Similar to the computer programs of the preceding papers, the computer program below seeks to solve an integer nonlinear program based on Li and Sun's Problem 14.4, [12, p. 415], but with 10000 unknowns instead of 100 unknowns. Like Schittkowski's Test Problems 294-299, their problem refers to the Rosenbrock function--see Schittkowski [16] and Li and Sun [12, p. 415]. Specifically, the test example here is as follows:
Minimize
10000-1
SIGMA [ 100* ( X(i+1)-X(i)^2 )^2 + ( 1-X(i) ) ^2 ]
i=1
subject to
-3<=X(i)<=3, X(i) integer, i=1, 2, 3,..., 10000.
The following computer program uses Microsoft's GW-BASIC 3.11 interpreter.
0 DEFINT J,K,B,X
2 DIM A(10001),X(10001)
81 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10000
114 A(J44)=-3+FIX(RND*7)
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+RND*.3)
140 B=1+FIX(RND*10000)
167 IF RND<.5 THEN X(B)=A(B)-1 ELSE X(B)=A(B) +1
168 REM IF A(B)=0 THEN X(B)=1 ELSE X(B)=0
169 NEXT IPP
170 FOR J44=1 TO 10000
171 IF X(J44)<-3 THEN X(J44 )=A(J44 )
172 IF X(J44)>3 THEN X(J44 )=A(J44 )
173 NEXT J44
200 SUMNEWZ=0
203 FOR J44=1 TO 9999
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 10000
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)
1777 PRINT A(6),A(7),A(8),A(9),A(10)
1778 PRINT A(9991),A(9992),A(9993),A(9994),A(9995)
1779 PRINT A(9996),A(9997),A(9998),A(9999),A(10000)
1953 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 [13]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31999 is shown below:
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
0 -32000
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
0 -31999
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 10000 A's, only the 20 A's of line 1771 through 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 basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output through JJJJ=-31999 was 17 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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