The nodes in mobile wireless sensor networks (MWSNs) are usually with limited hardware resources, which leads to the limitation of transmission range and energy. To extend the communication distance of a single sensor node, distributed collaborative beamforming (DCB) based on a virtual node antenna array (VNAA) can be used in MWSNs. The locations and excitation current weights are the key factors that affect the performance of DCB, thus the nodes of a MWSN can move to better locations to achieve a lower maximum sidelobe level (SLL) of the beam pattern, thereby reducing the communication interferences and enhancing the directivity. However, the moving energy consumption will be increased. In this paper, a joint optimization problem for optimizing the maximum SLL of beam pattern, transmission power and moving energy consumption of DCB nodes in MWSNs is proposed, and the NP-hardness of the formulated problem is proven. Then, we propose a distributed parallel cuckoo search algorithm (DPCSA), which is a nature-inspired approach, to solve the formulated joint optimization problem. Simulation results verify that the maximum SLL, transmission power and moving energy consumption of DCB nodes can be optimized effectively. Moreover, the performance and stability of the proposed DPCSA are evaluated.

移动无线传感器网络（MWSN）中的节点通常具有有限的硬件资源，这导致了传输范围和能量的限制。为了扩展单个传感器节点的通信距离，可以在MWSN中使用基于虚拟节点天线阵列（VNAA）的分布式协作波束成形（DCB）。位置和激励电流权重是影响DCB性能的关键因素，因此MWSN的节点可以移至更好的位置，以实现较低的波束方向图最大旁瓣电平（SLL），从而减少通信干扰并增强方向性。但是，移动能量消耗将增加。本文提出了一种用于优化波束方向图最大SLL的联合优化问题，提出了MWSN中DCB节点的传输功率和移动能耗，证明了所提问题的NP难点。然后，我们提出了一种分布式并行杜鹃搜索算法（DPCSA），它是一种自然启发方法，用于解决制定的联合优化问题。仿真结果表明，可以有效地优化DCB节点的最大SLL，传输功率和移动能耗。此外，评估了建议的DPCSA的性能和稳定性。可以有效地优化DCB节点的传输功率和移动能耗。此外，评估了建议的DPCSA的性能和稳定性。可以有效地优化DCB节点的传输功率和移动能耗。此外，评估了建议的DPCSA的性能和稳定性。