Optimal domain decomposition via -median methodology using ACO and hybrid ACGA

In this paper an efficient method is developed for decomposing large-scale finite element meshes. A weighted incidence graph is used to transform the connectivity properties of finite element models into those of graphs. A graph G_c of manageable size is obtained from the main graph model by a coarsening algorithm. The p-medians of this graph are selected using two approaches. The first algorithm uses an ant colony optimization and the second algorithm employs a hybrid ant colony together with genetic algorithm. Here, p is the number of subdomains which the finite element meshes is intended to be decomposed. Once the medians are obtained, the nodes in G_c associated with each median are selected. In an expansion process, the nodes of the subdomains in G are obtained. The capabilities of both ant colony optimization, and hybrid ant colony and genetic algorithm are evaluated using many examples of different topology.