Machine Learning in Production Systems Design Using Genetic Algorithms

Transcription

1 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 achne Learnng n Producton Systems Desgn Usng Genetc Algorthms Abu Quder Jaber, Yamamoto Hdehko and Rzauddn Raml Abstract To create a soluton for a specfc problem n machne learnng, the soluton s constructed from the data or by use a search method. Genetc algorthms are a model of machne learnng that can be used to fnd nearest optmal soluton. Whle the great advantage of genetc algorthms s the fact that they fnd a soluton through evoluton, ths s also the bggest dsadvantage. Evoluton s nductve, n nature lfe does not evolve towards a good soluton but t evolves away from bad crcumstances. Ths can cause a speces to evolve nto an evolutonary dead end. In order to reduce the effect of ths dsadvantage we propose a new a learnng tool (crtera) whch can be ncluded nto the genetc algorthms generatons to compare the prevous populaton and the current populaton and then decde whether s effectve to contnue wth the prevous populaton or the current populaton, the proposed learnng tool s called as Keepng Effcent Populaton (KEP). We appled a GA based on KEP to the producton lne layout problem, as a result KEP keep the evaluaton drecton ncreases and stops any devaton n the evaluaton. Keywords Genetc algorthms, Layout problem, achne learnng, Producton system. I. INTRODUCTION O create a soluton to a specfc problem n machne T learnng, the soluton s constructed from the data or by use a search method to fnd nearest optmal soluton. Genetc algorthm (GA) s stochastc search whch s often used n machne learnng applcaton. An effectve GA representaton and meanngful ftness evaluaton s the keys of the success n GA applcatons. The effectveness of GA comes from ther smplcty as robust search algorthm as well as from ther power to dscover good solutons rapdly for dffcult hgh-dmensonal problems. GA s useful and effcent n the followng cases: 1 When the search space s large, complex or poorly understood. 2 When the doman knowledge s scarce or expert knowledge s dffcult to encode to narrow the search space. 3 If no mathematcal analyss s avalable. 4 When the tradtonal search methods fal. The advantage of the GA approach s that t can handle anuscrpt receved November 30, A. J. Author s wth Intellgent anufacturng Systems Laboratory, Gfu Unversty. 1-1 Yanagdo, Gfu Sh, , Japan. (e-mal: k @edu.gfu-u.ac.jp) Y. H. Author, s wth Intellgent anufacturng Systems Laboratory, Gfu Unversty. 1-1 Yanagdo, Gfu Sh, , Japan. (correspondng author, phone: ; fax: ;.e-mal: yam-h@gfu-u.ac.jp). R. R. Author s wth Intellgent anufacturng Systems Laboratory, Gfu Unversty. 1-1 Yanagdo, Gfu Sh, , Japan. (e-mal: k @edu.gfu-u.ac.jp) arbtrary knds of constrants and objectves; all such thngs can be handled as weghted components of the ftness functon, makng t easy to adapt the GA scheduler to the partcular requrements of a very wde range of possble overall objectves. GA s one of the wde applcablty of knowledge-learn problem-solvng tools that can provde an approach [1], [2]. Whle the great advantage of GA s the fact that they fnd a soluton through evoluton, ths s also the bggest dsadvantage. Evoluton s nductve; n nature lfe does not evolve towards a good soluton but t evolves away from bad crcumstances. Ths can cause a speces to evolve nto an evolutonary dead end. In order to reduce the effect of ths dsadvantage a learnng tool s add to the GA to decde whether s effectve to contnue wth the generated populaton or the current populaton, ths learnng tool s called hereafter as keepng effcent populaton (KEP). II. GENETIC ALGORITHS The GA paradgm has been proposed to solve a wde range of problems [2][3][4]. GA has been successfully appled to optmzaton problems n dverse felds and t s dffers from other search technques whch depend on natural genetc evaluaton process. GA starts wth an ntal set of solutons selected randomly called populaton. A sutable encodng for each soluton n the populaton s used to allow computaton of the ftness. The soluton set n the populaton, called as chromosome or ndvdual, represents a soluton to the optmzaton problem. Each ndvdual contans a number of genes. The ndvduals n the ntal populaton are evaluated to measure ts ftness. To create the next populaton, new ndvduals are formed by ether mergng two ndvduals from the current populaton usng a crossover operator or modfyng an ndvdual soluton usng mutaton operator. Based on the ndvduals ftness, the ndvduals to be ncluded n the next populaton are then probablstcally selected from the set of ndvduals n current populaton. The teraton, called a generaton s contnued untl the ftness reaches ts maxmum value, wth the hope that strong parent wll create a ftter generaton of the chldren. The best overall soluton becomes the canddate soluton to the problem. To create the next generaton GA based on three operatons: Selecton, crossover and mutaton. A. Basc Genetc Algorthm The outlne of the basc GA s descrbed below. 1. [Start] Generate random populaton of n ndvduals (sutable solutons for the problem). 72

2 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 2. [Ftness] Evaluate the ftness f(x) of each ndvdual x n the populaton. 3. [New populaton] Create a new populaton by repeatng followng steps untl the new populaton s complete. [Selecton] Select two parent ndvduals from a populaton accordng to ther ftness (the better ftness, the bgger chance to be selected) [Crossover] Wth a crossover probablty cross over the parents to form a new offsprng (chldren). If no crossover was performed, offsprng s an exact copy of parents. [utaton] Wth a mutaton probablty mutate new offsprng at each locus (poston n ndvdual). [Acceptng] Place new offsprng n a new populaton 4. [Replace] Use new generated populaton for a further run of algorthm 1. The sze of the populaton of solutons, whch wll determne the dversty of solutons that the algorthm evaluates, and therefore the chance of an optmal soluton beng found [5]. 2. The ablty of the algorthm to mantan dversty n the populaton [6]. The flow chart of GA operatons s shown n fgure 1. B. Usng Genetc Algorthms as the Search Procedure Genetc algorthms typcally mantan a constant-szed populaton of ndvduals whch represent samples of the space to be searched. Each ndvdual s evaluated on the bass of ts overall ftness wth respect to the gven applcaton doman. New ndvduals (samples of the search space) are produced by selectng hgh performng ndvduals to produce "offsprng" whch retan many of the features of ther "parents". The result s an evolvng populaton that has mproved ftness wth respect to the gven goal. The soluton process wll generate a large amount of nformaton that can be used to carry out some form of learnng. Gen. 0 Create ntal random Evaluate ftness of each ndvdual n populaton Is the ftness become constant? No I=0 Gen. =Gen.+1 yes I=? No Prnt the result Select Genetc Operaton Probablstcally Pm Pc Select two ndvdual Based on ftness yes Select two ndvdual Based on ftness Prnt the result End Select two gene places randomly and exchange t Copy nto new Populaton I=I+1 Perform Crossover Insert two offsprng nto new populaton I=I+1 5. [Test] If the end condton s satsfed, stop, and return the best soluton n current populaton 6. [Loop] Go to step 2 The success of a genetc algorthm depends largely on two factors: Fg. 1 GA operatons flow chart C. Keepng effcent populaton In the conventonal GA, the set of possble solutons from one populaton are taken and are used to construct a new populaton. Ths s motvated by a hope that the new populaton wll be ftter than the old one. Evoluton evolves away from 73

3 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 bad crcumstances. Ths can cause a speces to evolve nto an evolutonary dead end. Ths research ams to keep the evaluaton drecton ncrease and stop any devaton n the evaluaton. In order to acheve ths, we proposed a KEP. KEP s anew learnng tool whch can be ncluded nto the genetc algorthms operatons to keep the effcent populaton. KEP s added to the GA to decde whether s effectve to contnue wth the prevous populaton or the current populaton. The man dfference between the conventonal GA and GA wth KEP s that the conventonal GA are used the current populaton for learnng to produce the next generaton. In contract, GA wth KEP s frst compare the current populaton wth the prevous populaton, and then decdes whether s effectve to contnue wth the prevous populaton or the current populaton. By ths way KEP s stopped any devaton n the evaluaton. III. PRODUCTION LINE LAYOUT PROBLE One of the problems encountered of the desgn and mplementaton of a flexble transfer lne (FTL) s the layout of the FTL n the restrcted area. The layout of the FTL has an mportant mpact on producton cost. The effcent layout desgn of the FTL can reduce the cost of materal handlng by at least 10-30%. Dependng on the producton system, between 15% - 70% of the total producton cost can be attrbuted to materal handlng [7]. Thus, the FTL layout s mportant to reduce producton cost. The FTL layout problem s dentfed as a NP-complete problem [8], and many heurstc approaches have been developed to solve ths problem for near optmum soluton [7] [19]. However, despte the many exstng methodologes regardng the FTL layout problem, almost all approaches studng ths problem neglect mportant operatonal detals such as the buffer sze between the machnes and restrcted areas n the plant area.in ths paper operatonal detals ncludng the movement of the products between machnes are consdered, n addton to the restrcted areas n the ste. In order to fnd FTL layout ncludng machnes and a materal handlng path between each par of machnes, an effcent FTL layout desgn procedure called a One by One Layout ethod (OOL) n conjuncton wth GA s proposed. The OOL generates an effcent soluton for a set of rregularly shaped machnes through a restrcted plant area. The OOL s not lmted to a sngle statc envronment, but s hghly flexble, wthn the plant structure. A CAD system s lnked to the proposed OOL to draw the FTL layout. The problem can be descrbed mathematcally as follows: Gven: A set of K rregular-shaped machnes and ther dmensons; Spaces and machne allocaton lmtatons; The plant restrctons, such as plant columns, walls, and any other restrctons n the plant area; The buffer sze vector [B 1, B 2,, B K-1 ]. Determne: FTL layout desgn. So as to mnmze A F. Wth the followng condton AF A P and D k s located at or s close to the FTL end pont. Where A F The requred area needed to create the new FTL layout. A P The avalable plant area. The last machne drop pont. D k IV. SEARCH A FTL LAYOUT USING GA In order to fnd an effcent layout of the FTL components through the avalable plant area, a GA s ncluded nto the OOL. The OOL s conducted usng the followng algorthm. Before descrbng the algorthm, the notatons and terms used n algorthm are defned. A. Notatons K Number of machnes n the FTL. B Buffer allocaton between machnes and +1. c Sl Sde length of each cell. L Overall machne length. W Overall machne wdth. L Overall plant length. W Overall plant wdth. l Sde length of the buffer space. Blocked-cells() Number of cells ncluded n blocked area. achne-cells() Number of cells ncluded n machne layout. Blocked-areas Number of blocked areas throughout the extended area. C start Cell through the plant area that represents the FTL start pont. C end Cell through the plant area that represents the FTL end pont. c j p Locaton of cell j n a machne cell map relatve to the machne pck pont. cb k Locaton of cell k n blocked area. cp Cell locaton of the machne pck pont through the plant area. cd Cell locaton of the machne drop pont through the plant area. B. Defntons In order to fnd an effcent layout of the FTL components through the avalable plant area, a GA s ncluded nto the OOL. The OOL s conducted usng the followng algorthm. Before descrbng the algorthm, the notatons and terms used n algorthm are defned. [Defnton 1] achne pck pont,p : The machne pck pont s the pont where the parts nput nto machne. [Defnton 2] achne drop pont,d : The machne drop pont s the pont where the parts leave machne. [Defnton 3] achne cells group, cells group : The machne cells group s the set of cells that has been mapped to machne relatve to the P cell. [Defnton 4] Buffer-cell rato, B m-c : The buffer cell rato s 74

4 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 the smallest nteger number greater than or equal to the dvson of the buffer sde length to the cell length; B m-c can be calculated by usng equaton 2. l B m c = (1) c Sl [Defnton 5] FTL Components: FTL components nclude the machnes and buffer spaces. [Defnton 6] FTL Component locaton, CO locaton : The component locaton s the locaton of the next component wth respect to the current component n the FTL. The component can be located n one of four locatons wth respect to the current component (up, down, rght or left). [Defnton 7] Extended plant area, A plant-ext : The extended plant area s the area of the rectangle that passes through some of the plant outsde wall and ncludes all plant facltes and sub walls. [Defnton 8] Blocked area: The blocked area s the area n the plant that has been restrcted by some robstacles such as plant columns, parttons, and sub areas used by bult statons, etc. The blocked areas are not usable for allocaton of machnes or buffers. In addton to the blocked areas n the plant area, the areas n the extended area that are not ncluded wthn the plant area are assumed to be blocked areas. [Defnton 9] Block area cells group, BAcells group : The blocked area cells group s the set of cells that have been mapped to the blocked area. [Defnton 10] achne cells map, map : The machne cells map s the set of cells that have been mapped to the machne layout. The locaton of each cell n the machne map s defned relatve to the machne pck pont. [Defnton 11] achne drop pont possble locatons, Cdrop ( j ) : The machne drop pont possble locatons are the locatons of the machne drop ponts wth respect to a gven machne pck pont. As follows [19], the machne can be located at 0, 90, 180 or 270, thus 1 j 4. To descrbe the machne drop pont s possble locatons, the followng example s ntroduced. Example: Based on machne wth ts pck and drop ponts as shown n Fgure 2. If the machne pck pont s located at cell (I,J) then the locaton of the drop pont possble locatons are as follows: k P Fg. 2 achne model (I,J + 3) f map BAcells groups k = 1K blocked - areas, (I,J - 3) f k map BAcells groups k = 1K blocked - areas, (I + 1,J) f k map BAcells groups k = 1K blocked - areas, (I -1,J) f k BA k = 1K blocked- areas map cells groups D The possble locatons of the drop pont are cells 1, 2, 3 and 4 n Fgure 3. Fg. 3 Possble locatons of machne drop pont [Defnton 12] Buffer space possble locatons, BSdrop ( j ) : The buffer space possble locatons are the locatons of the buffer space wth respect to the locaton of the component -1. To descrbe the buffer space possble locatons, the followng example s ntroduced. Example : Consder machne n Fgure 2 and assume that the buffer sze next to ths machne s 5. The possble locatons of all buffers are shown n Fgure 4 below. The possble locatons of the frst buffer space are the cells coded by the number 1, and the possble locatons of the second buffer space are the cells that are coded by te number 2, and so on P D Fg. 4 The possble locatons of the buffers. [Defnton 13] FTL area, A F : The FTL area s the area used by the FTL components. [Defnton 14] Plant area, A P : The plant area s the avalable factory area. C. OOL Algorthm Step 1: Defne the matrx that represents the extended plant layout area as follows : Followng [18], the plant n ths study s defned as unform squares connected together and denoted n ths paper as cells as shown n Fgure 2. The restrcted areas (obstacles) ncludng the plant columns and any other obstacles are ndcated on the plant layout. The start pont and the end pont of the FTL locatons are gven and are represented on the plant layout. The plant model can be defned by usng the followng steps. 1. Draw the smallest rectangle that passes through the outsde walls to nclude all plant facltes and sub walls. The area covered by ths rectangle s denoted n ths paper as the extended plant area. 2. Dvde the extended plant area nto unform cells that are equal to each other and connected to each other. 3. Defne a matrx that represents the extended plant layout area as shown n equaton 1, 2 3 p

5 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 C C C m ( ) C( 1,2) L C( 1, j) L C( 1,n 1) C( 1,n) ( 2 1, ) C( 2,2) L L L C( 2,n 1) C( 2,n) C 11, ( 1, ) C(,2) L C(, j) L C(,n 1) C(,n) ( 11, ) C( m 1,2) L C( m 1, j) L C( m 1,n 1) C( m 1,n) C( m 1, ) C( m,2) L C( m, j) L C( m,n 1) C( m,n) (2) K K 1 2 ( L W ) + ( B l ) A = (3) T = 1 = 1 Step 19: Carry out the followng rule. If: the evaluate equaton 4 s satsfed, AF - AT 0 (4) Then: draw the FTL, Else: read new buffer sze vector [B 1, B 2,, B K-1 ]. where C(,j) represents the cell located n row and column j. Step2:Set C( k) = C,j ( ) k = 1,2, K,(m n), = 1,2, K,mandj = 1,2, K,n. Step 3: Read the FTL start pont. = c, j, 1, K,m, j 1, K,n Set ( ) { } { } C start k cells groups and c(, j) BA k = 1K blocked - areas. Step 4: Read the FTL end pont. = c, j, 1, K,m, j 1, K,n Set ( ) { } { } C end k cells groups and c(, j) BA k = 1K blocked - areas. Step 5: Defne the cells map for all machnes, relatve to the P cell. cells group cells group = 1 p 2 p machne cells() p. Set { c,c, K,c } = 1, K, K Step 6: Defne the drop cell for machne, relatve to the P cell. Step 7: Defne all blocked areas cells group through the extended plant area, BA cells group { cb,cb,, cb } cells group = 1 2 K Blocked cells( ) BA. Set BAcells group Aplant-ext, = 1,2, K,Blocked area. Step 8: Set the frst machne pck pont at the FTL start pont. Set P =. 1 Cstart Step 9: Fnd all possble locatons of the frst machne drop 1 ponts, cd, as descrbed n defnton 11. Step 10: Randomly select one of the possble locatons of the machne drop ponts. Step 11: Fnd all possble locatons of the frst buffer space wth respect to the machne drop pont as descrbed n defnton 12. Step 12: Randomly select one of the possble locatons of the frst buffer space. Step 13: Fnd all possble locatons of the next buffer space wth respect to the current buffer space locaton and randomly select one of these locatons. Step 14: Repeat step 13 to fnd one locaton for each space of buffer sze. Step 15: Fnd all possble locatons of the next machne pck ponts, cp, wth respect to the last buffer space and randomly select one of these locatons. Step 16: Repeat steps to fnd one of the possble locatons of all machnes and spaces of all buffers. Step 17: Apply the GA operatons to fnd the best locatons for all of the FTL components. Step 18: Calculate the FTL area by usng equaton 3. V. GENETIC ALGORITHS OPERATIONS FOR PRODUCTION LINE LAYOUT PROBLE The GA operatons for the producton lne layout problem are descrbed n sectons V.A ~ V.D. A. Encodng One of the mportant jobs to use GA s how to express a chromosome. One of the man dffcultes n encodng ths problem s that each par of components n the FTL s located relatve to each other, whch t means that each component s locaton should be specfcally dentfed n the ndvdual. Ths research adopts each component s locaton n the FTL as the gene, each machne n the FTL represented by two genes one for the machne pck pont locaton and the other for the machne drop pont locaton. The other component s locatons are represented by one gene for each. The conventonal GA operatons are generally based on an ndvdual wth a smlar gene sze. In the case that we are studyng here, namely FTL layout, t s dffcult to use a smlar gene sze n ndvduals. Ths s because the number of possble component locatons s not equal for all components. The number of possble locaton for next component s decded accordng to the state of locatons up, down, left and rght of the current component. For example f component s located at cell (I, J), then the number of possble locatons, NPL, of component +1 s as follows: 0 f the costrans 1,2,3,and 4 are satsfed 1 f three costrans from costrans 1, 2, 3, and 4 are satsfed (5) NPL= 2 f two costrans from costrans 1, 2, 3, and 4 are satsfed 3 f one costrans from costrans 1, 2, 3, and 4 s satsfed 4 f the costrans 1, 2, 3, and 4 are not satsfed Constran 1: (I,J + 1) { cb1,cb2, K,cbBlocked cells( ) } = 1,2, K,Blocked area Constran 2: (I, J 1) { cb1,cb2, K,cbBlocked cells ( ) } = 1,2, K,Blocked area Constran 3: (I + 1, J) { cb1,cb 2, K,cb Blocked cells ( ) } = 1,2, K,Blocked area Constran 4: (I - 1, J) { cb1,cb 2, K,cb Blocked cells ( ) } = 1,2, K,Blocked area In ths research, we propose a new ndvdual encode method to express each ndvdual. The new encode method s called a one to one encodng method (OOE). The followng paragraph descrbes how to use OOE to encode the components n the FTL. The frst element n the ndvdual represents the locaton of the drop pont of the frst machne n the FTL. The locaton of the frst machne drop pont can be 76

6 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 determned wth respect to the locaton of the frst machne pck pont as descrbed n defnton 11. Elements 2, 3,, G B1+1 n the ndvdual represent the locaton of the spaces of the frst buffer. The locaton of the frst buffer space s determned wth respect to the locaton of machne drop pont and the locaton of next buffer space s determned wth respect to the current buffer space locaton and so on. Fgure 5 shows the encodng usng the OOE. The number of genes n each ndvdual, T, s calculated usng Eq. (6). T = 2K 1 + K 1 B (6) = 1 The number of tems n the ndvduals s not lmted, whch means that any producton lne wth any number of machnes and any buffer sze between each par of machnes can be dealt wth check the cell locaton leavng that cell locaton n the second parent. If the cell locaton s empty, choose the cell of the second parent otherwse choose the cell of the frst parent. For example, consder the two parents as shown n Fg. 6. If the frst ndvdual s chosen as the template, chld 1 can be generated usng the followng steps: Step 1: Select cell U (the frst cell locaton n the duvdual) as the frst cell locaton of chld 1. Step 2: Fnd the edges after gene 1 n both parents wth respect to the frst cell locaton of chld 1 : (frst cell locaton, U), read as the cell up to the frst cell locaton and (frst cell locaton, L), read as the cell left to the frst cell locaton, fnd the cell state of these two edges. If the cell located left to the frst cell locaton s empty (nether restrcted nor used by another components) then t wll be chosen as the second gene for the chld 1, otherwse, the cell up to the frst cell locaton wll be chosen as the second gene for the chld 1. Assumng that the cell up to the frst cell locaton s empty, we select U as the next gene of chld 1. 1 B 1 B B K-1 K Pck Drop S 1 S 2 Sk [G 1 G 2 G 3 G B1+1 G B1+2 G B1+3 G G T-1 G T ] Fg. 5 OOE Encodng method B. Intal populaton The ntal populaton s randomly selected. The ntal populaton contans (N) number of ndvduals. Each ndvdual expresses a buffer sze as shown n Fgure 6. The locaton of components should be specfcally dentfed n the ndvdual because each par of components n the FTL s located relatve to each other. The ntal populaton s determned as follows: Set ndvdual () = [G 1 G 2 G T-1 G T ] = 1,2, K, N Each ndvdual n the ntal populaton s determned by usng steps 8 ~ 16 n secton IV.C. C. Crossover The tradtonal crossover operaton s not sutable for ths type of representaton because the genes are selected one by one. The encode method to express each ndvdual usng OOE s dfferent from that whch s obtaned usng conventonal encodng method. The crossover operatons for our GA system are also dfferent. The man dfference between the OOE crossover and the conventonal methods crossover s that n the conventonal method the genes after the crossover pont are swapped between the two ndvduals wthout any constrans. In contrast, the genes after the crossover pont are selected one by one to avod a restrcton cells. OOE crossover selects the frst cell locaton of one parent, Step 3: Fnd the edges after gene 2: (second cell locaton, L), and (second cell locaton, L). The edges after gene 2 s the same, we select L as the next gene of chld 1. Step 4: Fnd the edges after gene 3: (thrd cell locaton, D), and (thrd cell locaton, U). Assumng that the cell up to the thrd cell locaton s not empty, we select D as the next gene of chld 1. Step 5: Fnd the edges after gene 4: (fourth cell locaton, R), and (fourth cell locaton, L). Assumng that the cells rght and left to the fourth cell locaton are not empty, we select D as the next gene of chld 1. Note that f cell down to gene 4 s also not empty n ths case the prevouse gene (gene 3 n ths example) s change to thrd possble choce whch s L, and contnue from ths pont agan. Step 6: Repeat the same rule n prevous step to generate all genes of chld 1. We can use the same procedure to generate chld 2 as shown n Fg. 6. After crossover, both offsprng encode legal path. 77

7 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 U U L D R R U L L D U L L U L R D R L U Indvdual 1 Indvdual 2 Before crossover U U U L U U L U L L U U L D U L L U U U L D D U L L U L U U L D D R U L L U L R U U L D D R D U L L U L R D U U L D D R D R U L L U L R D L U U L D D R D R L U L L U L R D L L Indvdual 1 Indvdual 2 After crossover Fg. 6 OOE crossover operaton D. utaton The mutaton of our GA system s dfferent from the tradtonal mutaton operator because the gene expresson adopts OOE. Instead of usng the tradtonal mutaton operator, we randomly select two mutaton ponts (two genes n one ndvdual) and swap ther values. After swap the two genes, the cells locatons of the two mutaton ponts and of the genes between the two mutaton ponts are test, f any of these cells belong to block area cells group, the two mutaton ponts are reselected. The new mutaton ponts are selected between the two old mutaton ponts. Ths process s repeated untl the cells belong to the genes between the two mutaton ponts s not restrcted. Thus, we stll have legal path after swap mutaton. The mutaton s carred out usng the followng steps. Step 1: Select one ndvdual randomly from the current populaton. Step 2: Select two mutaton ponts, P 1 and P 2, randomly. Step 3: Swap the two mutaton genes values. Step 4: Check the cells belong to the two mutaton ponts and all cells belong to the genes between the two mutaton ponts, f the cells of two mutaton pont and the cells between them after swap are empty (nether restrcted nor used by another components) then go to Step 7, otherwse go to Step 5. Step 5: Select new two mutaton ponts, but n ths tme between the current mutaton ponts Step 6: Go to Step 3. Step 7: Accept the mutaton. The follow chart n Fgure 7 shows the mutatons algorthm. Set the mutaton selecton perod Lower value =1, upper value =T Select two mutaton ponts randomly P 1 = Rand (lower value upper value) P 2 = Rand (lower value upper value) Swap the P 1 and P2 Are the cells n the perod [P 1, P 2 ] after swap are empty? No Set the mutaton selecton perod Lower value =P 1, upper value= P 2 Fg. 7 utaton algorthms Yes Stop VI. NUERICAL EXPERIENTS We appled the developed OOE to some of FTL examples as follows: A. Appled FTL example : 10 machnes and 9 buffers The FTL we adopted n ths example has 10 machnes and the 9 buffers. Each buffer space s assumed to be equal of the plant cells, B m-c = 1. The machnes shapes and specfcatons are as shown n Fgure 8. Table 1 gves the buffer sze between each par of machnes n the FTL. 78

8 Internatonal Journal of Computatonal Intellgence Volume 4 Number 1 TABLE I UNITS FOR AGNETIC PROPERTIES B1 B2 B3 B4 B5 B6 B7 B8 B achnes 1, 3, 5, 7 and 10 achnes2 and 8 achnes 4, 6 and 9 to the effcent use of the GA, new technques of GA mutaton and crossover are proposed. The 3D drawng of the FTL s drawn by lnk the CAD system to the proposed OOL. We used our developed OOL to determne some FTL layout desgn n dfferent restrcted areas. As a result, the FTL layout desgn achevng the best utlzaton of the plant area could be determned. The combnaton of the OOL and the GA can be appled to obtan the layout of any FTL n any plant restrcted area. REFERENCES Fg. 8 achnes shapes and specfcatons B. Results The 3D drawng of the FTL layout resulted by the OOL s drawn by the CAD system as shown n Fgure 9. Fg. 9 The 3D drawng of FTL layout VII. CONCLUSION Ths research ntroduces a new learnng tool whch can be ncluded nto the genetc algorthms operatons to keep the evaluaton drecton ncrease and stop any devaton n the evaluaton. GA wth KEP s frst compare the current populaton wth the prevous populaton, and then decdes whether s effectve to contnue wth the prevous populaton or the current populaton. GA operatons ncluded KEP learnng tool s appled to solve FTL layout problem as an applcaton of GA wth KEP learnng tool. In ths applcaton the ams s to fnd the effcent put of the FTL components ncludng the machnes layout and the materal handlng path between each par of machnes n the restrcted area by proposng OOL n conjuncton wth genetc algorthm. The combnaton of OOL and GA generates an effcent soluton for a set of rregularly shaped machnes through a restrcted plant area. Ths combnaton s effcently solved the FTL layout. In order [1] G. Tompkns and F. Azadvar, Genetc algorthms n optmzng Smulated Systems, In WSC 95. Proceedng of the 1995 Conference on Wnter Smulaton, AC, 1995, pp [2] S. Forrest, Genetc Algorthms, AC Computng Surveys, Vol. 28 No. 1, 1996, pp [3] D. Lawrence, Handbook of Genetc Algorthms, Van No strand Renhold, New York, [4] D. Goldberg, Genetc Algorthms n Search, Optmzaton, and achne Learnng, Addson-Wesley, New York, [5] D. Levne, A Parallel Genetc Algorthm for the Set Parttonng Problem, Ph.D. Thess ANL-94/23 The Argonne Natonal Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, [6] D. Whtley, The GENITOR algorthm and selecton pressure: Why rank-based allocaton of reproductve trals s best, In J. Shaffer, edtor: Proceedngs of the Thrd Internatonal Conference on Genetc Algorthms, San ateo, 1989, pp [7] J. A. Tompkns, J. A. Whte, Y. A. Bozer, E. H. Frazella and J.. Tanchoco, Facltes Plannng, 2 nd edton, Wley, New York, [8] G. Suresh and S. Sahu, ult objectve Faclty Layout Usng Smulated Annealng, Internatonal Journal of Producton Economcs, Vol. 32, 1993, pp [9] D. G. Conway and. A. Venkataramanan, Genetc Search and Dynamc Faclty Layout Problem. Computers and Operatons Research, Vol. 21 No. 8, 1994, pp [10] A. D. Raoot and A. Raksht, Fuzzy Heurstc for the Quadratc Assgnment Formulaton to the Faclty Layout Problem. Internatonal Journal of Producton research, Vol. 32, No. 3, 1994, pp [11] S. S. Heragu and A. S. Alfa, Expermental Analyss of Smulated Annealng Based Algorthm for the Layout problem, European Journal of Operatonal Research, Vol. 57, No. 2, 1992, pp [12]. Solmanpur, P. Vrat and R. Shankar, An Ant Algorthm for the Sngle Row Layout Problem n Flexble anufacturng System, Computers & Operatons Research, Vol. 32, 2005, pp [13] K. R. Kumar and G. C. hadjncola, A Heurstc Procedure for the Sngle Row Facltes Layout Problem, European Journal of Operatonal Research, Vol. 87, 1995, pp [14]. Bragla, Optmzaton of a Smulated Annealng Based Heurstc for Sngle Row achne Layout Problem by Genetc Algorthm, Internatonal Transacton n Operatonal Research, Vol. 3, No.1, 1996, pp [15] G. C. Lee and Y. D. Km, Algorthms for Adjustng Shapes of Departments n Block Layouts on the Grd-Based Plan, OEGA, Vol. 28, 2000, pp [16] T. Yang and B. Peters, Flexble achne Layout Desgn for Dynamc and Uncertan Producton Envronments, European Journal of Operatonal Research, Vol. 108, 1998, pp [17] T. Yang, B. Petersand. Tu, Layout Desgn for Flexble anufacturng Systems Consderng Sngle Loop Drectonal Flow Patterns, European Journal of Operatonal Research, Vol. 146, 2005, pp [18] S. Bock and K. Hoberg, Detaled Layout Plannng for Irregularly-Shaped achnes wth Transportaton Path Desgn, European Journal of Operatonal Research, to be publshed.. [19] Km, J. G. and Km, Y. D. (2000). Layout Plannng for Facltes wth Fxed Shapes and Input and Output Ponts. Internatonal Journal of Producton research, 38: