ANALYSIS AMONG THREE OPTIMIZATION TECHNIQUES TO SET CUTTING PARAMETERS IN TURNING OPERATIONS

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1 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil ANALYSIS AMONG THREE OPTIMIZATION TECHNIQUES TO SET CUTTING PARAMETERS IN TURNING OPERATIONS Luiz C. A. Rodigues, Mauicio I. Takano, Rafael V. B. Wiecheeck, Univesidade Tecnológica Fedeal do Paaná, PPGEM. Av. See de Seembo, Absac. Deeminaion of he opimal uning paamees of lahes locaed in a Flexible Manufacuing Sysem (FMS) (whee poducion is made on small los o even on individual los) will impose he maximizaion of poducion ae a boleneck esouces and he minimizaion of poducion coss a non-boleneck esouces. Wheneve poducion bolenecks ae idenified, i is impoan o speedup he poducion of hese boleneck asks as much as possible. Bu if a ask is no on a poducion boleneck, is poducion ime should be evised on a suggle fo ools and enegy economy. Theefoe, manufacuing indusies should be able o evise uning paamees a lahes accoding o poducion mix. Bu his is clealy no he case a indusies woldwide. Fom he lieaue, i can be obseved ha opimizaion of uning (o machining) paamees is a elevan poblem. Bu hee has only been a few aicles using Opeaions Reseach appoaches o solve his poblem and mos of his lieaue pesens he use of heuisic mehods. In his pape, an aemp o deemine he opimal cuing paamees using Mahemaical Pogamming commecial sofwae is epoed. A Mixed Inege Nonlinea Pogamming (MINLP) model is applied o he sofwae GAMS/Baon o deemine he opimal uning paamees. To opimize he cuing paamees in a FMS, minimizaion of poducion coss will be analyzed, aking ino accoun he consains of pemissible suface oughness, cuing paamees ange, and machine esicions. Theefoe, his wok is focused on: i) pesening a hoough evision of he lieaue; ii) descibing a nonlinea mahemaical pogamming model o he poblem aken fom he lieaue; and iii) compaing he soluion of a mahemaical pogamming sofwae o wo ohe heuisic appoaches (using simulaed annealing and geneic algoihms) poposed in he lieaue. This pape pesens he esuls of an ongoing eseach. Keywods: Opimizaion, cuing paamees, FMS, mahemaical pogamming, heuisic mehods. 1. INTRODUCTION A Flexible Manufacuing Sysem (FMS) is an auomaed poducion sysem which may be composed of seveal CNC machines. Accoding o Xiaobo and Ohno (1999), a FMS is composed of woksaions, a sysem fo maeials handling and a conol sysem. Each woksaion can conain inpu and oupu buffes, as well as CNC machines. The conol sysem is esponsible fo commanding he FMS hough a clien-seve conol achiecue. An inceasing invesmen in poducion auomaion is being obseved in manufacuing indusies, especially hough he acquisiion of CNC machines. Despie he fac ha his invesmen can be expensive, he poduciviy accomplished using CNC machines can be quesioned. The easons fo his inefficiency ae wofold: i) lack of ained pesonnel o povide impovemens; and ii) unawaeness of he poblem complexiy. Fo insance, deeminaion of he opimal uning paamees of lahes locaed in a Flexible Manufacuing Sysem (FMS) (whee poducion is made on small los o even on individual los) will impose he maximizaion of poducion ae a boleneck esouces and he minimizaion of poducion coss a non-boleneck esouces. I is impoan o noice ha bolenecks on a FMS ae only idenified afe poducion scheduling o sequencing. On he ohe hand, conside he case of cellula manufacuing whee, due o significan seup imes, poducion is made on los of hundeds o housands of manufacued pas. A his siuaion, bolenecks can be idenified simply by an analysis of equipmen loading. In boh siuaions, wheneve poducion bolenecks ae idenified, i is impoan o speedup he poducion a boleneck asks as much as possible. Bu if a ask is no on a poducion boleneck, is poducion ime should be evised on a suggle fo ools and enegy economy. Wha should be emaked fom he above menioned siuaions is ha a ask will o will no be on a boleneck esouce depending on he poducion mix and ha indusies may face significan poducion mix vaiaions on hei daily opeaions. Theefoe, manufacuing indusies should be able o evise uning paamees a lahes accoding o poducion mix. Fom he lieaue, i can be obseved ha opimizaion of uning (o machining) paamees, as descibed peviously is a elevan poblem. Accoding o Su and Chen (1999), cos, poduciviy, and qualiy of machined pas ae significanly affeced by is uning/machining paamees. Bu hee has only been a few aicles using Opeaions Reseach appoaches o solve his poblem and mos ecen lieaue pesens he use of heuisic mehods. The mos used heuisic mehods in he opeaions eseach lieaue ae: simulaed annealing (Aas, 1989), abu seach (Glove and Laguna, 1997), geneic algoihms (Goldbeg, 1989), and an colonies (Doigo e al., 1996). Accoding o Lee and Tang (000), he economical analysis of machining pocesses was saed in A Dynamic Pogamming appoach o his poblem was poposed by Agapiou (199a; 199b). Pasad e al. (1997) poposed a combinaion of Geomeic and Linea Pogamming o solve a muli-sage uning poblem, which was

2 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil implemened wihin a PC-based Compue-Aided Pocess Planning (CAPP) sysem. Lee and Tang (000) consuced a machining model based on a polynomial newok. Wang and Liu (007) fomulaed a pai of wo-level machining economics poblems o calculae he uppe and lowe bounds of he uni poducion cos, which wee ansfomed ino one-level convenional geomeic pogam, based on he dualiy heoem. Su and Chen (1999) pesened Simulaed Annealing appoaches o define uning paamees. Sanka e al. (007) poposed he use of Geneic Algoihms o solve a muli-sage uning poblem. Saavanan e al. (003) aemped o compae he mehods of Simulaed Annealing and Geneic Algoihms. The es of his wok has been oganized as follows. Secion pesens a nonlinea mahemaical pogamming model o he poblem. This wok aemps o compae hee diffeen appoaches: a poposed simulaed annealing, a geneic algoihms poposed by Saavanan e al. (003), and using GAMS/BARON/CPLEX which is a mahemaical pogamming sofwae. A secion 3, he poposed simulaed annealing appoach is pesened, as well as a bief descipion on how his poblem is solved using mahemaical pogamming. Resuls and conclusions ae pesened a secion 4 and 5, especively.. MATHEMATICAL MODEL The uning pocess of a pa is divided in wo sages, he ough and he finish machining. The ough pocess consiss in muliple ool passes emoving as much maeial as possible, wihou compomising he ool, he machine o he machined pa. The finish pocess, on he ohe hand, consiss in a single ool pass bypassing he pa afe mos of he maeial has been emoved in he ough pocess. In he finish machining he mos impoan is ha he pa ends up wih he oughness and accuacy ha was designed. Accoding o Saavanan e al. (003), Wang and Liu (007), Su and Chen (1999), and Sanka e al. (007) he paamees ha mus be opimized in he uning pocess ae he cuing speed, he feed ae, and he deph of cu. When i is equied o use wo o moe machines inside a manufacuing cell o poduce a ceain lo of diffeen pas, he opimal sequence of he manufacuing pocess is impoan, whee one can seek afe he lowes cos o he mos poducive sequence. This sequencing mus conside some manufacuing bounds o each pa in he lo, such as he loading level of he machines, ime o machine he pa, seup depending on he sequence, among ohes. In ode o have a lage pofi i is impoan ha he ime o manufacue a lo is as small as possible in he poducion boleneck, so a geae quaniy of pas is poduced in he same amoun of poducion ime. Hence, he fis sep o opimize he poducion sequence (in a manufacuing cell, fo example) is o define he minimum ime o machine each pa in each machine. In a machining pocess, highe cuing speed, feed ae, and deph of cu guaanee moe speed of maeial emoval. Howeve, he cuing ool consumpion may become oo high, causing moe changes of ools, heefoe educing he global ime o manufacue he pas. So, o calculae he minimum ime o machine he pas (Eq. 1), i is consideed he ime whils he ool is acually emoving maeial, he seup ime of a machine, and he ime o load and unload he pas in he machine. Table 1 shows he noaions of he mahemaical expessions used in he bound modeling. Accoding o Semme (001), Eq. 1 shows he minimum machining ime calculus and Eq. indicaes he calculus of machining coss. Also, he physical limis of he machine and he cuing ool mus be consideed, such as he minimum and maximum cuing speed, maximum machine powe and maximum empeaue suppoed by he cuing ool and he machined pa. The Eq. 3, 4, and 5 ae he cuing paamees bounds (Saavanan e al., 005). Equaion 6 is he ool life calculus, which depends exclusively of he cuing speed (Semme, 001). Equaion 7 is associaed o he calculus of seup imes, ha is consideed he ime o pepae he machine summed o he ime used o change he cuing ools (Semme, 001). The Eq. 8, 9, 15, and 16 ae he bounds of maximum machine powe, maximum cuing empeaue suppoed by he cuing ool and by he pa, dimensional consain, and he maximum oughness allowed in he pa afe he finish machining (Saavanan e al., 005). Equaions 10, 1, 13, and 14 ae he ime o emove maeial of he pa in saigh machining, whee hee is only diamee educion, linea machining, face machining, and cicula machining, as poposed by Su and Chen (1999). Equaion 11 shows he calculus used o se he angles θ used in Eq. 1, 13, and 14 (Su and Chen, 1999). Equaions 17, 18, 19, and 0 ae elaions beween he cuing paamees in ough and finish uning (Sanka e al., 007). The Eq. 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 13, and 14 ae used fo boh ough and finish machining and all equaions will be used diecly fo mahemaical pogamming, a simulaed annealing, and a he geneic algoihm. I is impoan o noice ha his secion pesens he equaions ha ae mos popula in he lieaue concening cuing paamees definiion. T = m + + m T = m + CONSTANT (1) p seup s p seup +

3 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil Table 1. Noaion used in he mahemaical expessions. Nomenclaue T Toal ime of he poducion cycle [min.] T s Seconday ime is he pa s loading/unloading ime which is a consan seup Sum of he imes used o change he cuing ools and he machine s seup ime [min.] p Sum of he ough and finish machining imes [min.], s Time of he ough and finish machining, sum of saigh, linea, face and cicula uning imes [min.] s, ss Time of saigh uning in ough and finish machining [min.] l, ls Time of linea uning beween any wo poins in ough and finish machining [min.] f, fs Time of face uning in ough and finish machining [min.] c, cs Time of cicula uning beween any wo poins in ough and finish machining [min.] m Quaniy of pas o be poduced K Toal coss of he poducion cycle [$] K c Consan coss fo each poduced pa, such as aw maeial [$/Pa] K p Machining ime cos [$] K Tool cos [$/Toll] T v, T vs Tool life in ough and finish machining [min.] C, n Consans of ool life equaion f Changing ool ime [min.] v c, v cs Cuing speed in ough and finish machining [m/min.] v cl, v cu Lowe and uppe bound of cuing speed in ough machining [m/min.] v csl, v csl Lowe and uppe bound of cuing speed in finish machining [m/min.] f,f s Feed ae in ough and finish machining [mm/ev.] f L, f U Lowe and uppe bound of feed ae in ough machining [mm/ev.] f sl, f su Lowe and uppe bound of feed ae in finish machining [mm/ev.] a p,a ps Deph of maeial o be emoved in ough and finish machining [mm] a pl, a pu Lowe and uppe bound of deph of cu in ough machining [mm] a psl, a psu Lowe and uppe bound of deph of cu in finish machining [mm] b,b s Chip widh in ough and finish machining [mm] h, h s Chip hickness in ough and finish machining [mm] K c1.1 Specific cuing pessue ha gives a chip wih bxh = 1x1 [N/mm ] mc Consan of cuing foce equaion P, P s Cuing powe duing ough and finish machining [kw] P U, P su Maximum cuing powe allowed duing ough and finish machining [kw] Q, Q s Tempeaue duing ough and finish machining [ºC] Q U, Q su Maximum empeaue allowed duing ough and finish machining [ºC] K g, T,Φ, δ Consans elaed o machining empeaue d, l Diamee and lengh of saigh uning opeaion [mm] Nose adius of he cuing ool [mm] x 1, x Radius of he iniial and final poins in linea, face o cicula uning [mm] x c Equivalen adius of he posiion of he cene of he cicula uning [mm] Δ Lengh beween he final and iniial poins in linea o cicula uning [mm] a Radius of he cicula uning [mm] θ Angle used in he calculus of linea and cicula uning [ad.] R max Maximum allowable suface oughness [mm] n c Numbe of ough cus [an inege] k 1, k, k 3 Consans fo ough and finish paamees elaions K s = m Kc + m K + + K p T Tv T () vs v cl v v (3) c cu f L f f (4) U

4 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil a pl a a (5) p p U T v 1 n C = v (6) c s = m f + m f SETUP (7) T T seup + v v s P = k f f μ a υ p v c P U (8) Q = K q v τ c f ϕ a υ p Q U (9) s π d l = 1000 v f c (10) 1 x f xi θ fi = an (11) Δ fi l 1 = π x x 1000 v f sinθ (1) c 1 f π = 1000 v c f x x 1 (13) c π a = xc ( θc θc1 ) a ( cosθc cosθc1) (14) 500 v f c c δ 1 = v f a p (15) f s Rmax. 8 (16) a p d a p = s (17) n c a v p cs f k 1 a (18) p s k v (19) f s c k 3 (0) 3. SOLUTION METHODOLOGY To opimize he cuing paamees in a FMS, minimizaion of poducion coss is analyzed, aking ino accoun he consains of pemissible suface oughness, cuing paamees ange, and machine esicions. This pape analyzes

5 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil hee opimizaion echniques o se cuing paamees in uning opeaions, which ae simulaed annealing, geneic algoihm, and mahemaical pogamming. The geneic algoihm appoach used in his pape was poposed by Saavanan e al. (003) and he eade should efe o his pape fo deails concening his appoach Mahemaical Pogamming A banch of eseach in mahemaical pogamming is he so called Global Opimizaion which seeks o solve mixed inege nonlinea poblems (MINLP) o opimaliy. A nonlinea poblems a significan numbe of local opimal soluions can be found. The geaes challenge on such poblems is on how o sepaae a concave suface ino a collecion of seveal convex hulls (whee each convex hull will possess a single opimal soluion). Theefoe global opimizaion appoaches aemp o fom a collecion of convex subpoblems. A way o obain convex subpoblems is by using an Oue Appoximaion appoach (Hos and Tuy,199), which make use of cuing planes o ansfom a nonlinea poblem ino seveal linea subpoblems. Each linea subpoblem (whose soluion is found wihin pseudopolynomial ime) becomes a elaxed convex hull which conains one o moe local opimal soluions of he nonlinea poblem wihin i. These linea subpoblems can be submied o a Banch-and-Bound seach (Hos and Tuy, 199) o o a Disjuncive Pogamming appoach (Tawamalani and Sahinidis, 00) which idenifies he mos pomising subpoblem. The mos pomising subpoblem eceives addiional cuing planes o pune i. The goal of Global Opimizaion is only o idenify a local opimal soluion if i is pomising candidae o become a global opimal soluion. Noice ha if Banch-and-Bound (o Disjuncive Pogamming) is solved unil is end, he global opimal soluion will be idenified due o is combinaion of mixed inege linea pogamming (MILP) and nonlinea pogamming (NLP) seach appoaches. Fo insance, eades ineesed in he subjec can efe o he books by Hos and Tuy (199) and Tawamalani and Sahinidis (00). In ode o solve he poposed poblem using mahemaical pogamming, a sofwae fo mixed inege nonlinea pogamming (MINLP) poblems was used. The chosen sofwae was GAMS/BARON/CPLEX, whee GAMS is a modeling plafom fo mahemaical pogamming poblems, CPLEX is a MILP solve which is conolled by BARON, ha is a MINLP solve developed by Tawamalani and Sahinidis (00). Since hee is a paadigm ha heuisic mehods ae he bes choice o solve MINLP poblems (due o is complexiy), he auhos have decided o es GAMS/BARON/CPLEX a he poposed poblem. In ode o use his sofwae o solve he poposed poblem, equaions pesened in secion have been modeled in GAMS. GAMS was se o use BARON as is solve, demanding no addiion acions o solve he poposed poblem. 3.. Simulaed Annealing Unlike he GA (poposed by Saavanan e al. (003)) and he mahemaical pogamming appoaches (which only equied he modeling wihin GAMS), a simulaed annealing (SA) algoihm is poposed in his wok o be compaed o he wo ohe appoaches. The simulaed annealing is a pobabilisic local seach echnique based in an analogy wih he change of he sae of he maeial when simulaing is cooling afe being heaed o is liquid sae (Aas, 1989). The analogy beween he opimizaion echnique and he change of he sae of he maeial is vey diec, whee he objecive funcion is associaed o he evaluaion on he amoun of inenal enegy. The seveal saes of he maeial ae he possible soluions. The mea-sable saes of he maeial ae he local opima and he cysalline sucue is he possible local opimum (consideing a cysal being cooled). The iniial value of he empeaue which will have no physical meaning a opimizaion poblems and is decemen expession ae impoan facos o he good pefomance of SA. This wok inends o compae diffeen opimizaion appoaches. Theefoe, his pape ess diffeen SA appoaches, which ae compaed o he SA appoach poposed by Saavanan e al. (003; 005). In ode o enable an easie compaison o he appoach poposed by Saavanan e al. (003; 005), all he esed SA appoaches use he same iniial empeaue, equal o 475 (which was poposed by Saavanan e al., 005). Noice ha Saavanan e al. (003; 005) have pesened seveal heuisic appoaches o solve his poblem bu hey do no pesen o compae diffeen paamees fo each heuisic. Due o his, SA appoaches a his pape ae esed fo diffeen cooling facos α which assumed he values 0.9 and 0.99 and wih he use o no of e-heaing. Re-heaing is used o e-sa he SA using he las soluion which is expeced o be close o o a a local opimum as he iniial soluion. Wheneve used, e-heaing is pefomed 10 imes. The SA poposed by Saavanan e al. (005) only used a cooling faco equal o 0.9 and did no use e-heaing. The seps o pefom he simulaed annealing which ae diffeen fom hose of pevious papes ae as follows. The goal is o es he influence of hese paamees o SA. The seps o pefom he simulaed annealing ae as follows. The vaiable s* epesens he bes soluion found duing he execuion of he algoihm. Minimum empeaue was se o 30, as a limi when SA behaves as a Hill-Climbing appoach; ha is, SA sas pefoming a local seach. C i is used o coun he amoun of ieaions wihin local seach ha have been pefomed. C f indicaes he maximum numbe of ieaions wihin local seach. K indicaes he cos of a soluion.

6 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil Sep 1 Sep Sep 3 Sep 4 SET C i = 0, C f, T 0, iniial soluion (s). Randomly geneae a neighbo soluion (s ). IF K(s ) K(s), THEN: s = s IF K(s ) K(s*), THEN: s* = s ENDIF ELSEIF K(s ) > K(s), THEN: Δ = K(s ) - K(s) IF R EXP(Δ /T), THEN: s = s ENDIF ENDIF. SET T = αt IF T < 30, THEN: C i = C i + 1 IF C i > C f, THEN: C i = 0 T = T 0 COUNT RE-HEATING ENDIF ENDIF Sep 5 IF RE-HEATING STOP_CRIT, THEN: GOTO STEP Sep 6 Pesen bes soluion found (s*) 4. RESULTS Thee was an effo o use only daa exaced fom Saavanan e al. (005) in ode o compae hei esuls wih all hee esuls fom ou opimizaion echniques, bu some bounds and consideaions wee no pesened by hem. Then, daa used in his pape wee exaced fom Saavanan e al. (005), Sanka e al. (007), and Semme (001) and ae descibed in Tab. 3. Table 3. Cuing model daa. Paamee/ Paamee / Paamee / Values Values Consain Consain Consain Values v cu 550 m/min. v cl 50 m/min. f U 1.0 mm/ev. f L 0. mm/ev. a pu 3.0 mm a pl 1.0 mm v csu 550 m/min. v csl 50 m/min. f su 1.0 mm/ev. f sl 0. mm/ev. a psu 3.0 mm a psl 1.0 mm C 300 n 0. k f 108 μ 0.75 υ 0.95 P U 00 kw K q 13 Τ 0.4 Φ 0. Q U 1000 C Q su 1000 C δ mm R max µm k k 1.0 k f 3.0 min. m 1.0 K 15 $/Tool K p.0 $/min. Mainenance imes and fixed coss o each poduced pa wee consideed as consans and ignoed fo he calculus of Eq. 1 and, because hey do no influence in he choice of he value of he cuing paamees. The sofwae used o solve non-linea pogamming was GAMS/BARON/CPLEX. All equaions wee included in he mahemaical model (including ough and finish uning bounds) calculaion of poducion ime and he objecive funcion which in his model is o educe coss. A pa/componen exaced fom Saavanan e al. (005) was used o analyze he hee opimizaion echniques and o compae he esuls. The ime o machine his pa was calculaed using Eq. 10, 11, 1, 13, and 14. Figue 1 shows he componen used fo he ess.

7 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil Figue 1. Componen used o es he hee opimizaion echniques (Saavanan e al., 005) Using a Penium IV PC wih.4 GHz and GB of RAM memoy, GAMS/BARON/CPLEX sofwae ook 0.31 seconds o solve he non-linea mahemaical pogamming, while SA was pefomed wihin seconds and GA was solved wihin 87 seconds. The esuls obained using simulaed annealing, geneic algoihms, and mahemaical pogamming ae in Tab. 4. Fisly, i is possible o idenify ha SA was oupefomed by he wo ohe appoaches, boh in he bes soluion found, aveage cos (when mahemaical pogamming seems o have always conveged o he opimal soluion), and compuaional ime. This is an indicaion ha hee ae so-called global opimizaion sofwae (Neumaie, 009) which ae able o deal wih non-linea mahemaical pogamming poblems. The esuls using mahemaical pogamming and GA indicae ha i is no possible o selec he bes appoach. Many woks in he lieaue y o poin o he bes appoach wihou a saisical backgound, as in (Saavanan e al., 003) and in Saavanan e al. (005). Analysis of Vaiance (ANOVA) was used o check he hypohesis ha hee is no significan diffeence among he aveage of all eamens (o appoaches) (Mongomey, 1991). Wih he use of ANOVA and epeaing each eamen 0 imes, i was no possible o efuse his hypohesis. Tha is, due o he vaiance (o sandad deviaion) of he esuls, hee will be a supeposiion of he nomal cuves fo all hese wo appoaches. Table 4. Resuls obained using simulaed annealing, geneic algoihms and mahemaical pogamming. Opimizaion Technique SA (α=0.9 and no e-heaing) SA (α=0.9 and wih e-heaing) SA (α=0.99 and no e-heaing) SA (α=0.99 and wih e-heaing) Minimum Cos K [$] Aveage Cos K [$] v c [m/min.] v cs [m/min.] f [mm/min.] f s [mm/min.] a p [mm] a ps [mm] T [min.] ± ± , ± ± GA ± Mahemaical Pogamming ± CONCLUSION AND DISCUSSIONS This pape is pa of wo ongoing M.Sc. degee woks which sudies he opimizaion of cuing paamees a uning opeaions. Thee diffeen appoaches have been esed mahemaical pogamming, simulaed annealing

8 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil (SA), and geneic algoihms (GA). The goal was o analyze he behavio of SA and GA (oiginally pesened by Saavanan e al. (003; 005)), compaing hei esuls o a mahemaical pogamming appoach. As pa of an ongoing eseach, SA has been esed wih diffeen cooling facos and wih he possibiliy of pefoming e-heaing. Thee was an effo o use only daa exaced fom Saavanan e al. (005) in ode o compae esuls, bu hee was no enough daa o epea hei wok. Theefoe, daa has been colleced fom diffeen souces. The esuls indicae ha SA was oupefomed by mahemaical pogamming and GA. Bu he sandad deviaion on SA and GA indicae ha hee is oom fo impovemens on boh heuisic appoaches. As anohe fuue wok, he fac ha Saavanan e al. (003; 005) used minimizaion of poducion coss as hei objecive funcion suggess ha his wok can be exended o he maximizaion of poducion on flexible manufacuing cells (FMC). In ode o accomplish his, i is necessay o use minimizaion of poducion imes as he objecive funcion. Wih he minimum ime o manufacue each pa in each machine i is possible o opimize he sequence of he lo poducion, looking o educe he ime of idle machines, educing, heeby, he global ime of he poducion cycle. Using he GANTT diagam i is possible o find whee he imes of idle machines ae. Cuing ou compleely he machine idleness is ideal o educe he poducion ime of he lo. Howeve, his is vey difficul o happen in pacice. The idleness in manufacuing can be filled by inceasing he poducion ime of he pas a he idle imes of he machines. Tha is, if i is no possible o eliminae idleness, i is possible o seek poducion cos educion a idle machines. A idle imes of machines, he educion on cuing speed, feed ae, and deph of cu will incease he ime o emove maeial, bu he cuing ool consumpion will also be educed and, consequenly, he manufacuing coss will end o become smalle. Theefoe wheneve hee is machine idleness i will be impoan o seek coss educion. Opimizaion of FMC opeaion is also poposed as a fuue wok. 6. ACKNOWLEDGEMENTS This pape has been paially suppoed by CAPES (Mauício I. Takano). 7. REFERENCES Aas, Emile H.L. and Kos, J., 1989, Simulaed Annealing and Bolzmann Machines : A Sochasic Appoach o Combinaoial Opimizaion and Neual Compuing, Ed. Wiley, Chichese, New Yok, 7 p. Agapiou, J. S., 199, The opimisaion of machining opeaions based on a combined cieion, Pa-1: he use of combined objecives in single pass opeaions, ASME Jounal of Engineeing fo Indusy, Vol. 114, pp Agapiou, J. S., 199, The opimizaion of machining opeaions based on a combined cieion, Pa : muli pass opeaions, ASME Jounal of Engineeing fo Indusy, Vol. 114, pp Doigo, M., Maniezzo, V. and Coloni, A.., 1996, An Sysem: Opimizaion by a Colony of Coopeaing Agens, IEEE Tansacions on Sysems, Man, and Cybeneics - Pa B, Vol.6, pp Glove, F. and Laguna, M., 1997, Tabu Seach, Ed. Kluwe Academic, Nowell, Massachuses, 38 p. Goldbeg, D.E., 1989, Geneic Algoihms in Seach, Opimizaion and Machine Leaning, Ed. Addison-Wesley, Boson, Massachuses, 37 p. Hos, R., Tuy, H., 199, Global Opimizaion: Deeminisic Appoaches, Ed. Spinge-Velag, Heidelbeg, Gemany, 698 p. Lee, B.Y. and Tang, Y.S., 000, Cuing-Paamee Selecion fo Maximizing Poducion Rae o Minimizing Poducion Cos in Mulisage Tuning Opeaions, J. of Maeials Pocessing Technology, Vol.105, pp Mongomey, D. C., 1991, Design and analysis of expeimens. 3d ed., J. Wiley, New Yok, USA, 649p. Neumaie, A., 009, Global Opimizaion Websie, 9 May 009, hp:// Pasad, A.V.S.R.K., Rao, P.N., Rao, U.R.K., 1997, Opimal selecion of pocess paamees fo uning opeaions in a CAPP sysem, Inenaional Jounal of Poducion Reseach, Vol. 35, Sanka, R.S., Asokan, P., Saavanan, R., Kumanan, S. and Pabhahaan, G., 007, Selecion of machining paamees fo consained machining poblem using evoluionay compuaion, In. J. Adv. Manuf. Technol., Vol.3, pp Saavanan, R., Asokan, P. and Vijayakuma, K., 003, Machining Paamees Opimisaion fo Tuning Cylindical Sock ino a Coninuous Finished Pofile Using Geneic Algoihm (GA) and Simulaed Annealing (SA), In. J. Adv. Manuf. Technol., Vol.1, pp Saavanan, R., Sanka, R.S., Asokan, P., Vijayakuma, K. and Pabhahaan, G., 005, Opimizaion of Cuing Condiions Duing Coninuous Finished Pofile Machining Using Non-Tadiional Techniques, In. J. Adv. Manuf. Technol., Vol.6, pp Semme, C.E.,001, Feamenas de Coe I, Ed. UFSC, Vol.1, Floianópolis, Bazil, 49 p. Su, Chao-Ton and Chen, Mu-Chen, 1999, Compue-Aided Opimizaion of Muli-Pass Tuning Opeaions fo Coninuous Foms on Cnc Lahes, IIE Tansacions, Vol.31, pp

9 Poceedings of COBEM 009 Copyigh 009 by ABCM 0h Inenaional Congess of Mechanical Engineeing Novembe 15-0, 009, Gamado, RS, Bazil Tawamalani, M., Sahinidis, N. V., 00, Convexificaion and Global Opimizaion in Coninuous and Mixed-Inege Nonlinea Pogamming: Theoy, Algoihms, Sofwae, and Applicaions, Ed. Spinge, Dodech, The Nehelands, 504 p. Wang, Rong-Tsu and Liu, Shiang-Tai, 007, An Economic Machining Pocess Model Wih Ineval Paamees, In. J. Adv. Manuf. Technol., Vol.33, pp Xiaobo, Z. and Ohno, K., 1999, Modeling fo Flexible Manufacuing Sysems Wih an FMS Blocking Mechanism and a BDSM Job Rouing, IIE Tansacions, Vol.31, pp RESPONSIBILITY NOTICE The auhos ae he only esponsible fo he pined maeial included in his pape.