The optimization of energy consumption in wireless sensor networks (WSNs) is a critical endeavor essential for sustaining network functionality and reliability, particularly given their widespread applications in fields such as disaster management, environmental monitoring, healthcare, and water quality assessment. WSNs are designed to prioritize data-centric tasks, necessitating high network efficiency and minimal transmission delays to support real-time data processing requirements [1–3]. Due to the dynamic nature of these networks, the management of their topology presents a significant challenge, emphasizing the need for efficiency, scalability, resource allocation, and reliability [4, 5]. Effective topology management plays a pivotal role in maintaining network stability, dependability, and performance consistency. In this context, Probabilistic Cluster Routing (PCR) emerges as a promising strategy to improve energy efficiency by dynamically selecting cluster heads based on factors such as node attributes, proximity to the sink node, and remaining energy levels. Through organizing nodes into clusters and intelligent data routing within these clusters, PCR aims to reduce energy consumption while upholding network performance standards, ultimately ensuring the sustainability and longevity of WSNs [6].