A genetic algorithm has been developed to determine the optimal design of a two-component catalyst for the diffusion-limited A + B --> AB up arrow reaction in which each species is adsorbed specifically on one of two types of sites. Optimisation of the distribution of catalytic sites on the surface is achieved by means of an evolutionary algorithm which repeatedly selects the more active surfaces from a population of possible solutions leading to a gradual improvement in the activity of the catalyst surface. A Monte Carlo simulation is used to determine the activity of each of the catalyst surfaces. It is found that for a reacting mixture composed of equal amounts of each component the optimal active site distribution is that of a checkerboard, this solution being approximately 25% more active than a random site distribution. Study of a range of reactant compositions has shown the optimal distribution of catalytically active sites to be dependent on the composition of the ratio of A to B in the reacting mixture. The potential for application of the optimisation method introduced here to other catalysts systems is discussed.