Benoît Descamps

Graph theory in evolutionary truss design optimization

This chapter explores how to integrate graph theory in evolutionary algorithms for efficient truss optimization. It turns out that truss assemblies fit well with graph-based representation through a real-value matrix encoding, which is demonstrated to be a sound and powerful alternative to vector encoding. Because the structural component sizes and the system connectivity are expressed in a compact formalism, sizing and topology optimization are naturally carried out simultaneously. Evolutionary operators are subsequently adapted and repair procedures to prevent unstable configurations are readily derived. The baseline evolutionary algorithm described hereafter is presented in its generic form so that the reader can adapt the material content in various ways (hybrid algorithm, bilevel optimization, and so on). Applications to three-dimensional structures illustrate the methodology.