This paper proposes a novel approach for fluid topology optimization using genetic algorithm. In this study, the enhancement of mixing in the passive micromixers is considered. The efficient mixing is achieved by the grooves attached on the bottom of the microchannel and the optimal configuration of grooves is investigated. The grooves are represented based on the graph theory. The micromixers are analyzed by a CFD solver and the exploration by genetic algorithm is assisted by the Kriging model in order to reduce the computational cost. Three cases with different constraint and treatment for design variables are considered. In each case, GA found several local optima since the objective function is a multi-modal function and each local optimum revealed the specific characteristic for efficient mixing in micromixers. Moreover, we discuss the validity of the constraint for optimization problems. The results show a novel insight for design of micromixer and fluid topology optimization using genetic algorithm.