Similar to the computer programs of the preceding papers, the computer program below seeks to solve an integer version of Schittkowski's Test Problem 281 [14, p. 105] but with 9000 unknowns instead 10 unknowns. The source of this Test Problem 281 is S. Walukiewicz; see Schittkowski [14]. Thus, the computer program below tries to minimize the following:
9000
[ SIGMA i^3*(X(i)-1)^2 ]^(1/3)
i=1
subject to
-5<= X(i) <=5, X(i) integer, i=1, 2, 3,..., 9000.
One notes line 214 and line 217, which are 214 IF X(J44)<-5 THEN 1670 and 217 IF X(J44)>5 THEN 1670, respectively,
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(9000),X(9000)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
110 FOR J44=1 TO 9000
112 A(J44)=-5+ RND*(10)
114 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 9000
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*9000)
144 GOTO 167
145 IF RND<.5 THEN 150 ELSE 163
150 R=(1-RND*2)*A(B)
160 X(B)=(A(B) +RND^3*R)
162 GOTO 168
163 IF RND<.5 THEN X(B)=(A(B)-.001) ELSE X(B)=(A(B) +.001 )
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1 )
168 REM IF A(B)=0 THEN X(B)=1 ELSE X(B)=0
169 NEXT IPP
211 FOR J44=1 TO 9000
214 IF X(J44)<-5 THEN 1670
217 IF X(J44)>5 THEN 1670
219 NEXT J44
400 SONE=0
401 FOR J44=1 TO 9000
403 SONE=SONE+J44^3*(X(J44)-1)^2
405 NEXT J44
666 PD1= -SONE^(1/3)
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 9000
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 REM IF M<-.5 THEN 1999
1923 PRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10)
1924 PRINT A(11),A(12),A(13),A(14),A(15),A(16),A(17),A(18),A(19),A(20)
1925 PRINT A(4991),A(4992),A(4993),A(4994),A(4995),A(4996),A(4997),A(4998),A(4999),A(5000)
1927 PRINT A(5991),A(5992),A(5993),A(5994),A(5995),A(5996),A(5997),A(5998),A(5999),A(6000)
1928 PRINT A(7991),A(7992),A(7993),A(7994),A(7995),A(7996),A(7997),A(7998),A(7999),A(8000)
1929 PRINT A(8991),A(8992),A(8993),A(8994),A(8995),A(8996),A(8997),A(8998),A(8999),A(9000)
1939 PRINT M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. See the BASIC manual [11]. Copied by hand from the screen, the computer program's complete output through JJJJ=-32000 is shown below:
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
0 -32000
M=0 is optimal; see Schittkowski [14, p.105].
Above there is no rounding by hand.
Of the 9000 A's, only the 60 A's of line 1923, line 1924, line 1925, line 1927, line 1928, and line 1929 are shown above.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output through JJJJ=-32000 was eight hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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