Jsun Yui Wong
The computer program listed below seeks to solve the illustrative example in Wu [27]:
Minimize X(1) * X(2) ^ .5 * X(3) ^ 1.2+ 2 * X(1)
subject to
2 * X(1) + X(2) + X(3)>=8,
X(2) + 2 * X(3)>=10.5,
X(1) + 2 * X(3)<=10,
1<= X(1), X(2), X(3)<=5.
X(4), X(5), and X(6) below are slack variables.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
22 FOR J55 = 1 TO 3
67 A(J55) = 1 + FIX(RND * 405) * .01
71 NEXT J55
128 FOR I = 1 TO 30000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 J = 1 + FIX(RND * 3)
183 REM r = (1 - RND * 2) * A(J)
187 REM X(J) = A(J) + (RND ^ (RND * 10)) * r
189 X(J) = 1 + FIX(RND * 405) * .01
191 NEXT IPP
200 FOR J44 = 1 TO 3
201 IF X(J44) < 1 THEN 1670
203 IF X(J44) > 5 THEN 1670
255 NEXT J44
301 X(4) = -8 + 2 * X(1) + X(2) + X(3)
305 X(5) = -10.5 + X(2) + 2 * X(3)
308 X(6) = 10 - X(1) - 2 * X(3)
333 FOR J44 = 4 TO 6
335 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
339 NEXT J44
359 POBA = -X(1) * X(2) ^ .5 * X(3) ^ 1.2 - 2 * X(1) + 1000000 * (X(4) + X(5) + X(6))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 6
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 REM GOTO 128
1670 NEXT I
1889 IF M < -9.5 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [25]. The complete output through JJJJ = -31999.90000000002 is shown below:
1 1.52 4.49 0 0
0 -9.475106820436846 -31999.99
1 1.5 4.5 0 0
0 -9.445616203848971 -31999.94000000001
1 1.5 4.5 0 0
0 -9.445616203848971 -31999.91000000001
1 1.5 4.5 0 0
0 -9.445616203848971 -31999.90000000002
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. One can compare the computational results above to the results in Wu [27].
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [25], the wall-clock time for obtaining the output through JJJJ= -31999.90000000002 was 15 seconds; most of these seconds were for creating the .EXE file.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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