IJPAM: Volume 66, No. 3 (2011)
ADAPTIVE NEIGHBORING IN HYBRID CELLULAR
AUTOMATA FOR TOPOLOGY OPTIMIZATION





University of Notre Dame
365, Fitzpatrick Hall, Notre Dame, Indiana, 46556, USA




Virginia Polytechnic Institute and State University
Mail Code 0106, Blacksburg, Virginia, 24061, USA
e-mail: ltw@cs.vt.edu
Abstract.The hybrid cellular automaton (HCA) method is a biologically
inspired algorithm capable of topology synthesis. Karush-Kuhn-Tucker
(KKT) optimality conditions have been derived to determine the
expression for the local evolutionary rules that guide synthesis
process. While averaging techniques have been used to mitigate
numerical instabilities such as checkerboard patterns and mesh
dependency, some questions have been raised whether KKT conditions
are fully satisfied in the final topologies. Furthermore, the
averaging procedure might result in cancellation or attenuation of
the error between the field variable and its target. The objective
of this work is to develop an adaptive neighboring scheme to
guarantee the satisfaction of the KKT conditions while minimizing
numerical instabilities. This approach is demonstrated in the topology optimization of a classic Mitchell-type structure using the
HCA method.
Received: November 4, 2010
AMS Subject Classification: 90C90
Key Words and Phrases: structural optimization, filtering, checkerboarding, optimality conditions, mathematical programming
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 66
Issue: 3