Jsun Yui Wong
The computer program listed below seeks to solve the following problem:
Minimize ((X(1) ^ 2 + X(2) ^ 2 + 2 * X(1) * X(3)) / (X(3) ^ 2 + 5 * X(1) * X(2))) + ((X(1) + 1) / (X(1) ^ 2 - 2 * X(1) + X(2) ^ 2 - 8 * X(2) + 20))
subject to
X(1) ^ 2 + X(2) ^ 2 + X(3)<=5,
(X(1) - 2) ^ 2 + X(2) ^ 2 + X(3) ^ 2<=5,
1<=X(1) <=33333,
1<=X(2) <= 33333,
1<=X(3) <= 33333,
X(1) through X(3) are integer variables.
The problem above is based on Jong's [16, page 16/21] Problem 6, which is as follows:
Minimize ((X(1) ^ 2 + X(2) ^ 2 + 2 * X(1) * X(3)) / (X(3) ^ 2 + 5 * X(1) * X(2))) + ((X(1) + 1) / (X(1) ^ 2 - 2 * X(1) + X(2) ^ 2 - 8 * X(2) + 20))
subject to
X(1) ^ 2 + X(2) ^ 2 + X(3)<=5,
(X(1) - 2) ^ 2 + X(2) ^ 2 + X(3) ^ 2<=5,
1<=X(1) <=3,
1<=X(2) <= 3,
1<=X(3) <= 2.
X(4) and X(5) below are added slack variables.
One notes the following line 193 through line 195 and line 201 through line 218.
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
72 A(1) = 1 + RND * 33333
75 A(2) = 1 + RND * 33333
77 A(3) = 1 + RND * 33333
128 FOR I = 1 TO 2000
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 r = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
193 X(1) = INT(X(1))
194 X(2) = INT(X(2))
195 X(3) = INT(X(3))
201 IF X(1) < 1 THEN 1670
203 IF X(1) > 33333 THEN 1670
211 IF X(2) < 1 THEN 1670
213 IF X(2) > 33333 THEN 1670
217 IF X(3) < 1 THEN 1670
218 IF X(3) > 33333 THEN 1670
311 X(4) = 5 - X(1) ^ 2 - X(2) ^ 2 - X(3)
314 X(5) = 5 - (X(1) - 2) ^ 2 - X(2) ^ 2 - X(3) ^ 2
333 FOR J44 = 4 TO 5
336 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
339 NEXT J44
388 REM POBA = -((X(1) - 1) ^ 2 + (X(2) - 1) ^ 2 + 1) * ((X(1) - 2) ^ 2 + (X(2) - 3) ^ 2 + 1) * ((X(1) - 4) ^ 2 + (X(2) - 2) ^ 2 + 1) + 1000000 * (X(3))
389 POBA = -((X(1) ^ 2 + X(2) ^ 2 + 2 * X(1) * X(3)) / (X(3) ^ 2 + 5 * X(1) * X(2))) - ((X(1) + 1) / (X(1) ^ 2 - 2 * X(1) + X(2) ^ 2 - 8 * X(2) + 20)) + 1000000 * (X(4) + X(5))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 5
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -111111 THEN 1999
1900 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 [40]. The complete output through JJJJ = -31999.95000000001 is shown below:
1 1 1 0 0
-.8333333333333334 -32000
1 1 1 0 0
-.8333333333333334 -31999.99
1 1 1 0 0
-.8333333333333334 -31999.98
1 1 1 0 0
-.8333333333333334 -31999.97000000001
1 1 1 0 0
-.8333333333333334 -31999.96000000001
1 1 1 0 0
-.8333333333333334 -31999.95000000001
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 [40], the wall-clock time for obtaining the output through
JJJJ= -31999.95000000001 was about 2 seconds, not including the time for "Creating .EXE file."
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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