A computer program to solve geometric programming problems: an illustration from Rijckaert and Martens [76, Problem 11]
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below attempts to solve the following nonlinear programming problem from Rijckaert and Martens [76, p. 231, Problem 11]:
Minimize
- X(1) + .4 * X(1) ^ .67 * X(3) ^ -.67
subject to
.05882 * X(3) * X(4) + .1 * X(1) <= 1
4 * X(2) * X(4) ^ -1 + 2 * X(2) ^ -.71 * X(4) ^ -1 + .05582 * X(2) ^ -1.3 * X(3) <= 1.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), G(128), J44(222), 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), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
87 RANDOMIZE JJJJ
88 M = -3D+30
99 FOR J44 = 1 TO 4
108 A(J44) = 0 + RND * 20
114 NEXT J44
128 FOR i = 1 TO 10000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 4)
141 B = 1 + FIX(RND * 4)
142 REM IF RND < .5 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
162 X(B) = A(B) + (RND ^ (RND * 15)) * r
164 GOTO 168
167 REM IF RND < .5 THEN X(B) = A(B) - 1 ELSE X(B) = A(B) + 1
168 NEXT IPP
229 X(1) = (1 - .05882 * X(3) * X(4)) / .1
236 IF 4 * X(2) * X(4) ^ -1 + 2 * X(2) ^ -.71 * X(4) ^ -1 + .05582 * X(2) ^ -1.3 * X(3) > 1 THEN 1670
411 FOR J44 = 1 TO 4
433 IF X(J44) < 0 THEN 1670
434 IF X(J44) > 20 THEN 1670
436 NEXT J44
972 PD1 = X(1) - .4 * X(1) ^ .67 * X(3) ^ -.67
979 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1778 IF M < 5.7222 THEN 1999
1888 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [103]. Its complete output of one run through JJJJ= -31992 is shown below:
8.173226 .6131424 .553552 5.610498 5.744114
-31999
8.103439 .6128766 .5734213 5.622999 5.74464
-31994
8.112604 .6094353 .5708106 5.62142 5.74479
-31993
8.073374 .6098516 .5819437 5.628485 5.743585
-31992
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 [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31992 was 2 seconds, counting from "Starting program...". One can compare the computational results above with those in R and Martens [76, p. 231, Problem 11].
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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