Jsun Yui Wong
Similar to the computer programs of the preceding papers, the computer program below seeks to solve a nonlinear integer programming problem with 10100 unknowns. 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, p. 106]. 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
-1 <= X(i) >= 1, X(i) integer, i=1, 2, 3,..., 10100.
One notes line 111 through line 117 and line 171 through line 177.
The following computer program uses Microsoft's GW-BASIC 3.11 interpreter for DOS.
0 DEFINT J,K,B,X
2 DIM A(10103),X(10103)
81 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 10100
116 A(J44)=-1+FIX(RND*3)
117 NEXT J44
128 FOR I=1 TO 32000
129 FOR KKQQ=1 TO 10100
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
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)<-1 THEN X(J9)=A(J9)
175 IF X(J9)>1 THEN X(J9)=A(J9)
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 SONE= - (X(1)-1)^2 - ( X(10100)-1)^2 -10100* SZ
689 PD1=SONE -5000000!*ABS(TS)
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 10100
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1559 GOTO 128
1670 NEXT I
1777 PRINT A(10100),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=-31995 is shown below:
1 -1E+07 -32000
1 -1E+07 -31999
1 -1E+07 -31998
1 -7.847851E+07 -31997
1 -2.799528E+08 -31996
1 0 -31995
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 A of line 1777, A(10100), is 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=-31995 was 38 hours.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[9] Jack Lashover (November 12, 2012). Monte Carlo Marching. www.academia.edu/5481312/MONTE_ CARLO_MARCHING
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[12] Duan Li, Xiaoling Sun, Nonlinear Integer Programming. Springer Science+Business Media,LLC (2006). http://www.books.google.ca/books?isbn=0387329951
[13] Microsoft Corp., BASIC, Second Edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C,Boca Raton, Floridda 33432, 1981.
[14] Harvey M. Salkin, Integer Programming. Menlo Park, California: Addison-Wesley Publishing Company (1975).
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[16] K. Schittkowski, More Test Examples for Nonlinear Programming Codes. Springer-Verlag, 1987.
[17] S. Surjanovic, Zakharov Function. www.sfu.ca/~ssurjano/zakharov.html
[18] Jsun Yui Wong (2012, April 23). The Domino Method of General Integer Nonlinear Programming Applied to Problem 2 of Lawler and Bell. http://computationalresultsfromcomputerprograms.wordpress.com/2012/04/23/
[19] Jsun Yui Wong (2013, September 4). A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Literature Problem with Twenty Binary Variables and Three Constraints, Third Edition. http://myblogsubstance.typepad.com/substance/2013/09/
[20] 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
