Jsun Yui Wong
The computer program listed below seeks to solve Example 4 in Chang [4, p. 383]:
Minimize
( ABS(X(5) ^ 1.8) * X(1) * X(3) ^ .3 * X(4) ^ 1.5 + X(2) * X(3) ^ 1.8 * X(4) ^ 1.3 * X(5) + X(1) * X(2) * X(3) ^ 1.7 ) / ( X(1) * X(3) * X(4) + X(2) * X(3) ^ 2.3 * X(4) ^ 1.4 )
subject to
2 * X(1) + X(1) * X(3) ^ 1.6>=5,
X(1) + X(2)>=1,
X(2) + X(4)<=6,
X(1) + X(2) + X(5)>=3,
1 <=X(3)<= 7 ,
1 <= X(4) <= 6,
1 <= X(5) <= 5 ,
X(1) and X(2) are binary variables,
X(3) and X(4) are continuous variables,
X(5) is absolute continuous variable.
X(6) through X(9) below are slack variables.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(199), N(199), A(199), H(199), L(199), U(199), X(1111), D(111), P(111), PS(133)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
71 IF RND < .5 THEN A(1) = 0 ELSE A(1) = 1
73 IF RND < .5 THEN A(2) = 0 ELSE A(2) = 1
84 A(3) = 1 + (RND * 7)
85 A(4) = 1 + (RND * 6)
86 A(5) = 1 + (RND * 5)
128 FOR I = 1 TO 30000
129 FOR KKQQ = 1 TO 5
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
132 REM GOTO 162
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
151 J = 3 + FIX(RND * 3)
153 r = (1 - RND * 2) * A(J)
157 X(J) = A(J) + (RND ^ (RND * 10)) * r
161 NEXT IPP
162 REM IF RND < .5 THEN 164
163 REM X(1) = INT(X(1))
164 REM IF RND < .5 THEN 197
165 REM X(2) = INT(X(2))
197 IF X(3) < 1 THEN 1670
199 IF X(3) > 7 THEN 1670
201 IF X(4) < 1 THEN 1670
203 IF X(4) > 6 THEN 1670
205 IF X(5) < 1 THEN 1670
207 IF X(5) > 5 THEN 1670
261 X(6) = -5 + 2 * X(1) + X(1) * X(3) ^ 1.6
264 X(7) = -1 + X(1) + X(2)
267 X(8) = 6 - X(2) - X(4)
269 X(9) = -3 + X(1) + X(2) + X(5)
281 FOR J99 = 6 TO 9
283 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
285 NEXT J99
311 ups = ABS(X(5) ^ 1.8) * X(1) * X(3) ^ .3 * X(4) ^ 1.5 + X(2) * X(3) ^ 1.8 * X(4) ^ 1.3 * X(5) + X(1) * X(2) * X(3) ^ 1.7
322 dow = X(1) * X(3) * X(4) + X(2) * X(3) ^ 2.3 * X(4) ^ 1.4
365 POBA = -ups / dow + 1000000 * (X(6) + X(7) + X(8) + X(9))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 9
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 REM GOTO 128
1670 NEXT I
1777 FOR J44 = 6 TO 9
1778 IF A(J44) < 0 THEN 1999
1779 NEXT J44
1889 IF M < -.5 THEN 1999
1908 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [28]. The complete output through JJJJ = -31999.88000000002 is shown below:
1 1 6.999999999990646 4.9999999999972
1.000000000004951 0 0 0
0 -.3632313212606416 -31999.96000000001
1 1 6.99999999999997 4.999999999991044
1.000000000003382 0 0 0
0 -.3632313212599075 -31999.90000000002
1 1 6.9999999999965 4.99999999999999
1.000000000001283 0 0 0
0 -.3632313212591524 -31999.88000000002
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. The computational results above can be compared with the results in Chang [4, p. 385].
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [28], the wall-clock time for obtaining the output through JJJJ= -31999.88000000002 was 3 seconds, not including the time for creating the .EXE file.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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