Jsun Yui Wong
The computer program listed below seeks to solve the following formulation which is based on the formulation for a car side impact design problem in Gamdomi, Yang, and Alavi [5, pp. 2333-2335].
The following X(12) through X[21} are slack varibles.
Minimize 1.98 + 4.90 * X(1) + 6.67 * X(2) + 6.98 * X(3) + 4.01 * X(4) + 1.78 * X(5) + 2.73 * X(7)
subject to
X(12) >= -1.16 + .3717 * X(2) * X(4) + .00931 * X(2) * X(10) + .484 * X(3) * X(9) - .01343 * X(6) * X(10) + 1
X(13) >= -.261 + .0159 * X(1) * X(2) + .188 * X(1) * X(8) + .019 * X(2) * X(7) - .0144 * X(3) * X(5) - .0008757 * X(5) * X(10) - .08045 * X(6) * X(9) - .00139 * X(8) * X(11) - .000001575 * X(10) * X(11) + .32
X(14) >= -.214 - .00817 * X(5) + .131 * X(1) * X(8) + .0704 * X(1) * X(9) - .03099 * X(2) * X(6) + .018 * X(2) * X(7) - .0208 * X(3) * X(8) - .121 * X(3) * X(9) + .00364 * X(5) * X(6) - .0007715 * X(5) * X(10) + .0005354 * X(6) * X(10) - .00121 * X(8) * X(11) + .32
X(15) >= -.74 + .61 * X(2) + .163 * X(3) * X(8) - .001232 * X(3) * X(10) + .166 * X(7) * X(9) - .227 * X(2) * X(2) + .32
X(16) >= -28.98 - 3.818 * X(3) + 4.2 * X(1) * X(2) - .0207 * X(5) * X(10) - 6.63 * X(6) * X(9) + 7.7 * X(7) * X(8) - .32 * X(9) * X(10) + 32
X(17) >= -33.86 - 2.95 * X(3) - .1792 * X(10) + 5.057 * X(1) * X(2) + 11.0 * X(2) * X(8) + .0215 * X(5) * X(10) + 9.98 * X(7) * X(8) - 22.0 * X(8) * X(9) + 32
X(18) >= -46.36 + 9.9 * X(2) + 12.9 * X(1) * X(8) - .1107 * X(3) * X(10) + 32
X(19) >= -4.72 + .5 * X(4) + .19 * X(2) * X(3) + .0122 * X(4) * X(10) - .009325 * X(6) * X(10) - .000191 * X(11) * X(11) + 4
X(20) >= -10.58 + .674 * X(1) * X(2) + 1.95 * X(2) * X(8) - .02054 * X(3) * X(10) + .0198 * X(4) * X(10) - .028 * X(6) * X(10) + 9.9
X(21) >= -16.45 + .489 * X(3) * X(7) + .843 * X(5) * X(6) - .0432 * X(9) * X(10) + .0556 * X(9) * X(11) + .000786 * X(11) * X(11) + 15.7
.5<=X(i) <=1.5, i=1, 3, 4
.45<=X(2) <=1.36 , (This change of 1.35 to 1.36 comes from the 1.36000 of the last column of Table 16 of Gandomi, Yang, and Alavi [5, p. 2335, Table 16.)
.5<=X(5) <= 2.625 (This change from 0.875 to .5 comes from the 0.50000s of the row of X(5) of Table 16 of Gandomi, Yang, and Alavi [5, p. 2335, Table 16].) .
.4<=X(6), X(7) <= 1.5. (This change from 1.2 to 1.5 comes from the 1.50000s of the row of X(6) of Table 16 of Gandomi, Yang, and Alavi [5, p. 2335, Table 16])
.192<=X(8), X(9)<= .345
-30<=X(10), X(11)<=30. (These changes of .5 and 1.5 to -30 to 30, respectively, come from the Erratum of G, Y, and Alavi [8].)
The .61 (instead of 0.061) of line 207 of the following computer program comes from Youn and Choi [26, p. 250].
The following computer program has these newer numbers.
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
72 FOR J44 = 1 TO 4
74 A(J44) = .5 + RND
79 NEXT J44
86 A(2) = .45 + RND * .9
87 A(5) = .5 + RND * 2.125
88 A(6) = .4 + RND * 1.1
89 A(7) = .4 + RND * 1.1
95 IF RND < .5 THEN A(8) = .192 ELSE A(8) = .345
96 IF RND < .5 THEN A(9) = .192 ELSE A(9) = .345
98 A(10) = -30 + RND * 60
99 A(11) = -30 + RND * 60
128 FOR I = 1 TO 5000
129 FOR KKQQ = 1 TO 11
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 4))
181 J = 1 + FIX(RND * 11)
183 r = (1 - RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
197 REM X(3) = INT(X(3))
198 IF RND < .5 THEN X(8) = .192 ELSE X(8) = .345
199 IF RND < .5 THEN X(9) = .192 ELSE X(9) = .345
201 REM X(3) =- (-.74 + .61 * X(2) + 0+ .166 * X(7) * X(9) - .227 * X(2) * X(2) + .32) / ( .163*x(8) -.001232*x(10) )
204 X(12) = -1.16 + .3717 * X(2) * X(4) + .00931 * X(2) * X(10) + .484 * X(3) * X(9) - .01343 * X(6) * X(10) + 1
205 X(13) = -.261 + .0159 * X(1) * X(2) + .188 * X(1) * X(8) + .019 * X(2) * X(7) - .0144 * X(3) * X(5) - .0008757 * X(5) * X(10) - .08045 * X(6) * X(9) - .00139 * X(8) * X(11) - .000001575 * X(10) * X(11) + .32
206 X(14) = -.214 - .00817 * X(5) + .131 * X(1) * X(8) + .0704 * X(1) * X(9) - .03099 * X(2) * X(6) + .018 * X(2) * X(7) - .0208 * X(3) * X(8) - .121 * X(3) * X(9) + .00364 * X(5) * X(6) - .0007715 * X(5) * X(10) + .0005354 * X(6) * X(10) - .00121 * X(8) * X(11) + .32
207 X(15) = -.74 + .61 * X(2) + .163 * X(3) * X(8) - .001232 * X(3) * X(10) + .166 * X(7) * X(9) - .227 * X(2) * X(2) + .32
213 X(16) = -28.98 - 3.818 * X(3) + 4.2 * X(1) * X(2) - .0207 * X(5) * X(10) - 6.63 * X(6) * X(9) + 7.7 * X(7) * X(8) - .32 * X(9) * X(10) + 32
216 X(17) = -33.86 - 2.95 * X(3) - .1792 * X(10) + 5.057 * X(1) * X(2) + 11.0 * X(2) * X(8) + .0215 * X(5) * X(10) + 9.98 * X(7) * X(8) - 22.0 * X(8) * X(9) + 32
217 X(18) = -46.36 + 9.9 * X(2) + 12.9 * X(1) * X(8) - .1107 * X(3) * X(10) + 32
218 X(19) = -4.72 + .5 * X(4) + .19 * X(2) * X(3) + .0122 * X(4) * X(10) - .009325 * X(6) * X(10) - .000191 * X(11) * X(11) + 4
219 X(20) = -10.58 + .674 * X(1) * X(2) + 1.95 * X(2) * X(8) - .02054 * X(3) * X(10) + .0198 * X(4) * X(10) - .028 * X(6) * X(10) + 9.9
220 X(21) = -16.45 + .489 * X(3) * X(7) + .843 * X(5) * X(6) - .0432 * X(9) * X(10) + .0556 * X(9) * X(11) + .000786 * X(11) * X(11) + 15.7
221 IF X(1) < .5 THEN 1670
222 IF X(1) > 1.5 THEN 1670
223 IF X(2) < .45 THEN 1670
224 IF X(2) > 1.36 THEN 1670
225 IF X(3) < .5 THEN 1670
226 IF X(3) > 1.5 THEN 1670
235 IF X(4) < .5 THEN 1670
236 IF X(4) > 1.5 THEN 1670
245 IF X(5) < .5 THEN 1670
246 IF X(5) > 2.625 THEN 1670
247 IF X(6) < .4 THEN 1670
248 IF X(6) > 1.5 THEN 1670
249 IF X(7) < .4 THEN 1670
250 IF X(7) > 1.5 THEN 1670
251 IF X(8) < .192 THEN 1670
252 IF X(8) > .345 THEN 1670
253 IF X(9) < .192 THEN 1670
254 IF X(9) > .345 THEN 1670
255 IF X(10) < -30 THEN 1670
256 IF X(10) > 30 THEN 1670
257 IF X(11) < -30 THEN 1670
258 IF X(11) > 30 THEN 1670
259 FOR J99 = 12 TO 21
269 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
270 NEXT J99
333 REM
355 POBA = -1.98 - 4.90 * X(1) - 6.67 * X(2) - 6.98 * X(3) - 4.01 * X(4) - 1.78 * X(5) - 2.73 * X(7) + 1000000 * (X(19) + X(20) + X(21) + X(12) + X(13) + X(14) + X(15) + X(16) + X(17) + X(18))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 21
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -22.59 THEN 1999
1900 PRINT A(1), A(2), A(3)
1903 PRINT A(4), A(5), A(6)
1906 PRINT A(7), A(8), A(9)
1907 PRINT A(10), A(11), A(12)
1908 PRINT A(13), A(14), A(15)
1909 PRINT A(16), A(17), A(18)
1910 PRINT A(19), A(20), A(21)
1912 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [22]. The complete output through JJJJ = -31991.2900000014 is shown below:
.5000005889982524 1.11192095479818 .5000002548373358
1.30987464494098 .4999999851212227 1.499999658347107
.3999999910600426 .345 .192
-20.35644718873207 4.23138571828183D-07 0
0 0 0
0 0 0
0 0 0
-22.57111470868293 -31996.82000000051
.5004298828587872 1.111506697535371 .4999999851051984
1.31034634007081 .499999985110199 1.499998784994892
.3999999910602496 .345 .192
-20.39603494791161 -1.451902692732694D-10 0
0 0 0
0 0 0
0 0 0
-22.57234476737785 -31991.2900000014
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 [22], the wall-clock time for obtaining the output through JJJJ= -31991.2900000014 was 25 minutes.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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