Jsun Yui Wong
The computer program listed below seeks to solve the following fractional programming problem in Wang and Chu [30, Example 4]:
Maximize ((3 * X(1) + 4 * X(2) + 50) / (4 * X(1) + 3 * X(2) + 2 * X(3) + 50)) + ((3 * X(1) + 5 * X(2) + 3 * X(3) + 50) / (3 * X(1) + 4 * X(2) + 5 * X(3) + 50)) + ((4 * X(1) + 2 * X(2) + 4 * X(3) + 50) / (5 * X(1) + 4 * X(2) + 3 * X(3) + 50))
subject to
6 * X(1) + 3 * X(2) + 3 * X(3)<=10,
10 * X(1)+ 3 * X(2) + 8 * X(3)<=10,
X(1) >= 0, X(2)> =0, X(3) >= 0.
X(4) and X(5) 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 -31999 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
70 FOR J44 = 1 TO 3
72 A(J44) = RND * 1000
73 NEXT J44
128 FOR I = 1 TO 100
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) < 0 THEN 1670
203 REM IF X(J99) > 10 THEN 1670
204 NEXT J99
308 X(4) = 10 - 6 * X(1) - 3 * X(2) - 3 * X(3)
309 X(5) = 10 - 10 * X(1) - 3 * X(2) - 8 * X(3)
325 FOR J99 = 4 TO 5
327 XX(J99) = X(J99)
330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
331 NEXT J99
359 POBA = ((3 * X(1) + 4 * X(2) + 50) / (4 * X(1) + 3 * X(2) + 2 * X(3) + 50)) + ((3 * X(1) + 5 * X(2) + 3 * X(3) + 50) / (3 * X(1) + 4 * X(2) + 5 * X(3) + 50)) + ((4 * X(1) + 2 * X(2) + 4 * X(3) + 50) / (5 * X(1) + 4 * X(2) + 3 * X(3) + 50)) + 1000000 * (X(4) + X(5))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 5
1456 XXX(KLX) = XX(KLX)
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -1000 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5)
1903 PRINT XXX(4), XXX(5)
1912 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [31]. The complete output through JJJJ = -31999.99 is shown below:
5.599804986187998D-15 3.333332349810712 3.742777017698164D-15
0 0
2.950567817945802D-06 2.950567776139278D-06
3.002923975208128 -32000
1.01350324964244D-14 3.333330847652206 3.39851779191871D-15
0 0
7.457043310417812D-06 7.457043252569016D-06
3.002923973069783 -3999.99
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 [31], the wall-clock time for obtaining the output through JJJJ= -31999.99 was 2 seconds, not including the time for "Creating the .EXE file." One can compare the computational results above to the results in TABLE II of Wang and Chu [30, Example 4].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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