Numerical predictions of heat transfer under laminar conditions in a square duct with ribs are presented in this paper. Ribs are provided on top and bottom walls in a square duct in a staggered manner. The flow rates have been varied between Reynolds number 200 and 600. Various configurations of ribs by varying length, width and depth have been investigated for their effect on heat transfer, friction factor and entropy augmentation generation number. Further artificial neural network integrated with genetic algorithm was used to minimize the entropy augmentation generation number (performance factor) by selecting the optimum rib dimensions in a selected range. Genetic algorithm is compared with microgenetic algorithm to examine the reduction in computational time for outlay of solution accuracy.