Jsun Yui Wong
The computer program listed below seeks to solve the following problem in Jong [12, p. 17, Problem 8]:
Minimize (X(1) ^ 2 - 4 * X(1) + 2 * X(2) ^ 2 - 8 * X(2) + 3 * X(3) ^ 2 - 12 * X(3) - 56) / (X(1) ^ 2 - 2 * X(1) + X(2) ^ 2 - 2 * X(2) + X(3) + 20) + ((2 * X(1) ^ 2 - 16 * X(1) + X(2) ^ 2 - 8 * X(2) - 2) / (2 * X(1) + 4 * X(2) + 6 * X(3)))
subject to
X(1) + X(2) + X(3)<=10,
- X(1) - X(2) + X(3)<=4,
X(1)>=1,
X(2)>=1,
X(3)>=1.
X(4) and X(5) below are slack variables.
Whereas line 199 of the preceding paper is 199 X(J99) = INT(X(J99)), here line 199 is 199 REM X(J99) = INT(X(J99)).
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
70 FOR J44 = 1 TO 3
72 A(J44) = RND * 50
73 NEXT J44
128 FOR I = 1 TO 500
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)
183 r = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
196 FOR J99 = 1 TO 3
199 REM X(J99) = INT(X(J99))
201 IF X(J99) < 1 THEN 1670
204 NEXT J99
205 REM
311 X(4) = 10 - X(1) - X(2) - X(3)
315 X(5) = 4 + X(1) + X(2) - X(3)
333 FOR J44 = 4 TO 5
336 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
339 NEXT J44
366 POBA = -(X(1) ^ 2 - 4 * X(1) + 2 * X(2) ^ 2 - 8 * X(2) + 3 * X(3) ^ 2 - 12 * X(3) - 56) / (X(1) ^ 2 - 2 * X(1) + X(2) ^ 2 - 2 * X(2) + X(3) + 20) - ((2 * X(1) ^ 2 - 16 * X(1) + X(2) ^ 2 - 8 * X(2) - 2) / (2 * X(1) + 4 * X(2) + 6 * X(3))) + 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 < -99999 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5)
1912 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [33]. The complete output through JJJJ = -31999.98 is shown below:
1.821631971584992 1.0000000000000462 1.0000000000045943
0 0
6.11983426932261 -32000
1.82163192140177 1.0000000000003429 1.0000000000000018
0 0
6.119834269363134 -31999.99
1.821631985088472 1.00000000000000011 1.000000000000444
0 0
6.119834269360302 -31999.98
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 [33], the wall-clock time for obtaining the output through
JJJJ= -31999.98 was two seconds, not including the time for "Creating .EXE file." One can compare the computational results above to the results in Jong [12, p. 18].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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