Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.3 but with 1000 unknowns of search intervals of -10 to 10 instead of 100 unknowns of search intervals of -5 to 5, [10, p. 414]. Specifically the computer program below tries to minimize the following:
1000-1
(X(1)-1)^2 + (X(1000) -1 )^2 + 1000* SIGMA (1000-i) * ( X(i)^2 - X(i+1)) ^2
i=1
subject to -10<=X(i)<=10, X(i) integer, i=1, 2, 3,..., 1000.
One notes line 114, line 174, and line 175, which are as follows:
114 A(J44 )=-10+FIX( RND*21)
174 IF X(J44)>10 THEN X(J44 )=A(J44 )
175 IF X(J44)<-10 THEN X(J44 )=A(J44 ).
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(10000),X(10000)
81 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 1000
114 A(J44 )=-10+FIX( RND*21)
115 REM IF RND<.5 THEN A(J44 )=2 +FIX(RND*4 ) ELSE A(J44)=-5+FIX(RND*6)
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 1000
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+.3)
140 B=1+FIX(RND*1000)
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 1000
174 IF X(J44)>10 THEN X(J44 )=A(J44 )
175 IF X(J44)<-10 THEN X(J44 )=A(J44 )
177 NEXT J44
401 SONE=0
402 FOR J44=1 TO 999
411 SONE=SONE+ (1000-J44) * ( X(J44)^2 - X(J44+1)) ^2
421 NEXT J44
551 SUMX=(X(1)-1)^2 + (X(1000) -1 )^2+1000*SONE
689 REM PD1=-SONE
699 PD1=-SUMX
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 1000
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 REM IF M<-100 THEN 1999
1936 PRINT A(1),A(2),A(998),A(999),A(1000)
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=-31994 is shown below:
0 0 0 0 0
-2 -32000
0 0 0 0 0
-2 -31999
0 0 1 2 4
-5010 -31998
1 1 -1 3 9
-15064 -31997
0 0 1 2 4
-5010 -31996
-1 1 1 2 4
-2013 -31995
1 1 1 1 1
0 -31994
Above there is no rounding by hand.
M=0 is optimal; see Li and Sun [10, p. 414].
Of the 1000 A's, only the 5 A's of 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=-31994 was nineteen hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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