, in paricular, deals wih allocaion of jobs o various machines under echnological consrains wih he objecive of meeing cerain performance measures. Therefore, he problem is combinaorial in naure and happens o be NP-hard. Formulaions of loading problems in FMS and soluion echniques have drawn he aenion of researchers for quie some ime. FMS planning problem formulaed as non-linear 0- mixed-ineger programming (MIP) (Secke, 983) and subsequenly a branch-and-bound algorihm was developed (Berrada and Secke, 986). Alhough analyical and mahemaical programming-based mehods are robus in applicaions ye hey end o become impracical when problem size increases. This moivaed he researchers o develop fas and effecive heurisics for solving loading problems in large-sized FMSs. One of he imporan heurisics uses he concep of essenialiy raio for maximizaion of hroughpu and minimizaion of sysem unbalance simulaneously (Mukhopadhyay e al., 992). Laer on, heurisics have been developed using fixed pre-deermined job ordering rules as inpu while solving loading problems (Tiwari e al., (997). However, i has been esablished ha shores processing ime (SPT) rule works well in comparison o oher rules viz., longes processing ime (LPT), firs-in-firs ou (FIFO), and las-in-firs-ou (LIFO) (Moreno and Ding, 993). Then, muli-sage programming approach has been incorporaed while developing heurisics for minimizing sysem unbalance (Nagarjuna e. al., 2006). The major limiaion of heurisics lies in he fac ha heir inabiliy o esimae he resuls in a new or compleely changed environmen as hey are generally rule-based and mosly rely on empirical daa. Therefore, numerous researchers have used mea-heurisic approaches for solving he 62

2 machine loading problem. Geneic algorihm (GA) based approaches for loading problem is found o ensure opimal soluion wih less compuaional effor (Tiwari e. al., 2007). Many researchers (Kumar and Shanker, 2000 and Swarnkar and Tiwari, 2004) have addressed machine-loading problem having he bi-crierion objecives of minimizing sysem unbalance and maximizing he hroughpu using a hybrid algorihm based on abu search (TS) and simulaed annealing (SA). The main advanage of his approach is ha a shor-erm memory provided by he abu lis can be used o avoid revisiing he soluion while preserving he sochasic naure of he SA mehod. Numerous mehods based on mahemaical, heurisics, and mea-heurisics have been suggesed by he researchers in he pursui of obaining qualiy soluions o loading problems and reduce compuaional burden. Bu hese approaches hardly capable of producing opimal/near opimal soluions or requires excessive compuaional effors o arrive a qualiy soluions. In order o alleviae hese difficulies, an aemp has been made in his paper o propose an algorihm based on paricle swarm opimizaion (PSO) o solve he machine loading problem of a random FMS wih he objecive of minimizaion of sysem unbalance while saisfying he consrains relaed o available machining ime and ool slos. However, PSO has inheren drawback of rapping a local opimum due o appreciable reducion in velociy values as ieraion proceeds and hence reduce soluion variey. This drawback has been addressed effecively by incorporaing muaion, a commonly used operaor in geneic algorihm, o improve he soluion qualiy. The remainder of his paper is organized as follows. Secion 2 formally defines he problem sudied in his paper along wih he objecives and assumpions made o solve he problem. The proposed algorihm based on PSO is presened in secion 3. In secion 4, resuls of benchmark problems from open lieraure are compared wih proposed mehod o illusrae is advanage over oher mehods. Finally, conclusions drawn from his sudy are summarized and direcion for fuure research is oulined in secion Problem Descripion The loading problem in manufacuring deals wih selecing a subse of jobs from a se of all he jobs o be manufacured and assigning heir operaions o he relevan machines in a given planning horizon wih he echnological consrains in order o mee cerain performance measures such as minimizaion of sysem unbalance and maximizaion of hroughpu. Sysem unbalance can be defined as he sum of unuilized or overuilized imes on all he machines available in he sysem whereas hroughpu refers o he summaion of he bach size of he jobs ha are o be produced during a panning horizon. Minimizaion of sysem unbalance is equivalen o maximizaion of machine uilizaion. The processing ime and ool slos required for each operaion of he job and is bach size are known before hand. There are wo ypes of operaions; essenial and opional associaed wih he par ypes. Essenial operaions can be carried ou on a paricular machine using a cerain number of ool slos while he opional operaion can be performed on a number of machines wih same or differen processing ime and ool slos. The FMS under consideraion derives is flexibiliy in selecion of machine for opional operaion of he job. Generally, he complexiy of hese problems depends on wheher he FMS is of a dedicaed ype or a random ype. A dedicaed FMS is designed o produce a raher small family of similar pars wih a known and limied variey of processing requiremens while in a random-ype sysem a large family of pars having a wide range of characerisics wih random elemens is produced and he produc mix is no compleely defined a he ime of insalling he sysem. This paper addresses he loading problem in a random FMS. The proposed approach has been esed on problems peraining o hree sizes of FMSs (he deails are given in Table ). The deails of daa relaed o problem of FMS ype (jobs, bach size, uni processing ime, machine opions, number of ool slos ec.) having four machines are given in Table 2. FMS ype Number of machines Table Deails of differen FMS scenarios Available ime on each machines Number of ool slos on each machines FMS min, 480 min, 480 min, 480 min 5, 5, 5, 5 FMS min, 960 min,960 min, 960 min,960 min 0, 2, 0, 2, 0 FMS min, 960 min,960 min, 960 min,960 min, 960min 4, 4, 4, 4, 4,6 In order o minimize he complexiies in analyzing he problem for a pracical FMS, he mahemaical model is based on he following assumpions: Iniially, all he jobs and machines are simulaneously available. Processing ime required o complee an enire job order is known a priori. Job underaken for processing is o be compleed for all is operaion before considering a new job. 622

3 Job Number Table 2 Deail descripion of jobs of problem number (FMS ) Bach size Operaion Machine Uni Tool slos number number processing needed ime(min) Toal processing ime ,2,3 7,7,7,, 70 2, , , 26,26 2, , ,3 22,22 2, This is called non-spliing of he job. Operaion of a job once sared on a machine is coninued unil i is compleed. Transporaion ime required o move a job beween machines is negligible. Sharing and duplicaion of ool slos is no allowed. Differen researchers have calculaed sysem unbalance in differen ways. Some researchers such as solved he machine loading problem by considering overloading of he machines (Mukhopadhyay e al. 992, Nagarjuna e al., 2006 and Tiwari e. al., 2007) while ohers have no permied overloading (Shanker e al., 989). In order o examine he efficiency of he proposed algorihm, he problem described above is formulaed in his paper by considering wo cases. In firs case, an opimal soluion is obained wihou permiing overloading on machines whereas overloading on machines is permied in he second case. Mahemaical formulaion of he problem for boh he cases are described in he followings. 2. Mahemaical formulaion 2... Noaions In order o formulae machine loading problem of FMS, he following noaions are inroduced: j: job index, j =,2 J m: machine index, m =,2,..M S m : ool slo capaciy of machine m o: number of operaions for job j, o =,2..O j B j :Bach size of job j T m : Lengh of scheduling period for m h machine P jom : Processing ime of operaion o of job j on machine m S jom : Number of ool slos required for processing operaion o of job i on machine m B(j,o): Se of machines on which operaion o of job j can be performed SU: Sysem Unbalance TH: Throughpu, if job j is seleced X j = 0, oherwise, if operaion o of job j is assigned on machine m X jom = 0, oherwise Case: Overloading no permied Objecive of he FMS loading problem is o minimize oal sysem unbalance and is represened by Eq. () Subjeced o he following consrains: Minimize M M Tm m= m= J Oj p jom Xjom j o B j () 623

4 J Oj p T m, m...(2) jom Xjom m j o B j = J Oj Xjom Sm j o S jom m =, M...(3) G B ( j,o) X jog j =,2...J o =,2... O j...(4) Oj M X joj o m X jom = j =, J (5) The consrain, Eq. (2), ensures ha overloading of machines is no permied. Eq. (3) is o ensure he jobs will be loaded only when here is availabiliy of ool slos on each machine. Eq. (4) ensures ha a paricular operaion of a job is done only on one machine and Eq. (5) ensures ha he job canno be spli. Case2: Overloading permied Objecive of he FMS loading problem is o minimize he absolue value of oal sysem unbalance and is represened in Eq. (6). Minimize M J Oj T m Bj X jom m j o p jom = Subjeced o following consrains: M J Oj M p T m, m jom Xjom j o B j m m m = = = (6) (7) J O j SjomX jom Sm j= o= m =,2...M...(8) G B ( j,o) X jog j =,2...J o =,2... O j...(9) Oj M XjOj o m X jom = j =, J ( 0) The consrain, Eq. (7), ensures ha overloading of machines is permied. Eq. (8) is o ensure he jobs will be loaded only when here is availabiliy of ool slos on each machine. Eq. (9) ensures ha a paricular operaion of a job is done only on one machine and Eq. (0) ensures ha he job canno be spli. 3. Proposed Mehodology 3.. Paricle Swarm Opimizaion Paricle Swarm Opimizaion (PSO) algorihm, originally inroduced by Kennedy and Eberhar in 995, is a populaion-based evoluionary compuaion echnique. I is moivaed by he behavior of organisms such as bird flocking and fish schooling. In PSO, each member is called paricle, and each paricle moves around in he mulidimensional search space wih a velociy which is consanly updaed by he paricle s own experience and he experience of he paricle s neighbors or he experience of he whole swarm. The members of he enire populaion are mainained hroughou he search procedure so ha informaion is socially shared among individuals o direc he search owards he bes posiion in he search space. Two varians of he PSO algorihm have been developed, namely PSO wih a local neighborhood, and PSO wih a global neighborhood. According o he global neighborhood, each paricle moves owards is bes previous posiion and owards he bes paricle in he whole swarm, called he gbes model in he lieraure. On he oher hand, based on he local varian so called he pbes model, each paricle moves owards is bes previous posiion and owards he bes paricle in is resriced neighborhood. Generally, PSO is characerized as a simple heurisic of well balanced mechanism wih flexibiliy o enhance and adap o boh global and local exploraion abiliies. Compared wih GA, PSO has some aracive characerisics. I has memory ha enables o reain knowledge of good soluions by all paricles whereas previous knowledge of he problem is desroyed once he populaion changes in GAs. Due o he simple concep and easy implemenaion, PSO has gained much aenion and been successfully applied o a wide 624

5 range of applicaions such as sysem idenificaion, neural nework raining, mass-spring sysem, ask assignmen, supplier selecion and ordering problem, power and volage conrol ec. (Yoshida, 2000). The mahemaic descripion of PSO is presened in he followings. Suppose i denoes a paricle and he dimension of he searching space is n. The posiion of he i h paricle a ieraion in n dimensional space is represened as X i = (x, i,x i2 x in ). The pbes of he i h paricle a ieraion in n dimensional space is represened as P i = (p i,p i2,..p in ). The index of gbes i.e he bes pbes among all he paricles is represened by he symbol G = (g,g 2,..g n ). The velociy for he i h paricle a ieraion in n dimensional space is represened as V i = (v i + v i2 + v in ). PSO is iniialized wih a populaion of random soluions of he objecive funcion. Afer finding he personal bes and global bes values, velociies and posiions of each paricle are updaed using Eq. and 2 respecively. v ij = w v ij + c r (p ij - xij ) + c2 r 2 (g j - xij )...() - x ij = xij + vij...(2) where v ij represens velociy of paricle i a ieraion wih respec o j h dimension (j =,2, n). pij represens he posiion value of he i h personal bes wih respec o he j h dimension. x ij is he posiion value of he i h paricle wih respec o j h dimension. c and c 2 are posiive acceleraion parameers, called cogniive and social parameer, respecively and r and r 2 are uniform random numbers beween (0,). w is known as ineria weigh which is updaed as: w = w - α.(3) where α is a decremen facor. The parameer w conrols he impac of he previous velociies on he curren velociy. Terminaion crierion migh be a maximum number of ieraion or maximum CPU ime o erminae he search. 3.. Soluion Represenaion One of he mos imporan issue when designing he PSO algorihm lies on is soluion represenaion. In order o consruc a direc relaionship beween he problem domain and he PSO paricles for he FMS loading problem, we presen n number of dimensions for n number of jobs. In oher words, each dimension represens a ypical job. In addiion, he paricle X i = (x i,x, i2 x in ) corresponds o he coninuous posiion values for n number of jobs in he loading problem. The paricle iself does no presen a permuaion. Insead, we use he Smalles Posiion Value (SPV) rule o deermine he sequence implied by he posiion values x ij of paricle X i. Table 3 illusraes he soluion represenaion of paricle X i for he FMS loading problem ogeher wih is corresponding velociy and sequence. According o he SPV rule, he smalles posiion value is x i = 0., so he dimension j= is assigned o he firs job x i =4 in he sequence; he second smalles posiion value is x i2 = 0.57, so he dimension j=2 is assigned o be he second job x i2 = 6 in he sequence, and so on. In oher words, dimensions are sored according o he SPV rule, i.e., according o he posiion values x ij o consruc he iniial sequence. Table 3 Soluion Represenaion of Paricle X i in PSO Dimension,j x i v ij Job sequence Lack of Diversiy and Muaion Operaor Paricle swarm opimizaion schemes described above ypically converge relaively rapidly in he firs par of he search and hen slow down or sop. This behavior has been aribued o he loss of diversiy in he populaion and a number of researchers have suggesed mehods o overcome his drawback wih varying degrees of success (Rige, 2002). Looking a he posiions of he paricles when he swarm had sagnaed, i was clear ha he poins were very ighly clusered and he velociies were almos zero. The poins were ofen no ha far from he global opimum bu he updaing equaions, due o he almos zero velociy, were unable o generae new soluions which migh lead he swarm ou of his sae. This behavior can also lead o he whole swarm being rapped in a local opimum from which i becomes impossible o escape. As muaion is capable of inroducing diversiy in he search procedure, wo ypes muaion have araced he researchers - muaion of global bes and muaion based on sharing informaion from neighbors. Because he global bes individual aracs all members of he swarm, i is possible o lead he swarm away from a curren locaion by muaing a single individual if he muaed individual becomes he new global bes. This mechanism poenially provides a means boh escaping local opima and speeding up he search. Looking a he individual componens of soluion vecors corresponding o he global bes funcion values revealed ha i was ofen only a few componens which had no converged o heir global opimum values. This suggesed he possibiliy of muaing a single componen only of a soluion vecor. The laer approach inroduces diversiy by muaing few individuals in he swarm. In his work, a muaion operaor is inroduced which muaes a posiion vecors of few paricles seleced 625

6 randomly. The muaion operaion is no execued in every ieraion. A funcion, randi (0, MAXT), is used o reurn an ineger greaer han or equal o 0 and less han MAXT. In each ieraion, if he elapsed ime wih no furher progress is greaer han his random value, muaion operaion is execued. Two reasons may accoun for his sraegy: ) if here is no premaure convergence happening, he execuion of PSO will no be affeced. 2) he algorihm will no increase compuaional overhead much. The muaion operaor swaps beween wo posiions of a paricle randomly. Then, permuaions are generaed for new posiions. PSO algorihm wih muaion operaion is as follows: // : ime // // P: populaions // // DELTA: he elapsed ime of no furher progress // // MAXT: maximum ime of no furher progress // =0 iniialize P() evaluae P() while (no-erminaion-condiion) do =+ updae swarm according o formulae () and (2) if (DELTA > randi (0, MAXT) do muaion end if evaluae he swarm End 3..3 Proposed Algorihm Sep. Inpu oal number of available machines, jobs, bach size, ool slos on each machine operaions of all he job (boh essenial and opional), and processing ime of every operaion of each job. Sep 2. Iniialize he parameers such as populaion size, maximum ieraion, decremen facor, ineria weigh, social and cogniive parameers. Generae iniial populaion randomly. Consruc he iniial posiion values of he paricle uniformly: x ij = x min + (x max x min ) U(0,) where x min =0.0,x max =4.0 and U(0,) is a uniform random number beween 0 and. Generae iniial velociies of he paricle v ij = v min + (v max v min ) U(0,) where v min =- 4.0,v max =4.0 and U(0,) is a uniform random number beween 0 and. Sep 3. Ge he iniial sequence by using SPV rule. Then selec he firs job from ha sequence and do he following: a) Firs load he essenial operaion on he machine if and only if available machining ime is greaer han he ime required by he essenial operaion oherwise rejec he job. b) Similarly load he opional operaion if and only if available machining ime and ool slo is greaer han he ime and ool slo required by he opional operaion on he basis of machine having maximum available ime oherwise rejec he job Sep 4. Evaluae each paricles finess (Sysem unbalance) by using equaion () for case and (6) for case 2 while saisfying heir respecive consrains. Sep 5. Find ou he personal bes (pbes) and global bes (gbes) Sep 6. If no progress in pbes value is observed for an elapsed period of DELTA, carry ou muaion of a paricle using he muaion sraegy as oulined in Secion 4.2 provided DELTA is greaer han a random number beween zero and maximum ime of no progress (MAXT) Sep 7. Updae velociy, posiion and ineria weigh by using equaion (), (2) and (3). Sep 8. Compue paricles finess similar o sep 3 and find new pbes and gbes. Sep 9.Terminae if maximum number of ieraions is reached and sore he gbes value. Oherwise, go o Sep Resuls and discussion In real-life siuaions, indusrial applicaion of he model will invariably face a large number of variables and consrain. The swarm opimizaion based approach is proposed for aking decisions in such scenarios. The proposed PSO algorihm for he FMS loading problem is coded in Visual C ++ and implemened in a Penium IV PC. The performance of he PSO algorihms is evaluaed by using en benchmark problems available in open lieraure represening hree differen FMS scenarios. For solving he problems, parameers are se as populaion size = 25, w=0.85, α=0.9 and c=c2=2 afer a horough examinaion of he resuls. Since differen mehods have been used by researchers for calculaion of sysem unbalance, he machine loading problem of FMS has been solved in his paper by considering wo cases o examine he robusness of he PSO algorihm. Compuaional resuls for case I and case II are summarized in 4 respecively using sandard PSO. The resuls obained by using PSO are summarized in Table 4. I may be noed ha ha boh sysem unbalance and hroughpu can be improved if overloading of machines are permied. However, economic jusificaion of overloading mus be looked ino before permiing overloading. 626

7 Problem Number Table 4 Summery of resuls obained from PSO algorihm (adoped from Tiwari e. al., 2007) Problem Number of Case I Case II Number par ypes SU TH SU TH One of he drawbacks of PSO is is premaure convergence. In order o eliminae his and o improve soluion qualiy, muaion operaor is adoped from geneic algorihm. The resuls of proposed MPSO (PSO wih muaion) are compared wih four sandard sequencing rules such as LPT, SPT, LIFO and FIFO in Table 5. The resuls indicae ha MPSO improves he soluion qualiy and ouperforms oher echniques available in lieraure in mos of he insances. N RECTETable 5 Comparison of resuls obained using PSO based approach wih oher mehods SPT LPT LIFO FIFO Tiwari e. al (SU, TH) (SU, TH) (SU, TH) (SU, TH) (2007) (SU, TH) MPSO Approach wihou overloading (SU, TH) MPSO Approach wih overloading (SU, TH) 288, 48 33, 29 58, 43 3, 44 63, 48 44,22 52, , 47 87, , , , 6 29,52 9, , 5 778, 46 89, 5 099, 43 89, 5 778,46 778, , , , , , ,37 482, , , , 0 68, 20 68, ,96 08, , , , , , ,86 0, , 5 38, 8 836, 08, 7 20, ,7 0, , 4 88, , , 53 9, 67 36,55 0, , 3 69, , 23 69, 28 69, ,28 569, , , , 20 20, 2 0, 46 7,2 0, 28 An imporan parameer in PSO is populaion size. To sudy he effec of populaion size on soluion qualiy, i is increased from 0 o 00 a he incremen of 0 for es problems keeping all oher parameers consan. Figure shows he effec of populaion on sysem unbalance for Problem No.. From his figure, i can be observed ha as he populaion size increases sysem unbalance decreases o cerain exen and furher increase of populaion has no effec on soluion qualiy. This may be aribued o he fac ha diversiy in soluion space increases as he populaion size increases bu large increase in populaion size causes a random or wors poin of search and increases he possibiliy of rapping a local opimum. However, he populaion size mus be mainained a leas wo imes of he number of jobs in order o obain improved soluion. Sysem Unbalance vs. Populaion size Sysem unbalance Populaion size Figure.Bes resuls obained a differen populaion size 627

8 5. Conclusions This paper presens an efficien and reliable evoluionary based approach o solve he FMS loading problem. The proposed approach uilizes he global and local exploraion capabiliies of PSO o search for he opimal soluion by considering availabiliy of ool slos and machining ime consrains ino accoun. The key advanage of PSO is is compuaional efficiency and less parameer is required o be adjused in order o ge he opimum resul compared o relaed echniques. Exensive compuaional experimens have been conduced on differen benchmark problems o show he effeciveness of he proposed approach. A comparaive sudy has been carried ou for same se of problems wih similar objecive funcions and consrains and he compuaional experience manifess ha proposed mea-heurisic approach based on PSO ouperforms he exising mehodologies as far as soluion qualiy is concerned wih reasonable compuaional effors. Alhough he objecive of his sudy is o minimize sysem unbalance, he proposed mea-heurisic based on PSO no only minimizes sysem unbalance bu also simulaneously increases he hroughpu for mos of he insances. To avoid premaure convergence, PSO algorihm is modified in his paper wih he inroducion of muaion operaion. The performance of his algorihm is compared oher relaed echniques. The resul obained by PSOM is promising and encouraging. I is eviden from his sudy ha overloading of machines is a viable proposiion for minimizing he sysem unbalance bu i involves cos. Therefore, a rade off beween balancing of loads on machines and cos incurred mus be made. In fuure, he sudy can be exended o solve loading problem by considering more realisic variables and consrains such as availabiliy of palles, jigs, fixures, AGVs ec in addiion o ool slos and machining ime. 6. References. Berrada, M and Secke, K.E. A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacuring Sysems. Managemen Science p Kennedy, J and Eberhar, R.C. Paricle Swarm Opimizaion. Proceedings of IEEE Inernaional Conference on Neural Neworks p Kumar, N and Shanker, K. A Geneic Algorihm for FMS Par Type Selecion and Machine Loading. Inernaional Journal of Producion Research p Moreno, A.A and Ding, F.Y. Heurisics for he FMS Loading and Par Type Selecion Problems. Inernaional Journal of Flexible Manufacuring Sysem.993. p Mukhopadhyay, S.K, Midha, S and Muralikrishna, V. A Heurisic Procedure for Loading Problems in Flexible Manufacuring Sysems. Inernaional Journal of Producion Research.992. p Nagarjuna, N, Mahesh, O and Rajagopal, K. A Heurisic based on Muli-Sage Programming Approach for Machine-Loading Problem in a Flexible Manufacuring Sysem. Roboics and Compuer Inegraed Manufacuring p Rige, J and Vesersroem, J.S. A Diversiy Guided Paricle Swarm Opimiser - he ARPSO. Dep. of Compuer Science, Universiy of Aarhus, Technical Repor. No EVA Life Shanker K, Srinivasulu A. Some Soluion Mehodologies for Loading Problems in a Flexible Manufacuring Sysem. Inernaional Journal of Producion Research p Secke, K.E. Formulaion and Soluion of Non-Linear Ineger Producion Planning Problem for Flexible Manufacuring Sysem. Managemen Science p Swarnkar, R and Tiwari, M.K. Modeling Machine Loading Problem of FMSs and is Soluion Mehodology is using a Hybrid Tabu Search and Simulaed Annealing-Based Heurisic Approach. Roboics and Compuer Inegraed Manufacuring p Tiwari, M.K, Hazarika, B, Vidyarhi, N.K, Jaggi, P and Mukhopadhyay, S.K. A Heurisic Soluion Approach o he Machine Loading Problem of an FMS and is Peri Ne Model. Inernaional Journal of Producion Research.997. p Tiwari, M. K., Saha, J and Mukhopadhyay, S. K. Heurisic Soluion Approaches for Combined-Job Sequencing and Machine Loading Problem in Flexible Manufacuring Sysems. Inernaional Journal of Advanced Manufacuring Technology p Vidyarhi, N.K and Tiwari, M.K. Machine Loading Problem of FMS: A Fuzzy-Based Heurisic Approach. Inernaional Journal of Producion Research P Yoshida, H, Kawaa, K, Fukuyama, Y and Nakanishi, Y. A Paricle Swarm Opimizaion for Reacive Power and Volage Conrol Considering Volage Securiy Assessmen. IEEE Transacions on Power Sysems p ORIGINAL ARTICLE RIGINAL 628