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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