Concept lattices represent a conceptual hierarchy inherent in a data set. A labeled line diagram for such a lattice represents this information diagrammatically.A diagram for a concept lattice may be algebraically generated by a set of vectors assigned to elements of the lattice. Such a diagram is called an additive line diagram, and is considered useful because it makes apparent the inherent structure of the lattice.This paper reports on experience with two approaches to automated concept lattice layout: (i) using genetic algorithms optimizing over a finite discrete space of diagrams, and (ii) force directed placement optimizing over a continuous rational space. The layout of concept lattices is of relevance to the layout of lattices in general since any lattice can be represented simply by a concept lattice.