Node clustering is an efficient technique for saving energy of wireless sensor networks (WSNs). In this paper we present a novel hybrid multi-level clustering scheme that combines a traditional, appropriately modified, gradient-based clustering protocol with an evolutionary optimization method that is mainly based on the Gravitational Search Algorithm (GSA). The proposed scheme aims at improved performance over large in size networks, where classical schemes in most cases lead to non-efficient

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... olutions. It first creates suitably balanced multi-hop clusters, in which the sensors energy gets larger as coming closer to the cluster head (CH). This scheme is then extended to generate a hierarchy of cluster-heads with the same characteristics; note that the energy savings increase with the number of levels in the hierarchy. In the last level of the proposed scheme a suitable protocol based on the GSA runs to associate sets of top-level cluster-heads to specific gateway nodes for the eventual relaying of data to the base station (BS). The fitness function was appropriately chosen considering both the distance from the cluster heads to the gateway nodes and the remaining energy of the gateway nodes, and it was further optimized in order to gain more accurate results for large instances. Extended experimental measurements demonstrate the efficiency and scalability of the presented approach over very large WSNs, as well as its superiority over other known clustering approaches of the literature, with the same objectives.