A Computer Program for Generalized Geometric Programming

A Computer Program for Generalized Geometric Programming

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following nonlinear programming problem based on Murray, Chandrasekaran, and Wierman [62, p. 281], which is based on Yan [106, p. 89]:

Minimize
-1 * ( -X(1) ^ .6 * X(2) - X(2) * X(3) ^ -.5 - 15.98 * X(1) - 9.0824 * X(2) ^ 2 + 60.72625 * X(3) )
subject to
X(2) ^ -2 * X(3) - X(1) * X(2) ^ -2 - .48 >= 0
X(1) ^ .5 * X(3) ^ 2 - X(1) ^ .25 * X(3) - X(2) ^ 2 - 5.75 >= 0
X(1) ^ 2 + 4 * X(2) ^ 2 + 2 * X(3) ^ 2 - 58 = 0
X(1) * X(2) ^ -1 * X(3) ^ 2.5 + X(2) * X(3) - X(2) ^ 2 - 16.55 = 0
.1 <= X(i) <= 1000, i=1, 2, 3.


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
92 FOR J44 = 1 TO 3
93 A(J44) = .1 + RND * 9.9
94 NEXT J44

128 FOR i = 1 TO 50000
129 FOR KKQQ = 1 TO 3

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

139 FOR IPP = 1 TO FIX(1 + RND * 4)
141 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 REM IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)

168 NEXT IPP

239 IF (-4 * X(2) ^ 2 - 2 * X(3) ^ 2 + 58) < 0 THEN 1670

244 X(1) = (-4 * X(2) ^ 2 - 2 * X(3) ^ 2 + 58) ^ .5

284 LHS = X(2) * X(3) - X(2) ^ 2 - 16.55 + X(1) * X(2) ^ -1 * X(3) ^ 2.5

288 IF X(2) ^ -2 * X(3) - X(1) * X(2) ^ -2 - .48 < 0 THEN 1670

298 IF X(1) ^ .5 * X(3) ^ 2 - X(1) ^ .25 * X(3) - X(2) ^ 2 - 5.75 < 0 THEN 1670

320 FOR J44 = 1 TO 3

322 IF X(J44) > 1000 THEN 1670

325 IF X(J44) < .1 THEN 1670

328 NEXT J44

464 PD1 = -X(1) ^ .6 * X(2) - X(2) * X(3) ^ -.5 - 15.98 * X(1) - 9.0824 * X(2) ^ 2 + 60.72625 * X(3) - 50000 * ABS(LHS)
466 P = PD1

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 3

1455 A(KLX) = X(KLX)
1457 LHSS = LHS

1459 NEXT KLX

1670 NEXT i

1777 IF M < 320.30 THEN 1999

1888 PRINT A(1), A(2), A(3), M, JJJJ, LHSS

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -16918 is shown below:

.1000675 .4624108 5.344843 320.4609 -27929
-5.081365E-06

.1004968       .4646226       5.344455       320.6226       -16918
-8.304387E-07

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -16918 was 20 minutes, counting from "Starting program...". One can compare the computational results above with those in Murray, Chandrasekaran, and Wierman [62, p. 281].
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.

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