We use a Generalized Hough transform (GHT) to detect and track instances of a class of sonar signals. This class consists of a four-dimensional set of curves and hence requires a four- dimensional transform space for the GHT. Many of the signals we need to detect are very weak. Such signals yield peaks in the transform space which are both very narrow and not too far above the random background variations. Finding such peaks is difficult. Exhaustive search over a predetermined discretization of the transform space will yield a nearly optimal point for a sufficiently fine discretization. However, even with an intelligently chosen discretization, exhaustive search requires searching over (and hence evaluating) many points in the transform space. We have therefore developed a genetic algorithm to more efficiently search the transform space. Designing the genetic algorithm to work properly has required experimentation with a number of its parameters. The most important of these are (1) the representation, (2) the population size, and (3) the number of runs.