Selection of function symbols from the grammar is biased

[gkronber]

Steps to reproduce:

• Create symbolic regression problem
• Also activate "Special Functions" group in the grammar
• Start a run

Expected: distribution of function symbols in the initial population should be nearly uniform. Actual: Symbols from the "Arithmetic Functions" group are much more likely then symbols from the "Special Functions" group.

As explained in the comments below the likely reason for this is that the tree creator (PTC2) introduces a bias against unary functions because it must also produce larger trees.

[mkommend]

This is simply not true. The symbol selection does not prefer any symbols, regardless of the group size. See the attached script which calculates the symbol distribution for any arbitrary number of created tree.

I suspect that the phenomena you are seeing results from the interplay between the grammar, the tree creator and the size constraints. All special symbols are unary symbols and to create larger trees within the depth limits, binary symbols have to be included in the trees.

[gkronber]

Thanks for inspecting this.

[gkronber]

Solution to this problem is to set very large depth limits.