Simulation settings.

In wireless sensor networks (WSNs), existing routing protocols mainly consider energy efficiency or security separately. However, these protocols must be more comprehensive because many applications should guarantee security and energy efficiency, simultaneously. Due to the limited energy of sensor nodes, these protocols should make a trade-off between network lifetime and security. This paper proposes a cluster-tree-based trusted routing method using the grasshopper optimization algorithm (GOA) called CTTRG in WSNs. This routing scheme includes a distributed time-variant trust (TVT) model to analyze the behavior of sensor nodes according to three trust criteria, including the black hole, sink hole, and gray hole probability, the wormhole probability, and the flooding probability. Furthermore, CTTRG suggests a GOA-based trusted routing tree (GTRT) to construct secure and stable communication paths between sensor nodes and base station. To evaluate each GTRT, a multi-objective fitness function is designed based on three parameters, namely the distance between cluster heads and their parent node, the trust level, and the energy of cluster heads. The evaluation results prove that CTTRG has a suitable and successful performance in terms of the detection speed of malicious nodes, packet loss rate, and end-to-end delay.