Jsun Yui Wong
The computer program listed below seeks to solve Li and Lu's Example 3 [27, p. 710], which is shown immediately below:
Minimize X(1) ^ (-2) * X(2) ^ .5 * X(3) ^ 1.2 - X(1) ^ (-2) * X(2) ^ .5 - X(2) ^ (.5) * X(3) ^ 1.2 - X(1) ^ (-2) * X(3) ^ 1.2
subject to
X(1) ^ (-2) * X(2) ^ .5 + X(2) ^ (.5) * X(3) ^ 1.2 + X(1) ^ (-2) * X(3) ^ 1.2>=31
X(1) ^ (-2) * X(2) ^ .5 + X(2) ^ (.5) * X(3) ^ 1.2 + X(1) ^ (-2) * X(3) ^ 1.2<=62
1<=X(i)<=32, i=1, 2, 3
X(1) through X(3) are positive integer variables.
See Li and Lu [27, p. 710] for a better description of the present problem.
X(4) and X(5) below are slack variables added.
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 31999.900 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
40 FOR J40 = 1 TO 3
41 A(J40) = 1 + FIX(RND * 32)
42 NEXT J40
128 FOR I = 1 TO 3000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 2))
181 j = 1 + FIX(RND * 3)
201 r = (1 - RND * 2) * A(j)
205 X(j) = A(j) + (RND ^ (RND * 10)) * r
222 NEXT IPP
255 FOR J41 = 1 TO 3
258 X(J41) = INT(X(J41))
262 NEXT J41
265 FOR J41 = 1 TO 3
268 IF X(J41) < 1## THEN 1670
269 IF X(J41) > 32## THEN 1670
272 NEXT J41
308 X(4) = -31 + X(1) ^ (-2) * X(2) ^ .5 + X(2) ^ (.5) * X(3) ^ 1.2 + X(1) ^ (-2) * X(3) ^ 1.2
310 X(5) = 62 - X(1) ^ (-2) * X(2) ^ .5 - X(2) ^ (.5) * X(3) ^ 1.2 - X(1) ^ (-2) * X(3) ^ 1.2
401 FOR J47 = 4 TO 5
402 IF X(J47) < 0 THEN X(J47) = X(J47) ELSE X(J47) = 0
403 NEXT J47
443 POBA = -X(1) ^ (-2) * X(2) ^ .5 * X(3) ^ 1.2 + X(1) ^ (-2) * X(2) ^ .5 + X(2) ^ (.5) * X(3) ^ 1.2 + X(1) ^ (-2) * X(3) ^ 1.2 + 1000000 * (X(4) + X(5))
466 P = POBA
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 5
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < 61.78 THEN 1999
1907 PRINT A(1), A(2), A(3), A(4), A(5), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [50]. The complete output through JJJJ = -31999.91000000001 is shown below:
32 26 8 0 0
61.78578762313648 -31999.96000000001
32 26 8 0 0
61.78578762313648 -31999.93000000001
32 26 8 0 0
61.78578762313648 -31999.91000000001
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [50], the wall-clock time (not CPU time) for obtaining the output through
JJJJ = -31999.91000000001 was 3 seconds, not including the time for “Creating .EXE file” (10 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those in Table 3 of Li and Lu [27, p. 711, Experiment 4].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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