1 9 9 9 2
A S tu dy on Optim iz ation u s ing D e s ig n of E x perim ent s an d Gen etic A lg orithm s
. 1 9 9 8 12
List of F igures List of T ables iii iv 1 1. 1 2. 2 2.1 2 2.2 5 2.3 13 2.4 14 15 1. 15 1.1 15 1.2 17 1.3 19 1.4 24 2 37 2.1 37 2.2 FMVSS 208 38 2.3 39 2.4 40 - i -
50 1 50 2 5 1 52 A b s tract 54 56 - ii -
Li s t of F ig ure s F ig, 1 Procedure of design of experim ent s 3 F ig. 2 F low chart of simple g enetic alg orithm s 11 F ig. 3 T he g eneral structure of g enetic alg orithm s 12 F ig. 4 S chem atic diagram for gas a ssist ed inj ection m olding 15 F ig. 5 Ga s assist ed injection m oldin g process 16 F ig. 6 Bum per sy st em 17 F ig. 7 One piece bum per dev elopm ent proces s 18 F ig. 8 Configur ation for pendulum t est 20 F ig. 9 F.E. m odel of reinforcem ent 21 F ig. 10 F in al deform ed shape 22 F ig. 11 F orce- deflection diagram 23 F ig. 12 T he procedure of GAIM an aly sis 25 F ig. 13 F.E. m odel for GAIM analy sis 26 F ig. 14 Sim plified m odel of g as ch ann el 26 F ig. 15 Definition of skin polym er fr action 27 F ig. 16 M ain effect 31 F ig. 17 M elt front adv ancem ent 33 F ig. 18 Skin polym er fraction 34 F ig. 19 Pres sure distribution 35 F ig. 20 Skin polym er fraction v s tim e 36 F ig. 21 Configur ation of sled test 37 F ig. 22 Sled t est u sin g g enetic alg orithm s 41 F ig. 23 Occupant behavior in sled test 47 F ig. 24 Best and av erag e v alues of each g eneration 48 F ig. 25 Comparison of acceleration 49 F ig. 26 Optim al result of g enetic alg orithm s 49 - iii -
Li s t of T ab le s T able 1 T erminology biology and genetic alg orithm s 6 T able 2 M ethod of scalin g 9 T able 3 P endulum t est con dition s 19 T able 4 M at erial properties 20 T able 5 Comparison of m as s an d pendulum intru sion 23 T able 6 F act or and lev el u sed in experim ent s 29 T able 7 Orthogonal array and th e result s 30 T able 8 M ain effect 31 T able 9 AN OVA t able 32 T able 10 Simulation param et er con dition 44 T able 11 Operation of gen etic algorithm s 46 - iv -
1..,,,,,..... (Design of Ex perim ent s ) ( ),,. (Genetic A lg orithm s ).,. (global optim um ). - 1 -
2. 2.1 (D e s ig n of E x perim ent s ) 1),,,. 2) 1932 R. A. F ish er,.,,. 3). (1), ( ) (2), ( ) (3) ( ) - 2 -
4),, F ig. 1.. F ig. 1 Procedure of design of ex perim ent s (1). (2). (3).,.... 2-5 6. - 3 -
(4), (randomization ). (5). (6).,,. (7),. 5) (An aly sis of v arian ce), (sum of squares ),.. - 4 -
2.2 (Gen etic A lg orithm ) 1), (gen eration ) (in dividu al) ( : population ) (fitn ess ), (cros sov er ) (m ut ation ). 2) 1975 (H olland ) A dapt ation in N atural and Artificial Sy st em ". (F og el). 1985 1 (ICGA ). 2. 80,. 3) (population size), (chrom osom e) (g en e). (locu s ), (allele). (phenotype), (g enotype). (epist asis ), (coding ) (decoding ). T able 1. - 5 -
T able 1 T erm in ology of biology an d g enetic alg orithm (chrom osom e) (strin g ) (gen e) (feature), (charact er ) (allele) (feature v alu e) (locu s ) (string position ) (gen otype) (ph enotype) (epistasis ) (stru cture) (param eter set ) (altern ativ e solution ) (decoded stru cture) (n onlinearity ) 4). (1) ( ), ( ). (2) ( ) ( ). (3). - 6 -
5) (1) (genetic operat or ) (selection ), (crossov er ) (m ut ation ),. (selection ) (natural selection ). (fitn ess function ).. a. :,. i pse lect (1). pselect = f i n j = 1 f i (1) b... c. ( ).. - 7 -
(cros sov er ). 2 (bit strin g ).. a. 1 (One - point cros sov er ),. A 1 0 0 1 1 1 1 1 0 0 1 0 0 0 B 0 0 1 1 0 0 0 0 0 1 1 1 1 1 b. (Multi- point crossov er ). A 1 0 0 1 1 1 1 1 0 1 1 0 1 1 B 0 0 1 1 0 0 0 0 0 0 1 1 0 0 (m ut ation ). (design space). (bit ).. (random search ),. 0.005-0.01. - 8 -
(2) (F itn ess function ) (objectiv e function ),.., (scalin g ),,. T able 2 f, f ',.,. T able 2 M ethod of scaling S c alin g M ode l Lin ear scalin g Sigm a truncation P ow er law scalin g F un c tion f ' = a f + b f ' = f - (f - c ) f ' = f k - 9 -
(3) (binary string ).,., x i [ a i, b i ],. ( b i - a i ) 10 5., m i m i. 2 m i - 1 < ( b i - a i ) 10 5 2 m i - 1 (2) x i. x i = a i + decim a l( 1001...001 2 ) ( b i - a i ) (2 m i - 1) (3),. decim a l ( 1001...0 01 2 ) - 10 -
(4) (simple g enetic alg orithm ) F ig. 2. F ig. 3. procedure S GA () initialize (P opulation ); ev aluat e (P opulation ); w hile n ot (t erm in al condition s atisfied) do M atingp ool = reprodu ce (P opulation ); Mut ationpool = crossov er (M atingp ool); P opulation = m utation (MutationPool); ev aluat e (P opulation ); end w hile en d procedure F ig. 2 F low chart of sim ple g en etic algorithm s - 11 -
F ig. 3 T he g eneral structure of g en etic algorithm s - 12 -
2.3.. (Inj ection m oldin g ). (Ga s - A ssist ed Injection M olding )., (sink m ark ), (w arpage ), (shrink age),,,..,.,,,,,,. - 13 -
2.4 F MV S S (F ederal M otor Vehicle S afety Standard) 208. (Sled test ), (, ),., (dum m y ), B - pillar,,. (Gen etic alg orithm ). - 14 -
1. 1.1 (Ga s - A s s i s t e d Inj e ct i on M oldin g ),,. F ig. 4. F ig. 4 S chem atic diagram for Gas A s sisted Injection M oldin g - 15 -
1),. (rib ) (boss ) (residu al stress ), (w arpage), (shrink age), (sink - m ark ). F ig. 5. F ig. 5 Gas assist ed injection m oldin g process - 16 -
1.2 (B um per S y s t e m ) 1) (Conv entional bum per ) (F ascia ), (En ergy Ab sorbing F orm ) (Reinforcem ent Beam ) (F ig. 6a ).,., GMT (Glass F ib er ). 2) (One piece bum per ),, (F ig. 6b ).,..,. (a ) Conv entional bumper sy st em (b ) One piece bum per sy st em F ig. 6 Bumper sy st em - 17 -
3) CAD,. F ig. 7., F MVS S 581,. P ro d u c t D e s i g n Cra s h A n a l y s i s (P A M - C RA S H ) St r u ct u r al st r engt h Cr a sh w or t h in es s GA IM A n a l y s i s ( C- GA S F L OW ) Design of exper im ent M old abilit y P r oces s con dit ion s P ra c t i c a l P ro d u c t D e s i g n M ol d D e s i g n F ig. 7 One piece bum per dev elopm ent process - 18 -
1.3 (Cra s h A n aly s i s ), 2.5 5. (F MV S S 581),. 1) (F MV S S 581) F MV S S 581 /. 1.5m ph, 2.5m ph 2.5m ph (fix ed b arrier ). (1) (lam ps sy stem ), (hood ), (trunk ), (door s ), (fuel and coolin g sy st em ), (ex hau st sy st em ), (propulsion ), (su spen sion ), (steerin g ), (braking ). (2) - Im pact ridge 34 AISI 4130. -. (3) T able 3 P en dulum t est condition s Im pa ct s pe e d T ri al F RT 2.5 mph 2 RR 2.5 mph 2 F RT CORNE R 1.5 mph 1 (20 inch) / 1 (16-20 inch) RR CORNER 1.5 mph 1 (20 inch) / 1 (16-20 inch) - 19 -
2) F MV S S 581 (pendulum t est ). F ig. 8, 1/ 2. F ig. 8 128 108, 2880 2778. F ig. 9 (a ), F ig. 9 (b ) (P olypropylene : PP ). T able 4. F ig. 8 Con figu r a t ion for p en du lu m t e st T a b le 4 M a t e r i a l p r op e r t ie s Y oun g 's M odulu s Y i eld S t ren g t h M a s s D en s it y T hi ck n e s s F ascia / Rib 1,300 17.93 1.5e- 09 ton/ 3.5 Reinforcem ent 200,000 210 7.8e- 09 ton/ 1.6-20 -
(a ) Con v e n t ion a l b u m p e r (s t e e l ) (b ) O n e p ie ce b u m p e r (P P ) F ig. 9 F.E. M odel of reinforcem ent - 2 1 -
3) F MV S S 581. F ig. 10,.,. (a ) Conv ention al bum per (b ) On e- piece bum per F ig. 10 F inal deform ed shape - 22 -
T able 5., 35%. F ig. 11.. T able 5 Com parison of m ass an d pendulum intru sion M a s s P e n d u l u m In t ru s i o n Con v en t ion a l b u m p e r 9.2 17 5.7 On e- p ie ce b u m p er 5.8 16 1.3 R a t io 0.6 3 F ig. 11 F orce- deflection diagram - 23 -
1.4 (Ga s - A s s i s t e d Inj e ct ion M ol din g A n aly s i s ),.,.,. (gas penetration ),,, (delay tim e ), /,.,,. F ig. 12 CAE. - 24 -
F E M o de lin g Runn er - Gate Gas Channel F illin g A n aly si s F l ow B al an c e R un n e r - Gat e B al an c e GA IM A n aly s i s D e s i g n of E x perim ent Process Condition Gas ch ann el L/ O F ig. 12 T he procedure of GAIM An aly sis - 25 -
1) F ig. 13. 2, F ig. 14 (part runn er elem ent ). 3206, 25m m. F ig. 13 F.E. m odel for GAIM analy sis F ig. 14 Sim plified m odel of gas channel - 26 -
2),,, (delay tim e) (packing tim e).... (1) (g as fing erin g ),., (sink m ark ). (2) skin polym er fraction. skin polym er fraction F ig. 15, 1, 0. F ig. 15 Definition of skin polym er fr action - 27 -
skin - polym er fraction 0 1, 1,. (4). = - 10 log [1 n n i = 1 1 y 2 i ] (4), SN (sign al- t o- n oise ratio), n, y i. y i skin - polym er fraction (5). y i = 1 l l 0 + 2 a (5), l, l 0, a Skin - polym er fraction, 1, 2.,. - 28 -
(3) (g as pen etration ),,,, /,. T able 6. (control fact or ),,,, (n oise fact or )., 3. T able 6 F actor and level u sed in experiment s F a ct or le v el 1 l ev el 2 lev el 3 A : Gas Injection P ress. [MPa] B : M elt T em perature [ ] C : Delay T im e [sec] D : Rib T hickn ess [mm] 5 210 0 3 10 230 1 3.5 15 250 1.5 4 E : Gas Ch ann el Dia. [mm] 10.5 12 13.5-29 -
T able 7 (trial). y i Skin polym er fraction (5), SN (4). T able 7 Orthog on al A rray an d the result s A B C D E 1 E 2 E 3 S N 1 2 3 4 5 6 7 8 9 1 1 1 1 1 2 2 2 1 3 3 3 2 1 2 3 2 2 3 1 2 3 1 2 3 1 3 2 3 2 1 3 3 3 2 1 1.245 1.376 1.514 1.457 1.544 1.398 1.414 1.499 1.439 1.450 1.444 1.534 1.556 1.690 1.622 1.734 1.515 1.598 1.744 1.558 1.690 1.908 1.587 1.632 1.893 1.592 1.635 3.159 3.248 3.938 4.129 4.102 3.743 4.310 3.715 3.806-30 -
(4) (V arian ce of An aly sis ) T able 7, T able 8, 9 M ain effect t able ANOVA t able., M ain effect (lev el) (fact or ). A NOVA t able (significance ). T able 8 M ain effect F ac t or L ev e l 1 L ev e l 2 L ev e l 3 A B C D 3.448 3.866 3.539 3.689 3.991 3.688 3.728 3.767 3.944 3.829 4.117 3.927 F ig. 16 M ain effect - 3 1 -
T able 9 ANOVA table F act ors dof S V F - ratio A 2 0.5425 0.2712 10.27* B (2) (0.0527) - - C 2 0.5206 0.2603 9.86* D 2 0.0886 0.0443 1.68 Error 2 0.0527 0.0264 T otal 8 1.2044 * At least 90% confiden ce AN OVA t able B (m elt t em perature) (poolin g ) F -., A (Gas injection pressure) C (Delay tim e ) 90%. A C, SN A 2 B 1 C 3 D 3. B (m elt temperature), (ga s fin gering ) 1. - 32 -
(5) F ig. 17.,.,. F ig. 18, 19 ANOVA t able A 2 B 1 C 3 D 3 E 1, E 2, E 3,. E 3 (dia.=13.5m m ). F ig. 20 Skin polym er fraction. Skin polym er fraction, 0 1, 1, 1. F ig. 17 M elt front adv an cem ent - 33 -
(a ) Ga s channel dia. = 10.5 m m ( E 1 ) (b ) Ga s channel dia. = 12.0 m m ( E 2 ) (a ) Ga s channel dia. = 13.5 m m ( E 3 ) F ig. 18 Skin polym er fraction - 34 -
(a ) Ga s channel dia. = 10.5 m m ( E 1 ) (b ) Ga s channel dia. = 12.0 m m ( E 2 ) (a ) Ga s channel dia. = 13.5 m m ( E 3 ) F ig. 19 Pres sure distribution - 35 -
F ig. 20 Skin polym er fraction v s tim e - 36 -
2. (Oc c upan t B e h av ior A n aly s is u s in g Gen e tic A lg orithm ) 2.1 (S l e d T e s t ) (sled t est )...,. F ig. 21. F ig. 21 Configur ation of sled t est - 37 -
2.2 F M V S S 208 (F ron t al c ra s h of v eh i cle ) 1) (dum m y ) 30m ph,. 2) (1) (HIC ; H ead Injury Criterion ) HIC 36 m sec (6). H IC = [ ( t 2 - t 1 ) t 1 2.5 a dt t 2 ] ( t 2 - t 1 ) < 1000 (6) (2) (CSI ; Ch est S ev erity In dex ) 3 m sec 60G. (3) (Chest compression ) 3 in ch, 2 inch. (4) (F L ; F em ur Load ) 2250 lbf(10000 N ). - 38 -
2.3 (Head Injury Crit erion ; HIC) (Chest S ev erity In dex : CSI), (F em ur Load ). (7), (8) Combin ed Probability (CP ). CP = ( P 1 + P 2 - P 1 P 2) (7) P 1 = 1 / ( 1 + E X P (5.02-0.00351 H IC ) P 2 = 1 / ( 1 + E X P (5.55-0.0693 CSI) (8), HIC (H ead Injury (Chest S ev erity In dex ). Criterion ), CSI - 39 -
2.4.. (v ent hole size) (seat belt elong ation ).,. S GI W ork station IRIX 6.2, PAM - CRA SH. P AM - CRA SH,, PAM - CRA SH. F ig. 22., (random num ber generat or ) (initial population ), (indiv idual), (fitness ). (gen etic operator ),. - 40 -
F ig. 22 Sled test u sing g en etic algorithm s. - 4 1 -
1) (F itness fun ction )., (HIC) (CSI) CP (Com bined Probability ). (v ent h ole size) (seat belt elong ation ), CP.. F (x 1, x 2 ) = CP ( m in im ize prob lem ) (9), x 1, x 2, x 1 0.03 x 1 0.07, x 2 0.6 x 2 2.0. 2) (bin ary string ),.., x 1, x 2 ( b i - a i ) 10 4.. 2 m i - 1 < ( b i - a i ) 10 5 2 m i - 1, m i. - 42 -
x 1 x 2. 2 m 1-1 2 m 2-1 < ( 0.07-0.0 3) 10 4 2 m 1-1 ; m 1 = 9 < (2.0-0.6) 10 4 2 m 2-1 ; m 2 = 14 x 1 x 2 9 14, 1 23., v i 9 x 1, 14 x 2. v i : (111101111 01101101110011) x 1 x 2, x 1,. x 2 x i = a i + decim a l( 1001...001 2 ) ( b i - a i ) ( 2 m i - 1), decim a l( 1001...001 2 )., x i [ a i, b i ]., x 1, x 2 [ 0.03, 0.07 ], [ 0.6, 2.0 ]. x 1 = 0.03 + decim a l( 111101111 2 ) x 2 = 0.6 + decim a l(01101101111001 2 ) 0.07-0.03 2 9-1 2.0-0.6 2 14-1 = 0.0588, = 1.2010-43 -
3) (fitn ess function ), (binary strin g )..,, 1 (population size), (P _cross ), (P_m utat e), (chrom osom e length ), (g eneration ) (fitnes s function ) (T able 10). T able 10 Sim ulation param et er condition P opulation size 8 P_cros s 0.5 P_m utat e 0.01 Chrom osom e length 23 Generation 9 F itn ess function F (x 1, x 2 ) = C P (m in im ize) - 44 -
. (in dividu al) (initial population ). v i ( I=1,,pop_size) ev al( v i ).. F = pop siz e i = 1 ev al ( v i ) v i ( I=1,,pop_size) p i. p i = ev al ( v i ) / F v i ( I=1,,pop_size) q i. q i = i p j j = 1. [ 0, 1] r. r < q 1, ( v 1 ), q i - 1 < r q i i v i ( 2 i pop_size ).,. [ 0, 1] r. r < p c,. [ 1, m - 1] pos (m ). pos.. [ 0, 1] r. r < p m,. - 45 -
T able 11 (CP ), CP. T able 11 Operation of g enetic alg orithm. G B in ary S t rin g V / H B/ E CP 1 11101010110011101111011 11001110001110101010101 00100001011000010011001 01100000110111011001010 01100101000110010011001 11000001100011110000111 11011110011000000100011 10100010001100010100011 0.0667 0.0622 0.0351 0.0451 0.0458 0.0602 0.0647 0.0553 1.4636 1.2416 1.6631 1.6235 0.8755 0.7646 1.6530 1.1389 0.1983 0.1136 0.2329 0.1603 0.1465 0.1164 0.1652 0.1212 2 01100101000110010011001 01100000110111001010101 01100101000110010011001 10100010000111011001011 11000001100011110000111 01001110000110101110101 10100010001000000100011 11000110001110101010101 0.0458 0.0451 0.0458 0.0553 0.0602 0.0422 0.0553 0.0610 0.8755 1.6135 0.8755 0.9236 0.7646 0.8943 0.9530 1.2416 0.1465 0.1590 0.1465 0.0992 0.1164 0.1645 0.1021 0.1032 9 10100010001000000101011 10100010001000001001011 10100010001000000101011 10100010101100000101011 10100010101100000110011 10101010001000000101110 10000010101100001101110 10100010001000000101011 0.0553 0.0553 0.0553 0.0554 0.0554 0.0566 0.0504 0.0553 0.9537 0.9564 0.9537 1.1287 1.1293 0.9539 1.1344 0.9537 0.0982 0.1145 0.0982 0.1174 0.1174 0.1136 0.1335 0.0982-46 -
F ig. 23. (a ) at 0 m sec (b ) at 120 m sec F ig. 23 Occupant beh avior in sled t est - 47 -
F ig. 24. 1 11.37%, 15.68%. 2 1.. 4 CP 9.823%. F ig. 24 Best and av erag e v alu es of each generation - 48 -
4) F ig. 25. (a ) (HIC), (b ) (CSI).. F ig. 26.. (a ) H ead acceleration (b ) Chest acceleration F ig. 25 Com parison of acceleration (a ) H ead acceleration (b ) Chest acceleration F ig. 26 Optim al result of g enetic alg orithm - 49 -
1.. 1.,. 2..,. 3.,. 4.. - 50 -
2.,. 1.. 2. 5.24%, 55.3mm, (CP ) 9.823% 11.4 % 1.2%. 3. 4,. 4. S GI W ork st ation 1 40, 9 2. 5.. - 5 1 -
[1] K.K. H o, C.S. Chen an d Y.C. Chen, "Application of C- GA SF LOW S oftw are An aly sis on the 15- inch Ga s - assist ed Injection M olding M onit or Cabin et ", CMUG, No. 13, 1995. [2] S.C. Chen, K.S. H su, N.T. Ch eng. an d W.R. Jong, "Characteristics of Ga s P en etration in Gas - A ssist ed Injection M olding ", CMUG, No.15, 1995. [3] S.C. Chen, J.G. Dong, an d W.R. Jong, "Effect of g as channel design on m oldin g w indow an d part m ech anical properties of Gas - A s sist ed Injection M olding ", pp.663-667. ANT E K, 1996. [4] H. H ay ashi, Y. F ujioka, M. Im ai, an d Y. Kan, "Dev elopm ent of Gas Injection M olding for Aut om otiv e bum per s", JSAE, 1994. [5] S.H. Paik, "Gas A s sisted Injection M olding Bumper - Perform ance and Proces sing ", CMUG, N o. 16. 1995. [6] P.M. Glance and G. Daroczy, "Com puter - Aided Design, Analy sis, & T estin g of Aut om otiv e Bumper ", SAE, 1988. [7] T.H. Han, J.H. Lim, an d J.H. Hw ang, "A Stu dy of Optimization of Coolin g F in U sin g Design of Ex perim ent s", KSME, pp.791-796, 1997. [8], " ",, pp. 631-657, 1995. [9],,,,, 1998 [10] J. Krottm aier, "Optim izing En gineerin g Design s", M cgraw - HILL, pp.87-114, 1993. [11] T.C. Kim, H.Y. Kim, J.J. Kim, "A Study on the Design of Ga s - A ssist ed Injection M olded Bum per U sing Design of Ex perim ent s", T he Korea - Japan P lastics Processin g Joint S em in ar, pp.25-31, 1998. [12] "CM OLD u ser ' s m anual", V95 [13] David E. Goldberg, "Genetic A lg orithm s in S earch, Optim ization & M achine Learnin g ", A ddison - W esley [14] Zbigniew Mich alew icz, "Gen etic Algorithm s + Dat a Stru ctures = Ev olution Program s", Sprin ger - V erlag [15] "Practical H an dbook of GENET IC ALGORIT HM S ", Lan ce - 52 -
Ch am ber s [16] M it su o GEN, Run w ei CHENG, "Genetic A lg orithm s and Engin eerin g Design ", W iley Int er scien ce [17] P eter J. An gelin e, Kenneth E. Kinn ear, Jr. "A dv an ces in Gen etic P rogram m ing " [18] J. Krottm aier, " Optimizin g En gineering Design s", M cgraw - HILL [19],,,, 1996 [20],,,, 1997 [21],,, 1996. [22],,, 1996. - 53 -
A St udy on Opt i mi zat i on Usi ng Desi gn of Exper i ment s and Genet i c Al gor i t hms Ki m, Tae Che o l D ep a r tm ent of M e chan ica l E ng ine e r ing Gra d ua t e S cho ol, K ang w on N a t iona l Un iv e rs ity Summar y T his study is con cerned w ith optim al design u sin g design of experim ents and genetic algorithm s. Recently developm ents of a com puter are able t o solv e complex engin eerin g problem s an d optim ized alg orithm s are b een dev elopin g an d applyin g for m any en gineering problem s t o obtain optim al solution s. One of these optim ized algorithm s is design of experim ent s and gen etic algorithm s. Design of ex perim ent s is applied t o obt ain optim al process con dition s in th e ga s as sisted inj ection m oldin g of on e piece bum per. T he process con dition s of gas assisted injection m oldin g are m ore difficult t o setup than the cas e of injection m oldin g becau se inert ga s is inj ect ed int o the m olt en polym er. It is v ery difficult t o predict the g as behavior an d the proces s param et er s are coupled w ith each other. T his study predict s the g as beh avior and present s th e optim al process condition s u sing design of experim ent s. Genetic algorithm s is applied to minimize occupant injury by optimizing the design parameter s for occupant restraint sy stem in sled test. T he design parameter s to optimize using genetic algorithm s are selected vent - 54 -
hole size of airbag and elongation of seat belt. T he criterion to judge Occupant injury are expressed as the combined probability (CP ) of head injury criteria (HIC) and chest sev erity in dex (CSI). T herefore, the goals of sled test are to obtain the minimum combined probability value and to determine the optimal values of design parameter s. T his study present s the optimal values of design parameter s to minimize combined probability u sing genetic algorithm s. K ey W ords : Design of Experiment s, Genetic Algorithm s, Optimization, Gas Assisted Injection Molding, Sled T est - 55 -
, 2.,,.,.,,,,,.,,,,,,,,,....,,.,.,,,,,.,,,. 1998 12-56 -