Final results from joint exploration and optimization in CATIA, OCTAVE, and EXCEL
using a simplex search methods for the minimum mean of the seamgaps in the joints, which were controllled by one parameter. The parameter controlls the distance of the circle center from the midline of the piece		  
 
Plot of the data featuring the amount of gap between pieces under load for the 6 cases
I would base my project on that data - the variation of the gap in the seam under momentum load on the two pieces. I would like to find the optimal offset of the circle center from the seam axis for the current configuration.
Data page - for 1 mm offset data page - for 8 mm offset data page - for 12 mm offset data page - for 16 mm offset data page - for 20 mm offset data page - for 28 mm offset
plot of the gap values for each of the joints  
 
superimposition of the 6 above plots
The -0.001 value is the pressure fit default gap width. Negative because it is a pressure fit joint that is prestressed through assembly. There is some features in this small data set already - one can guess the joint nodes and one side is showing more gap displacement then the other.

The plots of the mean values of the gap curves as they were queried by the simplex search method on the right.
The group on bottom are from a run that consistently produced the same value due to an unresolved bug - but the remaining data clearly shows a decrease in the gap size with higher center offset values.
Since the model does not take into consideration the difference in curvature of the male and female pieces there is no penalty for growing th ejoint larger which should be the case in the real joint.

 Screenshot of simplex seach algorythm after 10 steps - each step had to be manually fed back from CATIA which made it prohibively slow.  
           
 
corresponding text file logging the above simplex run in Java  

I used the simplex search method on the function of the seamgap mean value out put of the joint.
Each time I run the simplex it triggers a question for a particular value from the CATIA finite element modeller. This value was generated through a report that was passed on to Octave and returned the mean value of all the distances. The search algorythm centered in around 17.625 mm for the centeroffset of the circle. The search flattened out in the 16-17 mm region for reasons I could not reslove in the time at hand.

  
Several different methods were explored for the modeling of the seam line based on different parameters and number of parameters. Unfortunately the CATIA environment allows only planar or cylindrical based contact joints that are the basis for pressure fit definitions. Therefore the spline approach had to be abandoned in favor of the circle segment approach  
 
Joint exploration in two dimensions - radius of joint piece and offset from center line are the variable parameters  
 
 
 
 
 
plot of the two parameters as x and y and z as the mean of the gap clearance along the seam        
 
simplex search data log of a manual search
bash-2.05b$ appletviewer simplex.html
enter the value for offset value x: 38.5 y: 18.0
1.5885e+10
testloop 0 1.58849997E10 0
enter the value for offset value x: 33.0 y: 18.0
-8.4693e-04
testloop 0 -8.4693E-4 1
enter the value for offset value x: 38.5 y: 15.0
1.3738e+09
testloop 0 1.37379994E9 2
2 1 0
enter the value for offset value x: 33.0 y: 15.0
3.5739e+08
vals -8.4693E-4 1.37379994E9 3.57390016E8
enter the value for offset value x: 34.375 y: 15.75
0.00011328
test3
enter the value for offset value x: 37.125 y: 17.25
-4.6316e-04
test3
test4
test5
1 35.75
enter the value for offset value x: 35.75 y: 18.0
-4.2328e-04
testloop 0 -4.2328E-4 0
enter the value for offset value x: 33.0 y: 18.0
-8.4693e-04
testloop 0 -8.4693E-4 1
enter the value for offset value x: 35.75 y: 16.5
-2.9287e-04
testloop 2 -2.9287E-4 2
1 0 2
enter the value for offset value x: 33.0 y: 19.5
8.5464e+04
vals -4.2328E-4 -8.4693E-4 85464.0
enter the value for offset value x: 33.6875 y: 18.75
9.3565e+05
test3
enter the value for offset value x: 35.0625 y: 17.25
-6.6714e-04
test3
test4
test6
2 34.375

 enter the value for offset value x: 34.375 y: 18.0
-8.4367e-04
testloop 0 -8.4367E-4 0
enter the value for offset value x: 33.0 y: 18.0
-8.4693e-04
testloop 0 -8.4693E-4 1
enter the value for offset value x: 34.375 y: 17.25
-9.2517e-04
testloop 0 -9.2517E-4 2
2 1 0
enter the value for offset value x: 33.0 y: 17.25
-5.3602e-04
vals -8.4693E-4 -9.2517E-4 -5.3602E-4
enter the value for offset value x: 33.34375 y: 17.4375
-8.3007e-04
test3
enter the value for offset value x: 34.03125 y: 17.8125
-0.0058654
test3
3 34.03125
enter the value for offset value x: 34.03125 y: 17.8125
-0.0058654
testloop 0 -0.0058654 0
enter the value for offset value x: 33.0 y: 18.0
-8.4693e-04
testloop 1 -8.4693E-4 1
enter the value for offset value x: 34.37

Conclusion:
Due to the lack of automation in the function value production through CATIA it was not possible to get sufficently large values to make a prediction of a minimum for the two dimensional data