Computer program for solving nonlinear fractional programming problems: another illustration
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the immediately following formulation from Tsai [86, p. 406, Example 2]:
Minimize 200 * 2 ^ .5 * X(1) + 100 * X(2)
subject to
(2 ^ .5 * X(1) + X(2)) / (2 ^ .5 * X(1) ^ 2 + 2 * X(1) * X(2)) - 1 <= 0
1 / (X(1) + 2 ^ .5 * X(2)) - 1 <= 0
X(2) / (2 ^ .5 * X(1) ^ 2 + 2 * X(1) * X(2)) - 1 <= 0
0 < X(1), X(2) <= 1.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
121 A(1) = RND * 1
123 A(2) = RND * 1
126 REM A(3) = 2 + RND * 13
128 FOR i = 1 TO 50000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 2)
140 B = 1 + FIX(RND * 2)
144 IF RND < .5 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * r
165 GOTO 168
167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)
168 NEXT IPP
213 IF X(1) < .000001 THEN 1670
215 IF X(1) > 1 THEN 1670
222 IF X(2) < .000001 THEN 1670
224 IF X(2) > 1 THEN 1670
375 IF (2 ^ .5 * X(1) + X(2)) / (2 ^ .5 * X(1) ^ 2 + 2 * X(1) * X(2)) - 1 > 0 THEN 1670
378 IF 1 / (X(1) + 2 ^ .5 * X(2)) - 1 > 0 THEN 1670
388 IF X(2) / (2 ^ .5 * X(1) ^ 2 + 2 * X(1) * X(2)) - 1 > 0 THEN 1670
565 PD1 = -200 * 2 ^ .5 * X(1) - 100 * X(2)
569 p = PD1
1111 IF p <= M THEN 1670
1452 M = p
1454 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1775 IF M < -263.896 THEN 1999
1904 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [103]. Its complete output of one run through JJJJ= -31603 is shown below. GW-BASIC also can handle this computer program.
.7885383 .4086356 -263.8959 -31919
.7887109 .4081472 -263.8958 -31886
.7890227 .4072663 -263.8959 -31877
.7885319 .4086539 -263.8959 -31834
.7891097 .4070208 -263.896 -31824
.7883261 .4092365 -263.8959 -31740
.789149 .4069097 -263.896 -31714
.7887858 .4079355 -263.8958 -31603
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with QB64v1000-win [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31603 was 40 seconds, counting from "Starting program…". One can see other computational results in Tsai [86, p. 408, Table 2].
The computational results presented above were obtained from the following computer system:
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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