## 1 Introduction  
Wireless Sensor Networks have become a popular field of exploration for researchers and engineers [1]. WSNs find applications in various domains such as military, civilian, healthcare, industrial, agriculture, animal tracking, and habitat monitoring [2, 3]. These networks consist of distributed, random, low-power, and miniature sensor nodes that acquire data about the monitored environment through intermediate nodes. However, energy scarcity remains a major obstacle due to slow growth in battery capacity. Moreover, battery replacement is not a viable option due to the unattended nature and hazardous sensing conditions of sensor nodes. Therefore, energy efficiency is a fundamental concern in WSNs [4, 5], and several researchers have conducted relevant studies in this field. WSN routing techniques aim to enhance resource awareness and adaptability to prolong network lifespan and overcome low battery capacity [6, 7, 8]. Clustering approaches are often used to group sensor nodes due to their scalability, resource sharing, energy efficiency, low communication overhead, and efficient resource allocation. However, selecting cluster heads poses a critical optimization problem, which is considered NP-hard [9, 10, 11]. Furthermore, heterogeneous wireless sensor networks (HWSNs) are increasingly being utilized in practical applications. Therefore, there is a need to consider an optimization technique for cluster head selection in HWSNs [12, 13]. And swarm intelligence and metaheuristic methods offer several advantages in addressing the cluster head selection problem within HWSNs. These methods exhibit global search capabilities, adaptability, flexibility, scalability, parallel processing, and decentralization, among other benefits. These advantages make them effective tools for tackling large-scale and complex CH selection problems, ultimately enhancing the performance and energy efficiency of heterogeneous wireless sensor networks. Considering the aforementioned challenges, we propose the use of swarm intelligence and metaheuristic methods to improve the cluster head selection process. In order to prolong the lifespan of heterogeneous wireless sensor networks, we introduce an exploration-enhanced version of the Pelican Optimization Algorithm (POA), called Enhanced POA (EPOA). In general, existing clustering methods may suffer from incomplete, uncertain, and inconsistent information due to a lack of understanding of the measurement environment and limitations in sensor accuracy. Therefore, in our current work, we propose a novel algorithm that can address these challenges, aiming to enhance clustering performance and improve energy utilization efficiency. Regarding traditional fitness functions, they often come with certain limitations, such as local optima, problem dependency, convergence speed, and overfitting. Local Optima: Inappropriate fitness functions might cause the algorithm to become trapped in local optima, failing to find the global optimal solution. Problem Dependency: Different problems may require distinct fitness functions. A fitness function performing well on one problem might not be effective for another problem. Convergence Speed: The design of the fitness function can impact the algorithm's convergence speed. An unfit fitness function can result in slow convergence. Overfitting: Excessively complex fitness functions might perform well on the training set but exhibit poor generalization on unknown data. Hence, in our approach, we adopt a new fitness function to select efficient energy-saving cluster head nodes, aiming to overcome these limitations associated with traditional fitness functions. The following are this paper's key contributions:  
* The logistic-sine chaotic mapping method is employed to improve the initialization of random solutions, allowing for the generation of uniformly distributed and non-repetitive initial solution sets. * The levy flight algorithm is utilized to enhance global optimization capability and enrich the population diversity of the EPOA algorithm.