Shadow data for minimizing 

f1 = square of total displacement; 
f2 = total vol. in cu . ft.
f3 = maximum bar stress (1e-2 ksi)

shadowMin =

    0.1347
    1.2761
    1.7523


Phi =

         0    2.2943    0.0000
    3.6249         0    3.6249
         0    5.5702         0


shadow_x =

  Columns 1 through 7 

    3.0000    3.0000    3.0000   30.0000    1.1071    0.5880    0.0570
    0.8000    0.8000    0.8000   60.0007    0.7854    0.7854    0.3658
    3.0000    3.0000    3.0000   30.0000    1.1071    0.5880    0.0570

  Columns 8 through 9 

    0.3626  175.2347
    1.5150  732.2500
    0.3626  175.2347


normal =

   -0.2434
   -0.7691
   -0.5909



Since the minimizer for the first and third functions are the same, it makes
sense to just minimize the second and third functions.

Thus, minimizing volume and max stress


Report on number of floating point operations
 Number of flops in initial calculations: 71

         beta        #flops(in K)     
   1.0e+03 *

         0    0.0010         0
    0.0001    0.0009    0.2172
    0.0001    0.0009    0.2188
    0.0002    0.0008    0.2175
    0.0002    0.0008    0.2187
    0.0003    0.0008    2.2522
    0.0003    0.0007    0.3247
    0.0004    0.0006    0.3548
    0.0004    0.0006    0.3583
    0.0004    0.0006    0.8091
    0.0005    0.0005    0.2473
    0.0006    0.0004    0.3596
    0.0006    0.0004    0.3549
    0.0006    0.0003    0.3605
    0.0007    0.0003    0.3600
    0.0008    0.0003    0.3573
    0.0008    0.0002    0.3583
    0.0009    0.0001    0.3582
    0.0009    0.0001    1.4037
    0.0010    0.0000    0.5072
    0.0010         0         0


net_flops =

     9638413

Pareto_Fmat =

    4.9011    1.7523
    4.5563    1.7796
    4.2171    1.8154
    3.8864    1.8642
    3.5686    1.9329
    3.2674    2.0271
    2.9725    2.1310
    2.6923    2.2573
    2.4408    2.4280
    2.2322    2.6645
    2.0669    2.9674
    1.9229    3.3032
    1.7991    3.6700
    1.6916    4.0618
    1.5985    4.4757
    1.5178    4.9088
    1.4479    5.3583
    1.3871    5.8219
    1.3340    6.2974
    1.2954    6.7951
    1.2761    7.3225


Pareto_xmat =

  Columns 1 through 7 

    3.0000    3.0000    3.0000   30.0000    1.1071    0.5880    0.0570
    3.0000    3.0000    2.5411   30.0000    1.1071    0.5880    0.0339
    3.0000    3.0000    2.0896   30.0000    1.1071    0.5880    0.0035
    3.0000    3.0000    1.6492   30.0000    1.1071    0.5880   -0.0378
    3.0000    3.0000    1.2262   30.0000    1.1071    0.5880   -0.0961
    2.7757    3.0000    0.9644   30.0000    1.1071    0.5880   -0.1223
    2.4076    3.0000    0.8000   30.0000    1.1071    0.5880   -0.1119
    1.8060    3.0000    0.8000   30.0000    1.1071    0.5880    0.0012
    1.2662    3.0000    0.8000   30.0000    1.1071    0.5880    0.1540
    0.8356    3.0000    0.8000   34.3120    1.0513    0.6109    0.3153
    0.8000    2.6362    0.8000   32.5248    1.0741    0.6012    0.3328
    0.8000    2.2784    0.8000   30.0000    1.1071    0.5880    0.3359
    0.8000    1.9813    0.8000   30.0000    1.1071    0.5880    0.3222
    0.8000    1.7232    0.8000   30.0000    1.1071    0.5880    0.3075
    0.8000    1.4996    0.8000   30.0000    1.1071    0.5880    0.2920
    0.8000    1.3061    0.8000   30.0000    1.1071    0.5880    0.2758
    0.8000    1.1383    0.8000   30.0000    1.1071    0.5880    0.2590
    0.8000    0.9923    0.8000   30.0000    1.1071    0.5880    0.2417
    0.8000    0.8650    0.8000   30.0000    1.1071    0.5880    0.2239
    0.8000    0.8000    0.8000   36.0978    1.0292    0.6208    0.1851
    0.8000    0.8000    0.8000   60.0007    0.7854    0.7854    0.3658

  Columns 8 through 9 

    0.3626  175.2347
    0.3682  177.9603
    0.3756  181.5448
    0.3857  186.4176
    0.3999  193.2933
    0.4194  202.7142
    0.4409  213.0992
    0.4670  225.7341
    0.5023  242.7957
    0.5513  266.4493
    0.6140  296.7444
    0.6834  330.3224
    0.7593  367.0021
    0.8404  406.1804
    0.9260  447.5688
    1.0156  490.8773
    1.1086  535.8334
    1.2045  582.1923
    1.3029  629.7404
    1.4059  679.5064
    1.5150  732.2500


-----------------------------------------------------------------

Linear combinations

Report on number of floating point operations
                  w            #flops(in K)     failure
   1.0e+03 *

         0    0.0010         0         0
    0.0001    0.0009    1.3208         0
    0.0001    0.0009    8.6202    0.0020
    0.0002    0.0008    6.0782         0
    0.0002    0.0008    3.7979         0
    0.0003    0.0008    3.6877         0
    0.0003    0.0007    5.4025         0
    0.0004    0.0006    4.0618         0
    0.0004    0.0006    3.5245         0
    0.0004    0.0006    1.4522         0
    0.0005    0.0005    0.6713         0
    0.0006    0.0004    0.2417         0
    0.0006    0.0004    0.7656         0
    0.0006    0.0003    0.6600         0
    0.0007    0.0003    0.8139         0
    0.0008    0.0003    0.6287         0
    0.0008    0.0002    0.4409         0
    0.0009    0.0001    0.3888         0
    0.0009    0.0001    0.4728         0
    0.0010    0.0000    0.9528         0
    0.0010         0         0         0


net_flops =

    43982234

Fmatrix =

    4.9011    1.7523
    4.9010    1.7523
    4.3278    1.8025
    3.8840    1.8646
    3.6125    1.9216
    3.2953    2.0178
    2.8624    2.1749
    2.7034    2.2513
    2.5702    2.3311
    2.4551    2.4161
    2.3532    2.5082
    2.3127    2.5506
    2.2130    2.6924
    2.1479    2.8081
    1.9905    3.1359
    1.8521    3.5034
    1.6957    4.0454
    1.5340    4.8150
    1.3586    6.0681
    1.3023    6.6557
    1.2761    7.3225


xmatrix =

  Columns 1 through 7 

    3.0000    3.0000    3.0000   30.0000    1.1071    0.5880    0.0570
    3.0000    3.0000    3.0000   30.0000    1.1071    0.5880    0.0570
    3.0000    3.0000    2.2369   30.0000    1.1071    0.5880    0.0145
    3.0000    3.0000    1.6461   30.0000    1.1071    0.5880   -0.0381
    3.0000    3.0000    1.2846   30.0000    1.1071    0.5880   -0.0865
    2.8079    3.0000    0.9814   30.0000    1.1071    0.5880   -0.1224
    2.1714    3.0000    0.8000   30.0000    1.1071    0.5880   -0.0726
    1.8300    3.0000    0.8000   30.0000    1.1071    0.5880   -0.0042
    1.5440    3.0000    0.8000   30.0000    1.1071    0.5880    0.0673
    1.2969    3.0000    0.8000   30.0000    1.1071    0.5880    0.1434
    1.0782    3.0000    0.8000   30.0000    1.1071    0.5880    0.2259
    0.9912    3.0000    0.8000   30.0000    1.1071    0.5880    0.2639
    0.8000    3.0000    0.8000   35.5449    1.0360    0.6177    0.3300
    0.8000    2.8382    0.8000   34.1794    1.0530    0.6101    0.3310
    0.8000    2.4455    0.8000   31.0075    1.0938    0.5932    0.3353
    0.8000    2.1085    0.8000   30.0000    1.1071    0.5880    0.3284
    0.8000    1.7330    0.8000   30.0000    1.1071    0.5880    0.3081
    0.8000    1.3450    0.8000   30.0000    1.1071    0.5880    0.2794
    0.8000    0.9239    0.8000   30.0000    1.1071    0.5880    0.2325
    0.8000    0.8000    0.8000   32.2581    1.0775    0.5998    0.1974
    0.8000    0.8000    0.8000   60.0007    0.7854    0.7854    0.3658

  Columns 8 through 9 

    0.3626  175.2347
    0.3626  175.2347
    0.3729  180.2508
    0.3858  186.4588
    0.3976  192.1613
    0.4175  201.7822
    0.4500  217.4886
    0.4658  225.1283
    0.4823  233.1108
    0.4999  241.6095
    0.5189  250.8242
    0.5277  255.0580
    0.5571  269.2439
    0.5810  280.8066
    0.6488  313.5921
    0.7248  350.3433
    0.8370  404.5416
    0.9962  481.5011
    1.2555  606.8124
    1.3770  665.5712
    1.5150  732.2500

