The optimization of a single bit string by means of iterated mutation and selection of the best (a (1+1)-Genetic Algorithm) is discussed with respect to three simple tness functions: The counting ones problem, a standard binary encoded integer, and a Gray coded integer optimization problem. A mutation rate schedule that is optimal with respect to the success probabilityofmutation is presented for each of the objective functions, and it turns out that the standard binary code can hamper the search process even in case of unimodal objective functions. While normally a mutation rate of 1=l (where l denotes the bit string length) is recommendable, our results indicate that a variation of the mutation rate is useful in cases where the tness function is a multimodal pseudoboolean function, where multimodality may be caused by the objective function as well as the encoding mechanism.

The genetic algorithm (GA) is gaining increasing interest in both academia and industry in attempts to solve hard search problems quickly, accurately, and reliably. Various theories of what makes a problem difficult for the GA to solve have been put forward; yet, none of them has been completely confirmed experimentally. This thesis examines one theory of GA problem difficulty and investigates one facet of that theory that has received scant empirical attention and only passing theoretical consideration. The theory of problem difficulty assumed in this thesis is centered on the notion that GAs process building blocks in their search for optimal solutions. A source of difficulty commonly referred to in the literature is crosstalk, or nonlinear interactions among building blocks. The purpose of this thesis is to explore the effects of one type of crosstalk, fluctuating crosstalk, on population size, convergence time, and the number of function evaluations for boundedly difficult test functions. By modeling fluctuating crosstalk with Walsh coefficients, this thesis investigates fluctuating crosstalk effects on GA scalability by varying the order and magnitude of the crosstalk and the scaling of building blocks in the underlying fitness function. High-order fluctuating