Mapping between Currier A and B

[MarcoP]

I have run a few hill-climbing experiments, searching for B->A replacements resulting in a minimal bigram-frequency Bhattacharyya difference.
It seems that each run arrives at a different solution: this could be because the problem is not fit for hill-climbing, or because my code is not adequate. My impression is that both things are true.

These are the results for searches constrained to use strings 3-characters long or shorter and solution including at most three replacement rules (I list two experiments for each transliteration system considered). There is a certain agreement about the ed->od replacement (Cuva:ED->OD, Currier:C8->O8, it occurs in all results, but the second EVA experiment).

eva     [['oka'->'o'] ['hdy'->'hor'] ['ed'->'od']]
eva     [['oka'->'oda'] ['.l'->'.do'] ['edy'->'or']]
cuva    [['UDY'->'UO'] ['ED'->'OD'] ['OKU'->'OTS']]
cuva    [['OD'->'OTS'] ['UD'->'SOR'] ['ED'->'OD']]
currier [['.E'->'.8O'] ['CC8'->'COR'] ['C8'->'O8']]
currier [['OR'->'SO'] ['C8'->'O8'] ['O89'->'OR']]


All experiments were run for more than 10,000 iterations and, when I stopped them, had been unable to improve the current solution for a few thousand iterations. Typically, a solution reduces the difference between A and B to about half the difference between the two unmodified subsets of the text.

Here is an example (f104r.43) of the substitutions in the first EVA solution listed above:

ORIGINAL: tsheodl.qokaiin.qokchedy.ykchdy.pchedy.qokeedy.oteey.qokain.oteoldal
MODIFIED: tsheodl.qoiin.qokchody.ykchor.pchody.qokeody.oteey.qoin.oteoldal

Two of the newly generated words (qokchody and ykchor) appear in A and not in B: fine.
pchody and qokeody appear both in A and B: also OK.

But qoiin and qoin only appear in B and are extremely rare: they cannot be an acceptable A equivalent for the very common qokaiin and qokain.