Similar to the computer programs of the preceding papers, the computer program below seeks to solve an integer version of Schittkowski's Test Problem 273 [14, p. 97] but with 15 unknowns instead of 6 unknowns. The source of this Test Problem 273 is S. Walukiewicz; see Schittkowski [14]. Thus, the computer program below tries to minimize the following:
15 15
10* SIGMA (16-i)*(X(i)-1)^2 + 10* [ SIGMA (16-i)*(X(i)-1)^2 ]^2
i=1 i=1
subject to
-1000<= X(i) <=1000, X(i) integer, i=1, 2, 3,..., 15.
The lower bounds and the upper bounds are shown in line 112, which is 112 A(J44)=-1000+ RND*(2000).
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(1000),X(1000)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
110 FOR J44=1 TO 15
112 A(J44)=-1000+ RND*(2000)
114 NEXT J44
128 FOR I=1 TO 3200
129 FOR KKQQ=1 TO 15
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*15)
144 GOTO 167
145 IF RND<.5 THEN 150 ELSE 163
150 R=(1-RND*2)*A(B)
160 X(B)=(A(B) +RND^3*R)
162 GOTO 168
163 IF RND<.5 THEN X(B)=(A(B)-.001) ELSE X(B)=(A(B) +.001 )
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1 )
168 REM IF A(B)=0 THEN X(B)=1 ELSE X(B)=0
169 NEXT IPP
400 SONE=0
401 FOR J44=1 TO 15
403 SONE=SONE+(16-J44)*(X(J44)-1)^2
405 NEXT J44
410 STWO=0
411 FOR J44=1 TO 15
413 STWO=STWO+ ( 16-J44)*(X(J44) -1)^2
415 NEXT J44
666 PD1= -10*SONE -10*STWO^2
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 15
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 REM IF M<-2 THEN 1999
1923 PRINT A(1),A(2),A(3),A(4)
1929 PRINT A(5),A(6),A(7),A(8)
1943 PRINT A(9),A(10),A(11),A(12)
1945 PRINT A(13),A(14),A(15)
1949 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 [11]. Copied by hand from the screen, the complete output through
JJJJ=-31998 is shown below:
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1
0 -32000
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1
0 -31999
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1
0 -31998
Above there is no rounding by hand.
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=-31998 was ten seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[10] Duan Li, Xiaoling Sun, Nonlinear Integer Programming. Publisher: Springer Science+Business Media,LLC (2006). http://www.books.google.ca/books?isbn=0387329951
[11] 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.
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[14] K. Schittkowski, More Test Examples for Nonlinear Programming Codes. Springer-Verlag, 1987.
[15] S. Surjanovic, Zakharov Function. www.sfu.ca/~ssurjano/zakharov.html
[16] 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/
[17] 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/
[18] 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
