An Optimization Approach/Technique for Solving Graph Based Design Problems

This paper discusses a new topological optimization technique to solve graph based engineering design problems by decoupling parameters and topology changes. Using this approach optimal solutions are synthesized in the form of graph topologies for engineering problems. Currently we have successfully applied it to routing problems, resistive networks, neural networks, and sheet metal. This final problem has proven the most challenging but the results are not only novel and manufacturable but also satisfy multiple objective functions such as material cost and manufacturability. This paper presents Topological and Parametric Tune and Prune (TP²) as the first topology optimization method that has been developed specifically for domains representable by a graph grammar schema. The method is stochastic and incorporates distinct phases for modifying the topologies and modifying parameters stored within topologies. Thus far, with the problems that been tested, (TP²) had proven better than genetic algorithm in terms of the quality of solutions and time taken to acquire them.