Computer Program for Solving 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 formulation on page 444 (16/27) of Lu [55, p. 444 (16/27), Example 1; this is an open-access article]:

Minimize

X(1) + 2 * X(2) + X(3)

subject to

X(1) ^ .3 * X(2) ^ -4 * X(3) ^ .8 - .5 * X(1) + .8 * X(2) - .6 * X(3) <= 0

X(1) - X(2) + X(3) <= 2

X(1) + X(2) - X(3) = 0

.1 <= X(i) <= 10, i=1, 2, 3.

0 REM DEFDBL A-Z

1 REM DEFINT I, J, K

2 DIM B(99), N(99), A(20), H(99), L(99), U(99), X(20), 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)

79 FOR JJJJ = -32000 TO 32000

89 RANDOMIZE JJJJ

90 M = -3D+30

107 A(1) = RND * 5

109 A(2) = RND * 5

111 A(3) = RND * 5

123 FOR I = 1 TO 30000

129 FOR KKQQ = 1 TO 3

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 2)

140 B = 1 + FIX(RND * 3)

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) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)

168 NEXT IPP

191 X(3) = X(1) + X(2)

201 IF X(1) < .1 THEN 1670

202 IF X(1) > 10 THEN 1670

204 IF X(2) < .1 THEN 1670

205 IF X(2) > 10 THEN 1670

206 IF X(3) < .1 THEN 1670

207 IF X(3) > 10 THEN 1670

211 IF X(1) - X(2) + X(3) > 2 THEN 1670

218 IF X(1) ^ .3 * X(2) ^ -4 * X(3) ^ .8 - .5 * X(1) + .8 * X(2) - .6 * X(3) > 0 THEN 1670

444 PD1 = -X(1) - 2 * X(2) - X(3)

466 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 3

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1670 NEXT I

1889 IF M < -5.393922 THEN 1999

1899 PRINT A(1), A(2), A(3), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [101]. Its complete output of one run through JJJJ= -31727 is shown below:

.6808984 1.344041 2.02494 -5.39392 -31966

.683557 1.342265 2.025822 -5.393909 -31964

.6842895 1.34178 2.026069 -5.393918 -31912

.6809723 1.343992 2.024964 -5.393919 -31903

.6814798 1.343651 2.025131 -5.393912 -31894

.6844754 1.341657 2.026132 -5.393921 -31892

.6843782 1.341721 2.026099 -5.393919 -31855

.681281 1.343784 2.025065 -5.393914 -31819**.6825421 1.342941 2.025483 -5.393906 -31727**

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 [101], the wall-clock time (**not CPU time**) for obtaining the output through JJJJ = -31727 was 8 seconds, counting from "Starting program...". One can compare the computational results above with those in Lu [55: p. 444 (16/27), p. 445 (17/27), and Table 1].

**Acknowledgement**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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