A Generic Scheme for Graph Topology Optimization

This research offers a fundamental new approach to topology optimization. To date, topological synthesis approaches are simply augmentations of existing stochastic optimization techniques. While these algorithms are useful in complex parametric design spaces, they are not designed for all topology problems. This paper describes a generalized scheme for solving topological design problems. The approach combines aspects of existing optimization techniques, graph theory, mathematical programming, artificial intelligence, and shape and graph grammars. Specifically, the approach has advantages over modified parametric optimization algorithms in that 1) a two stage technique to developing solutions and searching the parametric design space more closely models the design process performed by humans and more thoroughly maps how various topologies are represented, 2) a graph grammar for generating candidate solutions minimizes the wasted search of infeasible topologies, and 3) a new stochastic guidance strategy intelligently distinguishes and independently controls the variables that alter topologies and the variables that represent dimensions and parameters. This automated design synthesis method is currently being developed to synthesize the best graph for a various applications, where the choice of nodes in the graph and how they are to be connected is determined through computational search. Such topological problems are prevalent in engineering design. Examples include truss structures, designing sheet metal components, designing the location and connection of roadways, and designing the choice and connection of processors in a chemical plant.