An efficient partial charging and data gathering strategy using multiple mobile vehicles in wireless rechargeable sensor networks Chandra Bhushan Kumar Yadav 1 • Dinesh Dash 1 Received: 4 December 2023 / Revised: 6 March 2024 / Accepted: 6 March 2024 Ó The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024 Abstract Wireless rechargeable sensor networks (WRSNs) are a popular and promising field of research that can be used in many different fields. The battery life and storage space of the sensors are limited, due to this it is hard to keep the network up for longer. Combining wireless energy transfer and wireless data gathering devices on a Mobile Vehicle (MV) is one solution to this challenge. The objective of this work is to reduce the number of dead sensors and packet delivery delay. We proposed the circle-covering based algorithm to determine sojourn point based on energy consumption rates and the location of sensors. An Improved Grey Wolf Optimization (IGWO) meta-heuristic algorithm partitions the network into the minimum number of regions, assigns a MV to each region, and ensures balanced sub-tour lengths among the regions. A novel weight function is proposed to determine the order of the sojourn points. To accomplish our objectives, we propose a heuristic partial charging and data gathering strategy to determine the sojourn times of the MVs at the sojourn points. The performance of our proposed PCDGS scheme is compared with IMPSS, PMCDC, MOAC and JERDC schemes. The simulation results show that our proposed PCDGS scheme outperforms the others. Keywords Wireless energy transfer  Mobile vehicle  Partial charging and data gathering  Meta-heuristic algorithm  Wireless rechargeable sensor networks 1 Introduction WRSNs based applications for agricultural and industrial services, such as environmental monitoring, traffic man- agement, and soil moisture surveillance, have been devel- oped [1, 2]. However, the major issue with WRSNs is that the sensors have a small amount of storage and battery capacity, which reduces the network’s lifespan and degrades performance. To improve the network lifespan various strategies have been developed for the sustain- ability of WRSNs. Two novel technologies, wireless energy transmission and wireless data collection using MV have the potential to significantly extend network lifetime. One of the essential aspects of WRSNs is data gathering. While transmitting and receiving the data, sensors consume more energy than other activities. The energy consumption of wireless data gathering can be reduced by minimizing the distance between the receiver and transmitter. In con- ventional data gathering methods [3], mobile sinks are often used to collect data by visiting each sensor. Due to the slow speed of mobility data collector, the data collec- tion delay is high [4]. To solve this difficulty, the WRSNs system has recently adopted the high-mobility data col- lector to enhance the performance of WRSNs [5]. Efficient path planning of mobility data collector increases the energy efficiency and reduces the packet delivery delay. In the traditional charging technique [6] the sensors receive energy from the environment energy sources [7–9]. Due to the variable or unpredictable environmental energy power, sometimes it is not easy to maintain the network live. Wireless charging [10] is a new method to increase the energy efficiency of WRSNs. The significant development in wireless energy transfer (WET) has created a new thing for radio frequency signals to be used for wireless charg- ing. This makes for a more reliable energy source. WET is a promising technology based on resonance coupling tech- nology [11, 12]. The energy can be transferred effectively & Dinesh Dash dd@nitp.ac.in Chandra Bhushan Kumar Yadav chandrabhushankumary.phd19.cs@nitp.ac.in 1 Department of Computer Science & Engineering, National Institute of Technology Patna, Patna, Bihar 800005, India 123 Cluster Computing https://doi.org/10.1007/s10586-024-04425-3