Computer program to solve very generalized geometric programming problems: an illustration from the literature
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following problem in Lin and Tsai [52, p. 24, SGP 6]:
Minimize
- X(1) +.4 * X(1) ^ .67 * X(3) ^ -.67
subject to
.05882 * X(3) * X(4) + .1*X()<=1
(4 * X(2) * X(4) ^ -1 + 2 * X(2) ^ -.71 * X(4) ^ -1) + (.05882 * X(2) ^ -1.3 * X(3)) <=1
.1<= X(1), X(2), X(3), X(4) <=10.
0 DEFDBL A-Z
1 REM DEFINT I, J
2 DIM B(99), N(99), A(200), H(99), L(99), U(99), X(200), 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 STEP .01
89 RANDOMIZE JJJJ
90 M = -3D+30
97 FOR J44 = 1 TO 4
101 A(J44) = INT(100 * (.1 + RND * 9.9 + .000001)) / 100
102 NEXT J44
124 FOR I = 1 TO 25000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO FIX(1 + RND * 3)
140 B = 1 + FIX(RND * 4)
144 IF RND < .5 THEN 160 ELSE GOTO 166
160 R = (1 - RND * 2) * A(B)
164 X(B) = A(B) + FIX((RND ^ (RND * 15)) * R)
165 GOTO 168
166 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) * .01 ELSE X(B) = A(B) + FIX(RND * 2) * .01
168 NEXT IPP
208 FOR J44 = 1 TO 4
210 IF X(J44) < .1 THEN 1670
211 IF X(J44) > 10 THEN 1670
212 NEXT J44
350 X(1) = (-.05882 * X(3) * X(4) + 1) / .1
369 IF (4 * X(2) * X(4) ^ -1 + 2 * X(2) ^ -.71 * X(4) ^ -1) + (.05882 * X(2) ^ -1.3 * X(3)) > 1 + 0 THEN 1670
408 FOR J44 = 1 TO 4
410 IF X(J44) < .1 THEN 1670
411 IF X(J44) > 10 THEN 1670
412 NEXT J44
465 PD1 = X(1) - .4 * X(1) ^ .67 * X(3) ^ -.67
466 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
1886 IF M < 5.738 THEN 1999
1899 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31997.44000000041 is shown below:
8.142229119999987 .5900000000000005 .5599999999999994
5.64O000000000046 5.738021124855221 -31998.34000000027
8.142229119999985 .5900000000000001 .5599999999999998
5.64O000000000045 5.73802112485522 -31998.1600000003
8.142229119999996 .59 .5599999999999994
5.64O000000000018 5.738021124855227 -31997.44000000041
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 = -31997.44000000041 was 10 seconds, counting from "Starting program...". One can compare the computational results above with those in Lin and Tsai [52, p. 22, Table 3, SGP 6].
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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