This paper addresses the problem of simultaneous localization and mapping (SLAM) by a mobile robot. The SLAM problem is defined as a global optimization problem in which the objective is to search the space of possible robot maps. A genetic algorithm is described for solving this problem, in which a population of candidate solutions is progressively refined in order to find a globally optimal solution. The fitness values in the genetic algorithm are obtained with a heuristic function that measures the consistency and compactness of the candidate maps. The results show that the maps obtained are very accurate, though the approach is computationally expensive. Directions for future research are also discussed.