Similar to the computer programs of the preceding papers, the computer program below seeks to solve 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
X(1)+X(2)+X(3)+X(4)+X(5) = 0
X(9996 )+X(9997 )+X(9998)+X(9999 )+X(10000) = 0
3*X(5001 )^3+7*X(5002)+2*X(5003)^2+5*X(5004 )+8*X( 5005 ) >= 20
-5<=X(i)<=5, 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
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
175 X(1)= 5 -X(2)-X(3)-X(4)-X(5)
177 X(10000)= 5 -X(9996 )-X(9997 )-X(9998)-X(9999 )
179 S= -20 +3*X(5001 )^3+7*X(5002)+2*X(5003)^2+5*X(5004 )+8*X( 5005 )
180 IF S<0 THEN S=S ELSE S=0
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 +50000!*S
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
1559 GOTO 128
1670 NEXT I
1943 PRINT A(1),A(2),A(3),A(4),A(5)
1945 PRINT A(6),A(7),A(8),A(9),A(10)
1953 PRINT A(11),A(12),A(13),A(14),A(15)
1957 PRINT A(5556),A(5557),A(5558),A(5559),A(5666)
1958 PRINT A(9881),A(9882),A(9883),A(9884),A(9885)
1959 PRINT A(9991),A(9992),A(9993),A(9994),A(9995)
1963 PRINT A(9996),A(9997),A(9998),A(9999),A(10000)
1969 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
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
-201 -32000
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
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 35 A's of line 1943 through line 1963 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 12 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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