Similar to the computer programs of the preceding papers, the computer program below seeks to solve an integer version of Schittkowski's Test Problem 270. The source of this Test Problem 270 is L. W. Cornwell et al. of Argonne National Laboratory Technical Memorandum No. 320; see Schittkowski [14, p. 94]. Thus, the computer program below tries to minimize the following:
X(1)*X(2) *X(3) *X(4)-3* X(1)*X(2)*X(4) - 4*X(1)* X(2)*X(3)+12* X(1)*X(2) -X(2) *X( 3)*X(4)+3*X(2)*X(4) +4*X(2)*X(3)-12*X(2)-2*X(1)*X(3)*X(4)+6*X(1)*X(4)+8*X(1)*X(3)-24*X(1)
+ 2 *X(3) *X(4)-6* X(4) - 8*X(3) +24 + 1.5* X(5)^4 -5.75 *X( 5)^3+5.25*X(5)^2
subject to
34 -X(1)^2-X(2)^2-X(3)^2-X(4)^2-X(5)^2 >= 0
X(i) integer, i=1, 2, 3, 4, 5.
and the bounds are specified in line 171 through line 182.
Line 91 through line 95 are noteworthy.
While line 1 of the preceding paper is 1 DEFINT J,K,B, here line 1 is 1 DEFINT J,K,B,X.
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(90),X(90)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-1.5D+38
91 A(1)=1+RND*300
92 A(2)=2+RND*300
93 A(3)=3+RND*300
94 A(4)=4+RND*300
95 A(5)=-300+RND*600
128 FOR I=1 TO 3000
129 FOR KKQQ=1 TO 5
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*5)
144 REM GOTO 167
145 IF RND<.5 THEN 150 ELSE 167
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
171 FOR J44=1 TO 5
174 IF X(J44)>300 THEN X(J44)=A(J44)
177 NEXT J44
178 FOR J44=1 TO 4
179 IF X(J44)<J44 THEN X(J44)=A(J44)
182 NEXT J44
555 Y(6)= 34 -X(1)^2-X(2)^2-X(3)^2-X(4)^2-X(5)^2
565 IF Y(6)>0 THEN Y(6)=0
681 PDA=- X(1)*X(2) *X(3) *X(4)+3* X(1)*X(2)*X(4) + 4*X(1)* X(2)*X(3) - 12* X(1)*X(2) +X(2) *X( 3)*X(4)-3*X(2)*X(4) -4*X(2)*X(3)+12*X(2)+2*X(1)*X(3)*X(4)-6*X(1)*X(4)-8*X(1)*X(3)+24*X(1)
684 PDB=- 2 *X(3) *X(4)+6* X(4) + 8*X(3) -24 - 1.5* X(5)^4 +5.75 *X( 5)^3-5.25*X(5)^2 +500000!*Y(6)
695 PD1=PDA+PDB
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 5
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<.1 THEN 1999
1923 PRINT A(1),A(2),A(3),A(4),A(5)
1939 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 computer program's complete output through JJJJ=-31982 is shown below:
1 2 3 4 2
1 -31998
1 2 3 4 2
1 -31996
1 2 3 4 2
1 -31989
1 2 3 4 2
1 -31982
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=-31982 was five 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
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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/
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[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
