The computer program listed below seeks to solve the following problem of eight continuous variables from Floudas et al. [7, pp. 51-52]:
Minimize X(1) + X(2) + X(3)
subject to
X(4) + X(6) - 100 - 300<=0
- X(4) + X(5) + X(7) - 300<=0
X(8) -X(5 -600+ 500<=0
X(1) - X(1) * X(6) + ((1D+05) / 120) * X(4) - ((1D+05) / 120) * 100<=0
X(2) * X(4) - X(2) * X(7) - ((1D+05) / 80) * X(4) + ((1D+05) / 80) * X(5)<=0
X(3) * X(5) - X(3) * X(8) - ((1D+05) / 40) * X(5) + ((1D+05) / 40) * 500<=0
100<= X(1) <= 10000
1000<= X(2) <= 10000
1000<= X(3) <= 10000
10<= X(i) <= 1000, i=4, 5, 6, 7, 8.
X(9) through X(14) below are slack variables.
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
92 A(1) = 100 + FIX(RND * 9901)
93 A(2) = 1000 + FIX(RND * 9001)
94 A(3) = 1000 + FIX(RND * 9001)
95 A(4) = 10 + FIX(RND * 991)
96 A(5) = 10 + FIX(RND * 991)
97 A(6) = 10 + FIX(RND * 991)
98 A(7) = 10 + FIX(RND * 991)
99 A(8) = 10 + FIX(RND * 991)
128 FOR I = 1 TO 20000
129 FOR KKQQ = 1 TO 8
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 j = 1 + FIX(RND * 8)
189 r = (1 - RND * 2) * A(j)
190 X(j) = A(j) + (RND ^ (RND * 10)) * r
222 NEXT IPP
230 IF X(1) < 100 THEN 1670
231 IF X(1) > 10000## THEN 1670
232 IF X(2) < 1000## THEN 1670
233 IF X(2) > 10000## THEN 1670
234 IF X(3) < 1000## THEN 1670
235 IF X(3) > 10000## THEN 1670
236 FOR J44 = 4 TO 8
237 IF X(J44) < 10 THEN GOTO 1670
238 IF X(J44) > 1000 THEN GOTO 1670
244 NEXT J44
246 X(9) = -X(4) - X(6) + 100 + 300
247 X(10) = X(4) - X(5) - X(7) + 300
248 X(11) = -X(8) + X(5) + 600 - 500
251 X(12) = -X(1) + X(1) * X(6) - ((1D+05) / 120) * X(4) + ((1D+05) / 120) * 100
253 X(13) = -X(2) * X(4) + X(2) * X(7) + ((1D+05) / 80) * X(4) - ((1D+05) / 80) * X(5)
255 X(14) = -X(3) * X(5) + X(3) * X(8) + ((1D+05) / 40) * X(5) - ((1D+05) / 40) * 500
260 IF X(1) < 100 THEN 1670
261 IF X(1) > 10000## THEN 1670
262 IF X(2) < 1000## THEN 1670
263 IF X(2) > 10000## THEN 1670
264 IF X(3) < 1000## THEN 1670
265 IF X(3) > 10000## THEN 1670
266 FOR J44 = 4 TO 8
267 IF X(J44) < 10 THEN GOTO 1670
268 IF X(J44) > 1000 THEN GOTO 1670
269 NEXT J44
450 FOR J47 = 9 TO 14
451 IF X(J47) < 0 THEN X(J47) = X(J47) ELSE X(J47) = 0
452 NEXT J47
453 POBA = -X(1) - X(2) - X(3) + 1000000 * (X(13) + X(14) + X(9) + X(10) + X(11) + X(12))
466 P = POBA
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 14
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -7512.27 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), A(13), A(14), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [54]. The complete output through JJJJ = -31990.270000000156 is shown below:
1018.685845387 1000 5493.58146949264
264.4621419608414 280.256741275952 135.5378318428512
284.2054002855197 380.2567412506235
0 0 0 0 0
0 -7512.267314879637 -31999.24000000012
1022.80236632016 1000 5489.437573718315
264.7605209044411 280.4224971073827 135.2394568180514
284.3380143800206 380.4224970818268
0 0 0 0 0
0 -7512.239940038475 -31995.11000000078
1021.27990286284 1000 5490.96997836527
264.6502811873032 280.3612014084006 135.3496207763103
284.2890692001287 380.3612011611714
0 0 0 0 0
0 -7512.249881228108 -31990.93000000145
1024.91756653315 1000 5487.316568929566
264.913320300725 280.5073372429737 135.0866538000017
284.4058796825021 380.5073372429025
0 0 0 0 0
0 -7512.234135462716 -31990.270000000156
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 = -31990.270000000156 was 47 minutes, total, including the time for “Creating .EXE file.” One can compare the computational results above with those on p. 52 of Floudas et al. [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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