The computer program listed below seeks to solve a nonlinear integer programming problem with 10100 general integer variables. The present problem is based on Li and Sun's Problem 14.3, [12, pp. 414-415], which is based on Walukiewicz/Schittkowski [16, Test Problem 282, page 106 and page 23]. Specifically, the test example here is as follows:
Minimize
10100-1
(X(1)-1)^2 + ( X(10100)-1)^2 +10100* SIGMA (10100-i)* ( X(i)^2-X(i+1) )^2
i=1
subject to
X(1)+X(2)+X(3)+...+X(10100) = 10100
-3 <= X(i) <= 3, X(i) integer, i=1, 2, 3,..., 10100.
One notes line 85 through line 86 and line 171 through line 177, which are as follows:
85 LB=- FIX(RND*4)
86 UB= FIX(RND*4)
171 FOR J9=1 TO 10100
173 IF X(J9)<LB THEN X(J9)=LB
175 IF X(J9)>UB THEN X(J9)=UB
177 NEXT J9
The following computer program uses the IBM Personal Computer BASIC Compiler--through A:\>bascom and A:\>link--Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft.
0 DEFINT J,K,B,X,A
2 DIM A(10103),X(10103)
81 FOR JJJJ=-32000 TO 32000
85 LB=- FIX(RND*4)
86 UB= FIX(RND*4)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10100
116 A(J44)=FIX(RND*2)
118 NEXT J44
128 FOR I=1 TO 32000
129 FOR KQ=1 TO 10100
130 X(KQ)=A(KQ)
131 NEXT KQ
139 FOR IPP=1 TO FIX(1+RND*.3)
140 B=1+FIX(RND*10103)
167 IF RND<.5 THEN X(B)=(A(B)-1) ELSE X(B)=(A(B) +1 )
169 NEXT IPP
171 FOR J9=1 TO 10100
173 IF X(J9)<LB THEN X(J9)=LB
175 IF X(J9)>UB THEN X(J9)=UB
177 NEXT J9
181 SJ=0
182 FOR J9=1 TO 10100
183 SJ=SJ+ X(J9)
184 NEXT J9
187 TS= 10100-SJ
200 SZ=0
203 FOR J9=1 TO 10099
205 SZ=SZ+ (10100-J9)* ( X(J9)^2-X(J9+1) )^2
207 NEXT J9
411 SO= - (X(1)-1)^2 - ( X(10100)-1)^2 -10100* SZ
689 PD1=SO -50000!*ABS(TS)
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KX=1 TO 10100
1455 A(KX)=X(KX)
1456 NEXT KX
1559 GOTO 128
1670 NEXT I
1771 PRINT A(1),A(2),A(3),A(4),A(5)
1773 PRINT A(10086),A(10087),A(10088),A(10089),A(10090)
1774 PRINT A(10096),A(10097),A(10098),A(10099),A(10100)
1777 PRINT M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM Personal Computer BASIC Compiler, Version 1.00. See the BASIC manual [12, page iii, Preface]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31997 is shown below:
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
-5.05E+08 -32000
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
-8.47991E+07 -31999
1 1 1 1 1
1 1 1 1 1
1 1 1 2 3
-4.55106E+07 -31998
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
0 -31997
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 15 A's of line 1771 through line 1774 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 Personal Computer BASIC Compiler, Copyright IBM Corp 1982 Version 1.00/Copyright Microsoft, Inc. 1982, the wall-clock time for obtaining the output through
JJJJ=-31997 was five hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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