Generating 3d structures using genetic programming to satisfy functional and geometric constraints

A system to generate a 3-dimensional (3D) structure, the system comprising:

• one or more processors;
• a procedure generation module at least one of controllable and executable by the one or more processors, and configured to initialize a plurality of vertex-rule-graph (VRG) systems, the VRG systems configured to provide rules that specify edge connections between vertices and property parameters of the vertices;
• a procedure application module at least one of controllable and executable by the one or more processors, and configured to apply the rules of the VRG systems to an initial set of vertices to generate a plurality of 3D graphs, each of the 3D graphs associated with one of the VRG systems, wherein the initial set of vertices is associated with a designated interaction surface of a 3D model;
• a skeleton geometry generation module at least one of controllable and executable by the one or more processors, and configured to generate a plurality of skeleton geometries, each of the skeleton geometries associated with one of the 3D graphs;
• an optimization module at least one of controllable and executable by the one or more processors, and configured to calculate an objective function for each of the skeleton geometries, the objective function configured to evaluate fitness of the skeleton geometries based on given constraints, wherein the given constraints comprise at least one of a fitting volume, an avoidance volume, a symmetry requirement, the interaction surfaces, a maximum total length of the edge connections, and a maximum mass of the 3D structure;
• and
• a genetic programming module at least one of controllable and executable by the one or more processors, and configured to generate the 3D structure through iterative application of genetic programming to a selected subset of the plurality of VRG systems, the genetic programming iterations to minimize the objective function, wherein the genetic programming module is further configured to perform graph crossovers of the VRG systems and to apply mutations to the rules and vertices of the VRG systems.