Useful Tips

 

Optimization

If you encounter a problem with many variables (more than 4) as free parameters:

 
  • do not forget to apply ranges, and 
 
  • begin with the gradient algorithm before trying the simulated annealing algorithm.

Gradient

The gradient behaves better with squares or quadratic functions (especially relevant for "Target Values"). Hence the following problem:

Given: volume=x*y*z.

Find, x, y and z such that volume = 1000.

is better solved if the following formula is given to the optimizer:
 objective = (volume)2

Chaining algorithms

In most cases the properties of the functions used inside the optimization problem are unknown. In this case, it is recommended to use the global search algorithm (Simulated Annealing). However, as this algorithm can take a long time to reach convergence (especially when there are many free parameters), it could be helpful to use a local search (gradient) for a few iterations before switching to the global search (Simulated Annealing). Eventually, when the global search has converged and that results must be refined, reduce the ranges around the found solution and restart a slow Local Search.

Several constraints
  • Some optimization problems can contain a large number of constraints with respect to the number of free parameters. In this case the optimization problem can be over-constrained i.e. there is no feasible region (set of free parameter values for which all constraints are satisfied). The Global Search (Simulated Annealing) helps to reduce the constraints values even in this later case. However, it does not guarantee any access to the feasible region even if it exists.
  • The evolution of the distances to satisfaction (that can be displayed with the graphs) is useful to identify constraints that are difficult to satisfy. It is sometime better to deactivate all other constraints to identify a potential zone of satisfaction for these constraints only.

Recommendations

Always use well-constrained sketches when they are involved in an optimization. Under-constrained sketches can lead to wrong solutions or collapsed geometries (see KwoCirclesSk.CATPart). It is also recommended to limit the ranges of the free parameters to reasonable values. 

Design of Experiments Tool

How to manually build graphics from a DoE Excel Output file?

The process described below is based on the following file: HowToManuallyBuildGraphsFromDoEExcelOutputFile.xls

Creating the Effects Graphs:

For each effect graph to build, i.e. for each array of the part entitled ARRAYS OF FACTORS EFFECTS,  for each output S and each factor X, perform the following actions in the Excel file:

  1. If not already done, open the DoE output Excel file.

  2. Click the Chart Wizard command.

  3. Select the Line as Chart type and click the NEXT command.

  4. In the Data Range tab:

    • Put the cursor in the Data Range field and select the following highlighted range in the sheet:
    • Check the Columns option in the Series In field.

  5. In the Data Range tab :

    • Do not modify the content of the Series frame.
    • Put the cursor in the Category (X) axis labels field and select the following highlighted range in the sheet :
    • Click NEXT.

  6. In the Titles tab:

    • Chart Title = Mean effect of FactorK on OutputN (surrounded by min. and max. effect)
    • Category (X) axis = VALUE of FactorK
    • Value (Y) axis = Average of OutputN (output's unit) responses (surrounded by min. and max. responses)

  7.  Leave the other tabs unchanged and click NEXT.

  8. Choose the As Object in : Sheet1 option.

  9. Click FINISH.

Creating the Interactions Graphs

For each interaction graph to build, i.e. for each array of the part entitled ARRAYS OF INTERACTIONS AVERAGES, perform the following actions in the Excel file :

  1. If not already done, open the DoE output Excel file.

  2. Click the Chart Wizard command.

  3. Select the Line as Chart type and click NEXT.

  4. In the Data Range tab:

    • Put the cursor in the Data Range field and select the following highlighted range in the sheet:
    • Check the Columns option in the Series In field

  5. In the Series tab :

    • Do not modify the content of the Series frame
    • Put the cursor in the Category (X) axis labels field and select the following highlighted range in the sheet:
    • Click NEXT.

  6. In the Titles tab :

    • Chart Title = Effect of FactorL on OutputN for each value of FactorK (no interaction if curves are parallel)
    • Category (X) axis = VALUE of FactorL
    (Y) axis = Average of OutputN (output's unit)

  7. Do not modify the other tabs and click NEXT.

  8. Choose the As Object in : Sheet1 option.

  9. Click FINISH.

Creating the Slopes Graphs

For each slope graph to build, i.e. for each array of the part entitled ARRAYS OF EFFECTS SLOPES,perform the following actions in the Excel file :

  1. If not already done, open the DoE output Excel file.

  2. Click the Chart Wizard command.

  3. Select the Line as Chart type and click NEXT.

  4. In the Data Range tab:

    • Put the cursor in the Data Range field and select the following highlighted range in the sheet:
    • Check the Columns option in the Series In field.

  5. In the Series tab :

    • Do not modify the content of the Series frame
    • Put the cursor in the Category (X) axis labels field and select the following highlighted range in the sheet :
    • Click NEXT.

  6. In the Titles tab :

    • Chart Title = Mean slope of the effect curve of FactorK on OutputN (surrounded by min. and max. slopes).
    • Category (X) axis = Range of study = [value at level i,value at level i+1] of factor FactorK
    • Value (Y) axis = Slope

  7. Do not modify the other tabs and click NEXT.

  8. Choose the As Object in : Sheet1 option.

  9. Click FINISH.