Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.5, [12, p. 416], but with 10100 unknowns instead of their 100 unknowns. Specifically, the test example here is as follows:
Minimize
10100 10100
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,..., 10100.
One notes line 81 through line 86, line 111 through line 117, and line 170 through line 173. Lines 111 through 117 give relatively hot starts. In the following computer program there is no line 172 of the preceding post, which is 172 IF X(J44)>UP THEN X(J44 )=A(J44 ).
The following computer program uses the IBM Personal Computer BASIC Compiler--through A:\>bascom and A:\>link--Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft, Inc. 1982.
0 DEFINT J,K,B,X
2 DIM A(10100),X(10100)
81 FOR JJJJ=-32000 TO 32000
85 LB=-FIX(RND*6)
86 UB=FIX(RND*6)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10100
114 REM A(J44)=-5+FIX(RND*11)
115 IF RND<.5 THEN A(J44)=0 ELSE A(J44)=1
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 10100
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*.3)
140 B=1+FIX(RND*10100)
167 IF RND<.5 THEN X(B)=(A(B)-1) ELSE X(B)=(A(B)+1 )
169 NEXT IPP
170 FOR J44=1 TO 10100
171 IF X(J44)<LB THEN X(J44 )=A(J44 )
173 NEXT J44
482 SUMY=0
483 FOR J44=1 TO 10100
485 SUMY=SUMY+X(J44)^4
487 NEXT J44
488 SUMNEWZ=0
489 FOR J44=1 TO 10100
490 SUMNEWZ=SUMNEWZ+ X(J44)
491 NEXT J44
492 PD1=-SUMY-SUMNEWZ^2
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 10100
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1559 GOTO 128
1670 NEXT I
1779 PRINT A(1),A(8000),M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM Personal Computer BASIC Compiler, Version 1.00. See the BASIC manual [13, page iii, Preface]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31990 is shown below:
1 -1 -5628 -32000
-1 1 -4922 -31999
0 0 -4924 -31998
-1 -1 -5640 -31997
0 0 0 -31996
-1 -1 -4974 -31995
0 0 0 -31994
0 0 -5640 -31993
-1 0 -4988 -31992
0 -1 -5592 -31991
0 0 -4962 -31990
Above there is no rounding by hand; it is just straight copying by hand from the screen.
M=0 is optimal. See Li and Sun [12, p. 416].
Of the 10100 A's, only the two A's of line 1779 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 Personal Computer BASIC Compiler, Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft, Inc. 1982, the wall-clock time for obtaining the output through JJJJ=-31990 was 5 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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