Similar to the computer programs of the preceding papers, the computer program below seeks to solve a problem based on Li and Sun's Problem 14.4, [12, p. 415], but with 10100 unknowns instead of their 100 unknowns and with lower bounds of -9s instead of their -5s and upper bounds of 9s instead of their 5s, [12, p. 415]. The function is based on the Rosenbrock function--see Schittkowski [16] and Li and Sun [12, p. 415]. Specifically, the test example here is as follows:
Minimize
10100-1
SIGMA [ 100* ( X(i+1) - X(i)^2 )^2 + ( 1-X(i) )^2 ]
i=1
subject to
-9<=X(i)<=9, X(i) integer, i=1, 2, 3,..., 10100.
One notes line 111 through line 117 and line 170 through line 173.
The following computer program uses Microsoft's GW-BASIC 3.11 interpreter for DOS.
0 DEFINT J,K,B,X
2 DIM A(10100),X(10100)
81 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10100
114 A(J44)=-9+FIX(RND*19)
117 NEXT J44
128 FOR I=1 TO 32000 STEP .5
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)<-9 THEN X(J44 )=A(J44 )
172 IF X(J44)>9 THEN X(J44 )=A(J44 )
173 NEXT J44
200 SUMNEWZ=0
203 FOR J44=1 TO 10099
205 SUMNEWZ=SUMNEWZ+ 100* ( X(J44+1)-X(J44)^2 )^2 + ( 1-X(J44 ) ) ^2
207 NEXT J44
511 SONE= - SUMNEWZ
689 PD1=SONE
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
1771 PRINT A(1),A(2),A(3),A(4),A(5)
1899 PRINT A(9996),A(9997),A(9998),A(10099),A(10100),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 [13]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31991 is shown below:
-1 1 1 1 1
1 1 1 1 1
-4 -32000
1 1 1 1 1
1 1 1 2 4
-101 -31999
-1 1 1 1 1
1 1 1 1 1
-4 -31998
-1 1 1 1 1
1 1 1 3 9
-209 -31997
1 1 1 1 1
1 1 1 2 4
-101 -31996
1 1 1 1 1
1 1 1 2 4
-101 -31995
-1 1 1 1 1
1 1 1 1 1
-4 -31994
1 1 1 1 1
1 1 1 2 4
-306 -31993
-1 1 1 1 1
1 1 1 1 1
-4 -31992
1 1 1 1 1
1 1 1 1 1
0 -31991
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. 415].
Of the 10100 A's, only the 10 A's of line 1771 and line 1899 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=-31991 was 115 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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