M athem aticalm odel and A lgo rithm of In telligen t T est Paper

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1 : (2004) ,,,, (, ) :,,,, : ; ; ; ; : T P319 : A M athem aticalm odel and A lgo rithm of In telligen t T est Paper A u to2generation System from Item Poo l W AN G You2ren, ZHAN G Zhai, CU I J iang, YAO R u i, CHU J ian2bo (Co llege of A utom ation and Engineering, N anjing U niversity of A eronautics and A stronautics, N anjing , Ch ina) Abstract: W ith the help of exam ination theo ry and education m athem atics, test paper are analyzed in detailṡ the requirem ents of the T he m athem aticalmodel of intelligent test paper generation system is set up. T he m ethod of test paper au to2generation based on imm une genetic algo rithm ( IGA ) is p ropo sed. Segm en ted coding, cro ssover and m u tation in segm en t, evaluation function of genetic are developed. In stance analysis to in telligen t system of test paper generation from test item poo l abou t analog electronic techno logy is p resenṫ T he experim ental results show that the IGA algo rithm can so lve the test paper au to2generation p rob lem in test item poo l effectively, and has better perfo rm ances of qu ick convergence to genetic algo rithm. Key words: education expert system; intelligent system of auto2generating test paper; characteristics of test paper; m athem atical m odel; imm une genetic algo rithm 1 (Com puter A ssistan t In struction- CA I),,, ( ),,,,,,,,, CA I [ 1-4 ],,,,, : : ( ), ( ),,,, Em ail: w angyrac@nuaa. edu. cn

2 ,, 2. 1, [ 1, 2 ] D = 1 P g 6 M ϖ Y d ig p i = 1 - P, (1), P, d i i, p i i, M, ϖ Y d i, d i, F = 1 P g 6 M F ig p i = a g + b. (2), F i i, a b ( ), F i, F i,,,,,,,,,,, : 2. 2, A a 1, 1 a1, 2 a 1, C A = a 2, 1 a2, 2 a 2, C g (3) an, 1 an, 2 an, C, N, C (, C = 9 ) A, :, A, A ( K 1, K 2,, K N ) K i i ( i ), K i = 1 i, K i = 0 i, C : K ig a i, 1 = P, P a i, 1 i ; K ig bi, s = P s, s P s a i, 2 = s bi, s = a i, 1, ;

3 9 87 K ig g i,m = W m, W m m a i, 3 m g i,m = a i, 1, g i,m 7 ( A B C D E F G) ; K ig a i, 1g a i, 4 = P gd, a i, 4 i, D K ig a i, 5 = T, T, a i, 5 i K ig u i, n = Z n, n Z n a i, 6 n u i, n = a i, 1, ; :, a i, 7 i, ; K ig a i, 1g a i, 8 = F, a i, 8 i ; : a i, 9 < ( ), a i, 9,, ( ) [ 5-8 ],, ( ),, ;,,, : ( ) ; ; ; ; ;?, 3. 2, : 1) N, 7 ( N 1 N 7 ) N, ( J 1 J 2 J N ), J k = 1, k, J k = 0 M, J k = M k= 1,, N, (J 1, 1, J N 1, 1),, (J 1, 7,, J N 7, 7) M 1,, M 7, 6 7 N k M k = M, : 6 J i, k = M k, ( k = 1,, 7 ), 2) E = 6 9 k= 1 Αk g ek, (4), ek = 0 1 k, 0 Φ Αk Φ 1 k= 1

4 ,,,,,, (1% - 5% ), k, ek = 0,, = ( ) 3) F it = (E + ) - 1, (5),,,,, : F it = ; F it > 95, ; ( 1000), F it < 95, 4) :,,, ( ) :,,,, 5) : ( ),,,,,,, : G = (0. 85g F itm ax F itm ax ), F itm ax k h k h k = (1 - Αh g G k) g F itk, (6) 6 F iti i, Αh = 0 1 ( ), F itk k : ; ; ; ; ; ;?, 4, 4. 1, : ( ), 100, , , 11-

5 ; ; A B C D E, (A ) (B ) (C ) (D ) (E 0. 2 ), ; 120 ;, 4. 2 ( ), 1 16 ( 1 ) , : : 100, p c = 0. 2, p m = , Αh = 0. 3 (SGA ), , 2 3,, G k, h k Αh, = % % 5 2 E D C B A ,, : [1 ],,. [J ]. ( ). 1999, 20 (2): W AN G L i2na, X IAO J ing, DON G X iao2m ei, et al. Study on general in telligen t item bank [ J ]. Jou rnal of N o rtheastern U n iversity (N atu ral Science), 1999, 20 (2): [ 2 ],,. [J ]. ( ), 1999, 45 (5): QU AN H u i2yun, FAN Guo2chuang, ZHAO T ing2lei. In tellignet system of test paper au to2generating from test bank based on genetic algo rithm s[j ]. J. W uhan U n iv. (N aṫ Sci. Ed. ), 1999, 45 (5): ( 97 )

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