The computer program listed below seeks to solve the following problem in Gandomi, Alavi, and Yang [4, pp. 25-27].
Minimize ABS((1 / 6.931) - ((X(3) * X(2)) / (X(1) * X(4))))
where the four unknowns are integers in the range 12-60.
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
71 FOR J40 = 1 TO 4
74 A(J40) = 12 + RND * 49
77 NEXT J40
128 FOR I = 1 TO 10000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 J = 1 + FIX(RND * 4)
183 R = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * R
222 NEXT IPP
223 FOR J41 = 1 TO 4
225 X(J41) = INT(X(J41))
235 NEXT J41
256 FOR J47 = 1 TO 4
257 IF X(J47) < 12 THEN 1670
258 IF X(J47) > 60 THEN 1670
259 NEXT J47
333 POBA = -ABS((1 / 6.931) - ((X(3) * X(2)) / (X(1) * X(4))))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -.000002 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4)
1902 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [15]. The complete output through JJJJ= -31999.67000000005 is shown below:
49 16 19 43
-1.643428473917233D-06 -31999.76000000004
43 19 16 49
-1.643428473917233D-06 -31999.67000000005
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.
The solution above is comparable to the four solutions presented in Table 15 of Gandomi, Alavi, and Yang [4, p. 27].
One notes that here the gear ratio=(16*19)/(49*43)=.144280968.
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [15], the wall-clock time for obtaining the output through JJJJ= -31999.67000000005 was 10 seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[15] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
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