Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.5, [10, p. 416], but with 3000 unknowns instead of 100 unknowns. Specifically the computer program below tries to minimize the following:
3000 3000
SIGMA (X(i))^4 + [ SIGMA X(i) ]^2
i=1 i=1
subject to -5<=X(i)=5, X(i) integer, i=1, 2, 3,..., 3000. See line 111 through line 117 and line 171 through line 177.
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(10000),X(10000)
81 FOR JJJJ=-32000 TO 32000
85 LB=-FIX(RND*6)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 3000
114 A(J44)=LB+FIX(RND*6)
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 3000
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+.3)
140 B=1+FIX(RND*3000)
143 GOTO 167
144 REM GOTO 168
145 IF RND<.5 THEN 150 ELSE 167
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
171 FOR J44=1 TO 3000
174 IF X(J44)>5 THEN X(J44 )=A(J44 )
175 IF X(J44)<LB THEN X(J44 )=A(J44 )
177 NEXT J44
401 SONE=0
402 FOR J44=1 TO 3000
411 SONE=SONE+ (X(J44))^4
421 NEXT J44
501 STWO=0
502 FOR J44=1 TO 3000
511 STWO=STWO+ (X(J44))
521 NEXT J44
688 PD1=-SONE-STWO^2
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 3000
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 REM IF M<-2 THEN 1999
1923 PRINT A(1),A(2),A(3),A(4),A(5)
1934 PRINT A(96),A(97),A(98),A(99),A(100)
1935 PRINT A(996),A(997),A(998),A(999),A(1000)
1936 PRINT A(2996),A(2997),A(2998),A(2999),A(3000)
1939 PRINT M,JJJJ,LB
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=-31999 is shown below:
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 -32000 0
-1 -1 0 0 1
-1 1 1 0 0
1 -1 0 -1 -1
0 -1 -1 0 -1
-1746 -31999 -2
Above there is no rounding by hand.
M=0 is optimal; see Li and Sun [10, p. 416].
Of the 3000 A's, only the 20 A's of line 1923 through line 1936 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=-31999 was one hour.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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