Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Ryoo and Sahinidis [43, p. 564, Example 7]:
Minimize - 9 * X(5) - 15 * X(9) + 6 * X(1) + 16 * X(2) + 10 * X(6)
subject to
X(1)+X(2) = X(3) + X(4)
X(3) + X(7)=X(5)
X(4) +X(8)= X(9)
X(7) + X(8)=X(6)
X(10) * X(3) + 2 * X(7)<=2.5*X(5)
X(10) * X(4) + 2 * X(8)<=1.5*X(9)
3 * X(1) + X(2) =X(10)* (X(3) + X(4))
0<= X(1) = 300
0<= X(2) = 300
0<= X(3) = 100
0<= X(4) = 200
0<= X(5) = 100
0<= X(6) = 300
0<= X(7) = 100
0<= X(8) = 200
0<= X(9) = 200
1<= X(10) = 3.
X(11) and X(12) below are slack variables added.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
84 A(1) = 0 + RND * 300
85 A(2) = 0 + RND * 300
86 A(3) = 0 + RND * 100
87 A(4) = 0 + RND * 200
88 A(5) = 0 + RND * 100
89 A(6) = 0 + RND * 300
90 A(7) = 0 + RND * 100
91 A(8) = 0 + RND * 200
92 A(9) = 0 + RND * 200
93 A(10) = 1 + RND * 2
128 FOR I = 1 TO 100000
129 FOR KKQQ = 1 TO 10
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 j = 1 + FIX(RND * 10)
189 r = (1 - RND * 2) * A(j)
190 X(j) = A(j) + (RND ^ (RND * 10)) * r
222 NEXT IPP
226 FOR J44 = 1 TO 9
227 IF X(J44) < 0## THEN 1670
229 NEXT J44
230 IF X(10) < 1## THEN 1670
234 IF X(10) > 3## THEN 1670
235 IF X(1) > 300## THEN 1670
236 IF X(2) > 300## THEN 1670
237 IF X(3) > 100## THEN 1670
238 IF X(4) > 200## THEN 1670
239 IF X(5) > 100## THEN 1670
240 IF X(6) > 3000## THEN 1670
241 IF X(7) > 100## THEN 1670
242 IF X(8) > 200## THEN 1670
243 IF X(9) > 200## THEN 1670
246 X(6) = X(7) + X(8)
247 X(3) = X(5) - X(7)
249 X(4) = X(9) - X(8)
251 X(1) = X(3) + X(4) - X(2)
261 IF ((3 * X(1) + X(2)) / ((X(3) + X(4)))) < 1 THEN 1670
264 IF ((3 * X(1) + X(2)) / ((X(3) + X(4)))) > 3 THEN 1670
266 X(10) = ((3 * X(1) + X(2)) / ((X(3) + X(4))))
447 X(11) = 2.5 * X(5) - X(10) * X(3) - 2 * X(7)
448 X(12) = 1.5 * X(9) - X(10) * X(4) - 2 * X(8)
450 FOR J47 = 11 TO 12
451 IF X(J47) < 0 THEN X(J47) = X(J47) ELSE X(J47) = 0
452 NEXT J47
453 POBA = 9 * X(5) + 15 * X(9) - 6 * X(1) - 16 * X(2) - 10 * X(6) + 1000000 * (X(11) + X(12))
466 P = POBA
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 12
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < 395 THEN 1999
1907 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8)
1908 PRINT A(9), A(10), A(11), A(12), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [54]. The complete output through JJJJ = -31997.93000000033 is shown below:
2.941007286239028D-04 100.0002941070896 6.361036753569613D-09
100.0005882014572 6.361036753569613D-09 99.99941179854277
6.838581110170434D-52 99.99941179854277
200 1.000005881979974 0 0
399.999411754016 -31998.41000000026
4.358111960129918D-04 100.0004358212102 1.001421964597826D-08
100.000871622392 1.001421964597826D-08 99.99912837760802
5.282118877464382D-74 99.99912837760802
200 1.000005881979947 0 0
399.9991283075091 -31997.93000000033
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [54], the wall-clock time (not CPU time) for obtaining the output through
JJJJ = -31997.93000000033
was 77 seconds, not including the time for “Creating .EXE file” (85 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those on p. 564 of Ryoo and Sahinidis [43, p. 564, Example 7].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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Date added to IEEE Xplore: 13 December 2010. Publisher:IEEE.
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