Convergence analysis of hybrid cellular automata for topology optimization
2009) Convergence analysis of hybrid cellular automata for topology optimization . Technical Report TR-09-07, Computer Science, Virginia Tech. (
The hybrid cellular automaton (HCA) algorithm was inspired by the structural adaptation of bones to their ever changing mechanical environment. This methodology has been shown to be an eﬀective topology synthesis tool. In previous work, it has been observed that the convergence of the HCA methodology is aﬀected by parameters of the algorithm. As a result, questions have been raised regarding the conditions by which HCA converges to an optimal design. The objective of this investigation is to examine the conditions that guarantee convergence to a Karush-Kuhn-Tucker (KKT) point. In this paper, it is shown that the HCA algorithm is a ﬁxed point iterative scheme and the previously reported KKT optimality conditions are corrected. To demonstrate the convergence properties of the HCA algorithm, a simple cantilevered beam example is utilized. Plots of the spectral radius for projections of the design space are used to show regions of guaranteed convergence.
|Item Type:||Departmental Technical Report|
|Keywords:||Fixed point iteration, spectral radius analysis, structural optimization, cellular automata convergence|
|Subjects:||Computer Science > Algorithms and Data Structure|
|Deposited By:||Administrator, Eprints|
|Deposited On:||20 March 2009|