Information transmission through genetic algorithm fitness maps

To bound the amount of information transmitted from a fitness map to a genetic algorithm population, we use a method suggested by Abu-Mostafa et al. [1] for measuring the information storage capacity of general forms of memory and represent the genetic algorithm as a communication channel. Our results show that a number of bits linear in the size of the search space can be stored in a fitness map, but on average only a logarithmic number of bits can be stored within a genetic algorithm population of bounded size and finite precision representation. Our results place an upper bound on the rate at which information can be transmitted through, or generated by and later extracted from, a genetic algorithm under fairly general conditions.