Genetic algorithms (GAs) are powerful combinatorial optimizers that are able to find close-to-optimal solutions for difficult problems by applying the paradigm of adaptation through Darwinian evolution. We describe a framework for GAs capable of solving certain optimization problems encountered in geographical information systems (GISs). The framework is especially suited for geographical problems since it is able to exploit their geometrical structure with a novel operator called the geometrically local optimizer. Three such problems are presented as case studies: map labeling, generalization while preserving structure, and line simplification. Experiments show that the GAs give good results and are flexible as well.