Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.3, [11, p. 414], but with 10000 unknowns instead of 100 unknowns and with two added equality constraints and one inequality constraint. The original version of this problem is due to S. Walukiewicz--see Schittkowski's Test Problem 282 [15, p. 106]. Specifically, the computer program below tries to minimize the following:
10000-1
(X(1)-1)^2+ ( X(10000)-1)^2 +10000* SIGMA (10000-i)* ( X(i)^2-X(i+1) )^2
i=1
subject to
X(1) +X(2)+X(3 )+X(4 )+X(5) = 5
X(1)^3+X(2)^3+X(3)^3+...+X(10000)^3 = 10000
X(1)+X(2)+X(3)+...+X(10000) <= 10000
-5<=X(i)<=5, X(i) integer, i=1, 2, 3,..., 10000.
One notes that line 128 is 128 FOR I=1 TO 32000 STEP .5. One also notes line 171 through line 177, which are as follows:
171 FOR J44=1 TO 10000
174 IF X(J44)>UB THEN X(J44 )=A(J44 )
175 IF X(J44)<-5 THEN X(J44 )=A(J44 )
177 NEXT J44.
0 REM
1 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 STEP .5
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
171 FOR J44=1 TO 10000
174 IF X(J44)>UB THEN X(J44 )=A(J44 )
175 IF X(J44)<-5 THEN X(J44 )=A(J44 )
177 NEXT J44
179 X(1)=5-X(2)-X(3 )-X(4 )-X(5)
180 SUMY=0
183 FOR J44=1 TO 10000
185 SUMY=SUMY+X(J44)^3
187 NEXT J44
188 U=10000-SUMY
194 SUMNEW=0
195 FOR J44=1 TO 10000
196 SUMNEW=SUMNEW+X(J44)
197 NEXT J44
198 X(10001)=10000- SUMNEW
199 IF X(10001)<0 THEN X(10001)=X(10001) ELSE X(10001)=0
200 SUMNEWZ=0
203 FOR J44=1 TO 9999
205 SUMNEWZ=SUMNEWZ+ (10000-J44)* ( X(J44)^2-X(J44+1) )^2
207 NEXT J44
411 SONE= - (X(1)-1)^2 - ( X(10000)-1)^2 -10000* SUMNEWZ
689 PD1=SONE +50000!*X(10001) -50000!*ABS(U)
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 10001
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1555 UU=U
1557 UUB=UB
1559 GOTO 128
1670 NEXT I
1931 PRINT A(1),A(2),A(3),A(4),A(5)
1932 PRINT A(56),A(57),A(58),A(59),A(60)
1935 PRINT A(4996),A(4997),A(4998),A(4999),A(5000)
1936 PRINT A(5996),A(5997),A(5998),A(5999),A(6000)
1938 PRINT A(7996),A(7997),A(7998),A(7999),A(8000)
1945 PRINT A(9996),A(9997),A(9998),A(9999),A(10000)
1947 PRINT A(10001)
1959 PRINT M,JJJJ,UU,UUB
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=-32000 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
0
0 -32000 0 1
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. 414].
Of the 10000 A's, only the 30 A's of line 1931 through line 1945 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=-32000 was 6 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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