Direct Finding Multiple Optimal Solutions in One Run of a Generalized Geometric Programming Problem: an Illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following problem from Liu, Wang, and Liu [56, p. 11, Example 4.1]:
Minimize
.5 * X(1) * X(2) ^ -1 - X(1) - 5 * X(2) ^ -1
subject to
.01 * X(2) * X(3) ^ -1 + .01 * X(2) + .0005 * X(1) * X(3) <= 1
70<= X(1) <= 150
1<= X(2) <= 30
.5<= X(3) >= 21.
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)
79 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
107 A(1) = 70 + RND * 80
109 A(2) = 1 + RND * 29
111 A(3) = .5 + (RND * 20.5)
123 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 * 2)
140 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 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 4) ELSE X(B) = A(B) + FIX(RND * 4)
168 NEXT IPP
291 IF X(1) < 70 THEN 1670
292 IF X(1) > 150 THEN 1670
293 IF X(2) < 1 THEN 1670
294 IF X(2) > 30 THEN 1670
301 IF X(3) < .5 THEN 1670
302 IF X(3) > 21 THEN 1670
303 IF .01 * X(2) * X(3) ^ -1 + .01 * X(2) + .0005 * X(1) * X(3) > 1 THEN 1670
461 PD1 = -.5 * X(1) * X(2) ^ -1 + X(1) + 5 * X(2) ^ -1
466 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT I
1889 IF M < -999999999999 THEN 1999
1899 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [101]. Its complete output of one run through JJJJ= -31998 is shown below:
150 29.99997 4.126872 147.6667 -32000
150 30 8.848320 147.6667 -31999
150 29.99997 7.401211 147.6667 -31998
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM, 64-bit Operating System, and QB64v1000-win [101], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31998 was 2 seconds, counting from "Starting program...". One can compare the computational results above with those in Liu, Wang, and Liu [56, p. 11, Example 4.1].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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