Jsun Yui Wong
The computer program listed below seeks to solve the following problem of seven continuous variables from Floudas et al. [7, pp. 38-39]:
Maximize (9 – 6 * X(1) – 16 * X(2) – 15 * X(3)) * X(4) + (15 – 6 * X(1) – 16 * X(2) – 15 * X(3)) * X(5) – X(6) + 5 * X(7)
subject to
X(3) * X(4) + X(3) * X(5)<=50
X(4) +- X(6)<=100
X(5) + X(7)<=200
(3 * X(1) + X(2) + X(3) – 2.5) * X(4) – .5 * X(6)<=0
(3 * X(1) + X(2) + X(3) – 1.5) * X(5) + .5 * X(7)<=0
X(1) + X(2) + X(3)=1
0<= X(1) <= 1
0<= X(2) <= 1
0<= X(3) <= 1
0<= X(4) <= 100
0<= X(5) <= 200
0<= X(6) <= 100
0<= X(7) <= 200.
In the following computer program, D of line 81 stands for discreteness, and X(8) through X(12) 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
81 D(1) = .0001
85 D(2) = .0001
86 D(3) = .0001
87 D(4) = .001
88 D(5) = .001
89 D(6) = .001
90 D(7) = .001
91 A(1) = FIX(RND * 1.01)
93 A(2) = FIX(RND * 1.01)
94 A(3) = FIX(RND * 1.01)
95 A(4) = FIX(RND * 101)
96 A(5) = FIX(RND * 201)
98 A(6) = FIX(RND * 101)
99 A(7) = FIX(RND * 201)
128 FOR I = 1 TO 10000
129 FOR KKQQ = 1 TO 7
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 j = 1 + FIX(RND * 7)
189 REM r = (1 – RND * 2) * A(j)
190 REM X(j) = A(j) + (RND ^ (RND * 10)) * r
195 IF RND < .5 THEN X(j) = A(j) – INT(RND * 10) * D(j) ELSE X(j) = A(j) + INT(RND * 10) * D(j)
222 NEXT IPP
223 REM FOR J44 = 4 TO 7
224 REM X(J44) = INT(X(J44))
225 REM NEXT J44
226 FOR J44 = 1 TO 7
227 IF X(J44) < 0## THEN 1670
229 NEXT J44
235 IF X(1) > 1## THEN 1670
236 IF X(2) > 1## THEN 1670
237 IF X(3) > 1## THEN 1670
238 IF X(4) > 100## THEN 1670
239 IF X(5) > 200## THEN 1670
240 IF X(6) > 100## THEN 1670
241 IF X(7) > 200## THEN 1670
246 X(1) = 1 – X(2) – X(3)
247 X(8) = 100 – X(4) – X(6)
249 X(9) = 200 – X(5) – X(7)
251 X(10) = 50 – X(3) * X(4) – X(3) * X(5)
277 X(11) = -(3 * X(1) + X(2) + X(3) – 2.5) * X(4) + .5 * X(6)
279 X(12) = -(3 * X(1) + X(2) + X(3) – 1.5) * X(5) – .5 * X(7)
326 FOR J44 = 1 TO 7
327 IF X(J44) < 0## THEN 1670
329 NEXT J44
335 IF X(1) > 1## THEN 1670
336 IF X(2) > 1## THEN 1670
337 IF X(3) > 1## THEN 1670
338 IF X(4) > 100## THEN 1670
339 IF X(5) > 200## THEN 1670
340 IF X(6) > 100## THEN 1670
341 IF X(7) > 200## THEN 1670
450 FOR J47 = 8 TO 12
451 IF X(J47) < 0 THEN X(J47) = X(J47) ELSE X(J47) = 0
452 NEXT J47
453 POBA = (9 – 6 * X(1) – 16 * X(2) – 15 * X(3)) * X(4) + (15 – 6 * X(1) – 16 * X(2) – 15 * X(3)) * X(5) – X(6) + 5 * X(7) + 1000000 * (X(8) + 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 12
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < 449.95 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 = -31999.97000000001 is shown below:
1.27675647831893D-15 .4999999999999991 .4999999999999996
1.413799632921098D-15 99.99999999999945 9.999999970941873D-04
100.00000000001 0
-9.407585821463727D-12 0 0 -5.506706202140776D-12
449.9989850857623 -32000
2.109423746787797D-15 .4999999999999997 .5000000000000001
9.99999998975422D-04 99.998999999999983 9.9999999968006617D-04
99.999000000000885 0
0 0 0 -4.931166586175095D-12
449.98799506889 -31999.97000000001
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 = -31999.97000000001 was 4 seconds, not including the time for “Creating .EXE file” (12 seconds, total, including the time for “Creating .EXE file.”) One can compare the computational results above with those on pp. 39-40 of Floudas et al. [7, pp. 39-40].
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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