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 10000 unknowns instead of 100 unknowns. Specifically the computer program below tries to minimize the following:
10000 10000
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,..., 10000.
One notes line 85 and line 175, which are 85 LB=-FIX(RND*6) and
175 IF X(J44)<LB THEN X(J44 )=A(J44 ).
For the purpose of testing, none of the 1000 elements of the starting solution vectors is made zero, the optimal; see line 111 through line 117, which are as follows:
111 FOR J44=1 TO 10000
114 A(J44)=1+FIX(RND*5)
117 NEXT J44.
The present edition has more computational results than the earlier edition.
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 10000
114 A(J44)=1+FIX(RND*5)
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 10000
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+.3)
140 B=1+FIX(RND*10000)
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 10000
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 10000
411 SONE=SONE+ (X(J44))^4
421 NEXT J44
501 STWO=0
502 FOR J44=1 TO 10000
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 10000
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)
1936 PRINT A(9996),A(9997),A(9998),A(9999),A(10000)
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=-31998 is shown below:
0 0 0 0 0
0 0 0 0 0
0 -32000 0
-1 -1 0 1 1
0 -1 -1 0 0
-6136 -31999 -1
0 0 0 0 0
0 0 0 0 0
0 -31998 0
Above there is no rounding by hand.
M=0 is optimal; see Li and Sun [10, p. 416].
Of the 10000 A's, only the 10 A's of line 1923 and line 1936 are shown above.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[15] S. Surjanovic, Zakharov Function. www.sfu.ca/~ssurjano/zakharov.html
[16] Jsun Yui Wong (2012, April 23). The Domino Method of General Integer Nonlinear Programming Applied to Problem 2 of Lawler and Bell. http://computationalresultsfromcomputerprograms.wordpress.com/2012/04/23/
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[18] Jsun Yui Wong (2014, June 27). A Unified Computer Program for Schittkowski's Test Problem 377, Second Edition. http://nonlinearintegerprogrammingsolver.blogspot.ca/2014_06_01_archive.html
