Direct Solution of Generalized Geometric Programming Problems: Another Illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below seeks to solve the following problem from Maranas and Floudas [57, p. 24, which is very informative]:
Minimize
-1* (.097515 * X(2) * (1 + .035272 * X(1)) + .096540 * X(1) * (1 + .097515 * X(2))) / ((1 + .096540 * X(1)) * (1 + .035272 * X(1)) * (1 + .097515 * X(2)) * (1 + .039191 * X(2)))
subject to
X(1) ^ .5 + X(2) ^ .5 <= 4
10^(-6) <= X(1), X(2) <= 16.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
111 FOR J44 = 1 TO 2
112 A(J44) = 10 ^ -6 + RND * 16##
113 NEXT J44
128 FOR I = 1 TO 500000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 1.3)
140 B = 1 + FIX(RND * 2)
144 IF RND < .5 THEN 160 ELSE GOTO 167
160 R = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * R
165 GOTO 168
167 IF RND < .5 THEN X(B) = A(B) - 1 ELSE X(B) = A(B) + 1
168 NEXT IPP
171 FOR J44 = 1 TO 2
173 IF X(J44) < 10 ^ -6## THEN 1670
175 IF X(J44) > 16## THEN 1670
176 NEXT J44
223 IF X(1) ^ .5 + X(2) ^ .5 > 4## THEN 1670
344 PD1 = (.097515 * X(2) * (1 + .035272 * X(1)) + .096540 * X(1) * (1 + .097515 * X(2))) / ((1 + .096540 * X(1)) * (1 + .035272 * X(1)) * (1 + .097515 * X(2)) * (1 + .039191 * X(2)))
466 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT I
1777 IF M < .387 THEN 1999
1904 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31960 is shown below:
15.99196 1.005774E-06 .3880247 -31998
15.992 1.000369E-06 .3880248 -31995
15.992 1.000832E-06 .3880248 -31991
15.99193 1.016792E-06 .3880247 -31975
15.992 1.001036E-06 .3880248 -31960
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM (3.89 GB usable), 64-bit Operating System, and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31960 was 16 seconds, counting from “Starting program…”. One can compare the computational results above with those in Maranas and Floudas [57, pp. 24-25].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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