A Graph Topology Optimization Method for the Synthesis of Robust And Efficient Routes

Several renowned classical tree search methods such as depth first, breadth first, A-star etc. are in place today for dealing with problems of topology and parametric optimization. We propose a novel optimization technique based on mathematical graph transformations in order to synthesize feasible and optimal graph topologies. This paper demonstrates the methodology and results from the application of this new optimization method to the Route test problem. The power of the approach lies in the high level of abstraction afforded by the usage of mathematical graphs and the fact that the entire optimization process is viewed as a large tree search. Additionally the generic nature of the method enables tackling problems of a multi-disciplinary nature to be a feasible proposition in the future. The optimization technique is broken up into four separate modules named representation, generation, guidance, and evaluation. The modules correspond to problem formulation (representation), synthesizing a broad spectrum of feasible topologies (generation), navigating the search process towards progressively better solutions (guidance) and evaluating the worth of each topology respectively (evaluation). This fundamentally new optimization method is specifically intended for performing topology optimization of graphs and thus has potential application in domains as varied as engineering, computer science and artificial intelligence