Jsun Yui Wong
The computer program listed below seeks to solve Tsai’s Example 3 [20, p. 408] plus the restrictions that X(1) and X(2) are integer variables. In other words,
minimize (2 + X(5)) / (X(1) * X(2) * (2 * X(3) + X(4))) – X(5) ^ .5 * X(3) ^ 1.5 + 2 * X(2) + X(4)
subject to
8 / (X(1) * (X(2) + 3 * X(4)) ^ 2) + 1 / (X(5) ^ 3)<=2,
– 2 * X(1) + X(3) – X(4)<=10,
X(1) + X(3) + .5 * X(5)<=8,
0.1<X(1), X(2), X(3), X(4), X(5)<=10,
X(1) and X(2) are integers.
One notes line 193 and line 195, which are 193 X(1) = INT(X(1)) and 195 X(2) = INT(X(2)).
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
70 FOR J44 = 1 TO 5
72 A(J44) = .1 + RND * 9.9
73 NEXT J44
128 FOR I = 1 TO 1000
129 FOR KKQQ = 1 TO 5
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 4))
181 J = 1 + FIX(RND * 5)
183 r = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
193 X(1) = INT(X(1))
195 X(2) = INT(X(2))
196 FOR J99 = 1 TO 5
201 IF X(J99) < .1 THEN 1670
203 IF X(J99) > 10 THEN 1670
204 NEXT J99
305 X(6) = 2 - 8 / (X(1) * (X(2) + 3 * X(4)) ^ 2) - 1 / (X(5) ^ 3)
306 X(7) = 10 + 2 * X(1) - X(3) + X(4)
307 X(8) = 8 - X(1) - X(3) - .5 * X(5)
325 FOR J99 = 6 TO 8
327 XX(J99) = X(J99)
330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
331 NEXT J99
357 POBA = -(2 + X(5)) / (X(1) * X(2) * (2 * X(3) + X(4))) + X(5) ^ .5 * X(3) ^ 1.5 - 2 * X(2) - X(4) + 1000000 * (X(6) + X(7) + X(8))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 8
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < 19.66716 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5)
1902 PRINT A(6), A(7), A(8)
1912 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [24]. The complete output through JJJJ = -31991.8900000013 is shown below:
1 1 5.305667124554657 .337658200135698
3.388665750861434
.0 0 0
19.66716832645138 -31996.3200000006
1 1 5.305604649517398 .3376577173193283.
3.388790700959914
.0 0 0
19.6671691557842 -31993.730000001
1 1 5.303200376710177 .3376391826591685.
3.393599246578964
.0 0 0
19.6671855740736 -31991.8900000013
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 [24], the wall-clock time for obtaining the output through JJJJ= -31991.8900000013 was 45 seconds, including the time for creating the .EXE file.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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