Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.4, [11, p. 415], but with 10000 unknowns instead of 100 unknowns. Schittkowski's Test Problems 294-299 refer to the Rosenbrock function--see Schittkowski [15] and Li and Sun [11, p. 415]. Specifically, the computer program below tries to solve the following:
Minimize
10000-1
SIGMA [ 100* ( X(i+1)-X(i)^2 )^2 + ( 1-X(i) ) ^2 ]
i=1
subject to
-5<=X(i)<=5, X(i) integer, i=1, 2, 3,..., 10000.
While line 128 of the earlier edition is 128 FOR I=1 TO 32000 STEP .5, here line 128
is 128 FOR I=1 TO 32000.
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
85 UB=1+FIX(RND*5)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10000
114 IF RND<.5 THEN A(J44)=1 ELSE A(J44)=0
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)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1 )
169 NEXT IPP
170 FOR J44=1 TO 10000
171 IF X(J44)>UB THEN X(J44 )=A(J44 )
172 IF X(J44)<-5 THEN X(J44 )=A(J44 )
173 NEXT J44
174 GOTO 200
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
411 REM SONE= - (X(1)-1)^2 - ( X(10000)-1)^2 -10000* SUMNEWZ
511 SONE= - SUMNEWZ
689 PD1=SONE
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 10001
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 SS=S
1558 REM PRINT A(1),A(2),A(3),A(9999),A(10000),M,JJJJ
1559 GOTO 128
1670 NEXT I
1953 PRINT A(1),A(2),A(3),A(9999),A(10000),M,JJJJ
1959 REM PRINT M,JJJJ,A(10001),SS
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=-31999 is shown below:
1 1 1 1 1
-201 -32000
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 [11, p. 415].
Of the 10000 A's, only the 5 A's of line 1953 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 eight hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[19] 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
