A very general computer program to solve geometric programming problems: another illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve the nonlinear programming formulation in Tsai and Lin [88, Example 2].
Minimize
X(1) ^ .5 * X(2) + 3 * LN(X(1))
subject to
-X(1) + X(2) <= 5
X(1) ^ .5 – X(2) <= 6
X(1) epsilon { .1, .5, .7, 1.2 }
-6 <= X(2) < = 4.
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
88 RANDOMIZE JJJJ
89 M = -3D+30
120 IF RND < 1 / 4 THEN A(1) = .1 ELSE IF RND < 1 / 3 THEN A(1) = .5 ELSE IF RND < 1 / 2 THEN A(1) = .7 ELSE A(1) = 1.2
123 A(2) = -6 + RND * 10
128 FOR i = 1 TO 3000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 2)
141 B = 1 + FIX(RND * 2)
155 IF B = 1 THEN 166 ELSE GOTO 160
160 r = (1 - RND * 2) * A(2)
164 X(B) = A(B) + (RND ^ (RND * 10)) * r
165 GOTO 270
166 IF RND < 1 / 4 THEN X(B) = .1 ELSE IF RND < 1 / 3 THEN X(B) = .5 ELSE IF RND < 1 / 2 THEN X(B) = .7 ELSE X(B) = 1.2
270 NEXT IPP
293 IF -X(1) + X(2) > 5 THEN 1670
297 IF X(1) ^ .5 - X(2) > 6 THEN 1670
324 IF X(1) < .1 THEN 1670
325 IF X(1) > 1.2 THEN 1670
343 IF X(2) < -6 THEN 1670
345 IF X(2) > 4 THEN 1670
449 PD1 = -X(1) ^ .5 * X(2) - 3 * LOG(X(1))
469 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1459 NEXT KLX
1670 NEXT i
1777 IF M < -99999999999 THEN 1999
1888 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= -31990 is shown below:
.1 -5.683772 8.705122 -32000
.1 -5.683772 8.705122 -31999
.1 -5.683772 8.705122 -31998
.1 -5.683772 8.705122 -31997
.1 -5.683772 8.705122 -31996
.1 -5.683772 8.705122 -31995
.1 -5.683772 8.705122 -31994
.1 -5.683772 8.705122 -31993
.1 -5.683772 8.705122 -31992
.1 -5.683772 8.705122 -31991
.1 1.712771E-07 6.907755 -31990
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 = -31990 was 2 seconds, counting from “Starting program…”. One can compare the computational results above with those in Tsai and Lin [88, Example 2, Table 1].
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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