Tuesday, September 19, 2017

Solving a Nonlinear Programming Formulation Based on a Formulation for a Car Side Impact Design Problem Using the Method of This Blog, Revised Edition

Jsun Yui Wong

Essentially the revision is changing old line 204 through old line 220 to become new line 304 through new line 320, respectively.


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

        198 IF RND < .5 THEN X(8) = .192 ELSE X(8) = .345

        199 IF RND < .5 THEN X(9) = .192 ELSE X(9) = .345


        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




        304 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


        305 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


        306 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




        307 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



        313 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



        316 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



        317 X(18) = -46.36 + 9.9 * X(2) + 12.9 * X(1) * X(8) - .1107 * X(3) * X(10) + 32


        318 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


        319 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



        320 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



        329 FOR J99 = 12 TO 21



            330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0

        331 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 21 minutes.

Acknowledgment

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

References

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