  In this paper, a genetic algorithm, one of the evolutionary algorithms
optimization methods, is used for the first time for the problem of finding
extremal binary self-dual codes. We present a comparison of the computational
times between a genetic algorithm and a linear search for different size search
spaces and show that the genetic algorithm is capable of finding binary
self-dual codes significantly faster than the linear search. Moreover, by
employing a known matrix construction together with the genetic algorithm, we
are able to obtain new binary self-dual codes of lengths 68 and 72 in a
significantly short time. In particular, we obtain 11 new extremal binary
self-dual codes of length 68 and 17 new binary self-dual codes of length 72.
