Optimizing brain networks topologies using multi-objective evolutionary computation.

The analysis of brain network topological features has served to better understand these networks and reveal particular characteristics of their functional behavior. The distribution of brain network motifs is particularly useful for detecting and describing differences between brain networks and random and computationally optimized artificial networks. In this paper we use a multi-objective evolutionary optimization approach to generate optimized artificial networks that have a number of topological features resembling brain networks. The Pareto set approximation of the optimized networks is used to extract network descriptors that are compared to brain and random network descriptors. To analyze the networks, the clustering coefficient, the average path length, the modularity and the betweenness centrality are computed. We argue that the topological complexity of a brain network can be estimated using the number of evaluations needed by an optimization algorithm to output artificial networks of similar complexity. For the analyzed network examples, our results indicate that while original brain networks have a reduced structural motif number and a high functional motif number, they are not optimal with respect to these two topological features. We also investigate the correlation between the structural and functional motif numbers, the average path length and the clustering coefficient in random, optimized and brain networks.