Network optimization which has to consider both the connection distance (detour) between different nodes and the total length (costs) of the network, belongs to the class of frustrated optimization problems Here, evolutionary strategies which include both thermodynamic and biological elements, are used to find different optimized solutions (graphs of varying density) for the network in dependence on the degree of frustration. We show, that the optimization process occurs on two different time scales, and that in the asymptotic limit a a fixed relation between the mean connection distance (detour) and the total lenght (costs) of the network exist.
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