## 1 Introduction  
Wireless sensor networks (WSNs) are widely applied in various fields due to their low cost, scalability, self-organizing dynamics, and fault tolerance characteristics [1], such as environmental monitoring [2], medical treatment [3], elderly care services [4], intelligent transportation [5], and manufacturing systems [6]. Despite these benefits, the development of WSNs is hindered by the limited battery capacity of the sensors [7]. Furthermore, frequent battery replacement is often cumbersome, costly, dangerous, and unrealistic. To address the problems mentioned above, researchers have made nodes passively collect solar [8], wind [9], or thermoelectric [10] energy from the environment in energy harvesting WSNs to prolong the network lifetime. However, these approaches could be more stable and predictable. In recent years, with the advancement of wireless power transfer technology, a new concept of wireless rechargeable sensor networks (WRSNs) has emerged, where mobile chargers (MC) with a large capacity provide a highly reliable and efficient energy supplement to the nodes. Therefore, the study of MC charging strategies in WRSNs has recently gained significant attention [11, 12, 13, 14, 15]. In practical network applications, the quality of information (QoI) is essential in network performance. Different performance indexes are used to evaluate network QoI for different applications, including quality of coverage [16, 17] in environmental monitoring networks, tracking accuracy [8] in target tracking networks, and detection probability [18, 19]in event detection networks. The energy consumption of nodes in the network is different. If the MC charging sequence scheduling is unreasonable, the nodes will run out of energy because they cannot be charged in time. It leads to the vulnerabilities in network sensing coverage, information loss, and reduced reliability. Although the optimization of QoI in WSNs has become more sophisticated [20], more research needs to be conducted on WRSNs. As a critical factor in evaluating the network coverage performance, quality of sensing coverage (QSC) is the foundation of network credibility. This paper studies the novel problem of mobile charging sequence scheduling for network QSC (MSSQ); how to optimize the mobile charging sequence of MC to maximize the network QSC. In the MSSQ problem, the state of all nodes changes correspondingly based on the same MC charging decisions made at different times, unlike in the traveling salesman problem. Thus, the MSSQ problem can be formulated as an extended traveling salesman problem (ETSP). Quantum-behaved particle swarm optimization (QPSO) is a novel optimization algorithm based on swarm intelligence with the potential to find practical solutions to NP complete problems due to the gravitational effect of quantum potential energy. To enhance the convergence efficiency of the algorithm, we present an improved QPSO (IQPSO) approach, which adaptively adjusts the contraction expansion coefficient during iterations to optimize convergence speed while ensuring convergence. The contributions of the paper are summarized as follows:  
(1) In this paper, the impact of nodes' sensing coverage contributions at different times on network QSC is considered in WRSNs, and a novel mobile charging sequence scheduling for network QSC (MSSQ) problem is studied. (2) The MSSQ problem is formulated as an ETSP based on a new performance index for network QSC, named the total sensing coverage and node survival rate (\(TSCNS\)), which considers the sensing coverage performance and node survival rate. (3) An effective IQPSO algorithm is proposed for MSSQ to obtain the suboptimal mobile charging sequence faster, to avoid falling into local optima. The rest of the paper is organized as follows: Section 2 introduces the related work. The mobile charging WRSNs and sensing coverage models are described in Section 3. The MSSQ problem is formulated mathematically in Section 4.