## 1 Introduction  
The imperative pursuit of sustainable development, encompassing the multifaceted dimensions of social, environmental, and economic well-being, demands innovative tools that effectively address complex challenges [1]. These challenges include broad issues like poverty and climate change, but also more specific and pressing concerns such as rice leaf disease [2] and implementing robust waste classification [3]. Tackling these intricacies requires a holistic approach that leverages cutting-edge solutions and embraces technological advancements to drive positive change and foster a resilient future for our planet. In this context, machine learning (ML) emerges as a potent force, enabling data-driven insights and solutions across diverse domains such as renewable energy optimization [4], climate change mitigation [5], and personalized healthcare [6]. However, traditional centralizedML approaches encounter limitations, particularly concerning data privacy concerns and resource constraints, especially in geographically distributed settings [7]. Federated learning (FL) is a transformative paradigm for sustainable development by decentralizing the ML model training process to the edges, where data reside on individual devices or local servers [8; 9]. This decentralized approach preserves data privacy and alleviates resource limitations, all while harnessing the collective power of geographically dispersed data [10]. Nonetheless, a fundamental challenge in FL lies in the communication bottleneck between the central server and the myriad of edge devices [11]. The frequent exchange of model updates during training incurs significant communication overhead, impeding scalability and sustainability in resource-constrained environments [12]. Metaheuristic algorithms, characterized by their ability to explore solution spaces efficiently, have become indispensable tools in overcoming challenges associated with optimization problems [13]. In the context of FL, where communication bottlenecks pose significant hurdles, leveraging metaheuristic algorithms offers a powerful strategy to enhance the efficiency of the training process [14]. Metaheuristic algorithms draw inspiration from natural optimization phenomena, often mirroring the evolutionary processes observed in biological systems, swarm behaviors, or physical phenomena [15; 16]. These algorithms exhibit a capacity for global optimization by navigating vast solution spaces in search of optimal or near-optimal solutions [17]. Importantly, metaheuristic algorithms are particularly well-suited for complex, non-linear, and high-dimensional problems, making them invaluable in the realm of ML [18]. The essence of metaheuristic algorithms lies in their ability to strike a delicate balance between exploration and exploitation [19]. Exploration involves systematically searching the solution space to discover new potential solutions, while exploitation focuses on refining and exploiting promising solutions to improve overall performance [20]. This balance is crucial in achieving a convergence of the algorithm towards optimal solutions while avoiding premature convergence to suboptimal solutions [21; 22]. In the case of FL, the communication bottleneck arises due to the constant exchange of model updates between the central server and distributed edge devices [23]. Metaheuristic algorithms offer an elegant solution by guiding the selection of relevant model updates strategically [24]. By minimizing the communication cost associated with sharing updates, these algorithms alleviate the strain on the network, enabling more scalable and sustainable FL systems [25]. Among the myriad metaheuristic algorithms, the Lemurs optimizer (LO) is particularly noteworthy for its distinctive qualities [26]. The LO is inspired by the cooperative foraging behavior of lemurs, showcasing a unique optimization approach. Its efficiency lies in its ability to dynamically adapt its exploration and exploitation strategies based on the evolving characteristics of the optimization landscape [27].