Jsun Yui Wong
The computer program listed below seeks to solve Problem 32 on page 430 of Himmelblau (1972) plus the restriction that X(4)= -10000, -9999, -9998,..., 0, 1, 2, 3,..., 9998, 9999, 10000. On page 171 Schittkowski (1987) cites the original Himmelblau problem. (The present paper's X(4) is Himmelblau's X(3).)
0 DEFDBL A-Z
3 DEFINT I,J,K
4 DIM X(42),A(42),L(33),K(33)
5 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
93 A(1)=-200+RND*400
94 A(2)=-200+RND*400
95 A(3)=-200+RND*400
96 A(4)=-10000+FIX(RND*20001)
126 IMAR=10+FIX(RND*1000)
128 FOR I=1 TO IMAR
129 FOR K=1 TO 4
131 X(K)=A(K)
132 NEXT K
811 IF RND<.99 THEN 903 ELSE 991
903 IF RND<1/3 THEN 911 ELSE IF RND<.6666 THEN 921 ELSE 931
911 IF RND<.5 THEN X(1)=-200+RND*400 ELSE X(1)=A(1)+(1-2*RND)*.001*A(1)
915 GOTO 1151
921 IF RND>.5 THEN X(2)=-200+RND*400 ELSE X(2)=A(2)+(1-2*RND)*.001*A(2)
925 GOTO 1151
931 IF RND>.5 THEN X(3)=-200+RND*400 ELSE X(3)=A(3)+(1-2*RND)*.001*A(3)
935 GOTO 1151
991 X(4)=-10000+FIX(RND*20001)
1151 PN1=( ( ( (X(1)^2+X(2)^2*0+X(4)^2*0^2)/(1+X(3)^2*0) )-7.391 ) /7.391 )^2
1412 PN2=( ( ((X(1)^2+X(2)^2*.000428+X(4)^2*.000428^2)/(1+X(3)^2*.000428) )-11.18 ) /11.18 )^2
1413 PN3=((((X(1)^2+X(2)^2*.001+X(4)^2*.001^2)/(1+X(3)^2*.001))-16.44)/16.44)^2
1414 PN4=( ( ((X(1)^2+X(2)^2*.00161+X(4)^2*.00161^2)/(1+X(3)^2*.00161) )-16.2 ) /16.2 )^2
1415 PN5=( ( ((X(1)^2+X(2)^2*.00209+X(4)^2*.00209^2)/(1+X(3)^2*.00209) )-22.2 ) /22.2 )^2
1416 PN6=( ( ( (X(1)^2+X(2)^2*.00348+X(4)^2*.00348^2)/(1+X(3)^2*.00348) )-24.02 ) /24.02 )^2
1417 PN7=( (( (X(1)^2+X(2)^2*.00525+X(4)^2*.00525^2)/(1+X(3)^2*.00525) )-31.32 ) /31.32 )^2
1488 P=-10000*(PN1+PN2+PN3+PN4+PN5+PN6+PN7)
1551 IF P<=M THEN 1670
1657 FOR KEW=1 TO 4
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1663 MM=PR
1666 GOTO 128
1670 NEXT I
1890 IF M>-318.58 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3)
1915 PRINT A(4),M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM basica/D interpreter, and the output produced in the first 135 minutes of running is presented below. (What immediately follows is a manual copy from the computer screen.)
2.714237050418973 140.4151258896569 31.49233633228084
-1705 -318.5732852674301 -31298
2.714280115627704 -140.2320246506003 31.42037915619026
1700 -318.5740851107986 -30759
-2.714207738385269 -140.6681589846467 -31.5975277066794
-1713 -318.5729772121449 -30490
2.714219334477566 140.659169951501 31.59590264214858
-1713 -318.5727862195563 -30038
-2.714275982647368 -140.6449146479193 31.5928202101209
-1713 -318.5725422579476 -29577
Interpreted in accordance with line 1912 and line 1915, the output through JJJJ=-29577 was produced in the first 135 minutes of running on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter.
References
D. M. Himmelblau (1972): "Applied Nonlinear Programming," McGraw-Hill, New York.
K. Schittkowski (1987): "More Test Problems for Nonlinear Programming Codes," Springer-Verlag, Berlin, Heidelberg, New York.
