Jsun Yui Wong
The computer program listed below seeks to solve the corrugated bulkhead design problem on page 23 of Gandomi, Yang, and Alavi [5, p. 23]; its Equation (33) is not used--see Gandomi, Yang, and Alavi [6].
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
75 FOR J44 = 1 TO 4
76 A(J44) = 1 + RND * 20
79 NEXT J44
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
191 NEXT IPP
199 IF X(3) < X(2) THEN 1670
200 X(5) = X(4) * X(2) * (.4 * X(1) + X(3) / 6) - 8.94 * (X(1) + ((X(3) ^ 2 - X(2) ^ 2) ^ .5))
202 REM X(6) = X(1) * X(2) - 180 - 7.375 * (X(1) ^ 2 / X(3))
203 X(6) = X(4) * X(2) ^ 2 * (.2 * X(1) + X(3) / 12) - 2.2 * (8.94 * (X(1) + ((X(3) ^ 2 - X(2) ^ 2) ^ .5)) ^ (4 / 3))
204 REM
205 X(7) = X(4) - .0156 * X(1) - .15
206 X(8) = X(4) - .0156 * X(3) - .15
208 X(9) = X(3) - X(2)
210 REM
221 IF X(1) < 0 THEN 1670
222 IF X(1) > 100 THEN 1670
223 IF X(2) < 0 THEN 1670
224 IF X(2) > 100 THEN 1670
225 IF X(3) < 0 THEN 1670
226 IF X(3) > 100 THEN 1670
228 IF X(4) < 0 THEN 1670
229 IF X(4) > 5 THEN 1670
268 FOR J99 = 5 TO 9
269 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
270 NEXT J99
328 POBA = -(5.885 * X(4) * (X(1) + X(3))) / (X(1) + (X(3) ^ 2 - X(2) ^ 2) ^ .5) + 1000000 * X(5) + 1000000 * X(6) + 1000000 * X(7) + 1000000 * X(8) + 1000000 * X(9)
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 9
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -5.74 THEN 1999
1900 PRINT A(1), A(2), A(3)
1903 PRINT A(4), A(5), A(6)
1907 PRINT A(7), A(8), A(9)
1909 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [19]. The complete output through JJJJ= -31999.13000000014 is shown below:
38.82681770033805 32.3641784744763 38.76431051342591
.7556983561252736 0 0
0 0 0
-5.735584584067152 -31999.4600000001
38.74108239461563 32.38600135389557 38.73441946649184
.7543608853560047 0 0
0 0 0
-5.733418010318105 -31999.13000000014
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 [19], the wall-clock time for obtaining the output through JJJJ= -31999.13000000014 was 80 seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[19] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[20] Jsun Yui Wong (2012, April 12). The Domino Method of General Integer Nonlinear Programming Applied to a Nonlinear Fractional Programming Problem from the Literature. http://myblogsubstance.typepad.com/substance/2012/04/12/
[21] Xin-She Yang, Christian Huyck, Mehmet Karamanoglu, Nawaz Khan (2014). True global optimality of the pressure vessel design problem: A benchmark for bio-inspired optimisation algorithms.
https://arxiv.org/pdf/1403.7793.pdf.
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