I am working with use of genetic algorithm to break transposition cipher. So in this work I have come across to a paper named Breaking Transposition Cipher with Genetic Algorithm by R. Toemeh & S. Arumugam.
In this paper they have used a fitness function. But i can not understand it completely. I can not understand the function of β and γ in the equation.
Can anyone please explain the fitness function please? Here is the picture of the fitness function:
The weights β and γ can be varied to allow more or less emphasis on particular statistics (they're determined "experimentally").
Kb(i, j) and Kt(i, j, k) are the known language bigram and trigram statistics. E.g. for English language you have (bigrams):
(further details in The frequency of bigrams in an English corpus)
Db(i, j) and Dt(i, j ,k) are the bigram and trigram statistics of
the message decrypted with key k.
In A Generic Genetic Algorithm to Automate an Attack on Classical Ciphers by Anukriti Dureha and Arashdeep Kaur there are some reference values of β and γ (and α since they use an extended form of the above equation) and three types of ciphers.
Some further details about β and γ.
They're weights that remain constant during the evolution. They should be tuned experimentally ("optimal" values depends on the target languages and the cipher algorithms).
Offline parameter tuning is the way to go, i.e.: