## 1 Introduction  
The widespread adoption of constantly connected devices over the past decade has led to a notable increase in energy consumption, creating challenges for the sustainability and efficiency of computational systems [1]. As global energy demands rise and electricity costs grow, the need to find effective solutions to optimize energy usage in communication and computation is becoming more evident [2, 3]. Resource Block Configurations (RBCs) provide a practical approach to addressing these challenges by reducing both the training time for neural networks and the energy consumption of computing clusters [4, 5].  
Artificial Neural Networks (ANNs), as mathematical constructs inspired by the structure and function of biological neural networks, have transformed various domains by enabling advancements in prediction, pattern recognition, and control [6]. Originating from early studies on cognitive processes, ANNs have evolved into powerful tools supported by learning algorithms, making them indispensable in tackling complex real-world problems. However, the computational demands associated with training and deploying ANNs remain a barrier, particularly as models grow in complexity and scale [7].  
Recent research has underscored the potential of machine learning (ML) algorithms, including ANNs, in diverse applications such as wireless networks, materials science, and industrial diagnostics [8; 9]. For instance, ML has been successfully applied to optimize wireless communication systems [10], automate diagnostics in industrial equipment [11], and predict material properties with high accuracy [12]. Yet, these applications often demand substantial computational resources, underscoring the importance of optimizing the underlying computational frameworks.  
Despite advancements in learning algorithms, ANNs still face fundamental challenges. For instance, the ability of ANNs to dynamically connect and integrate information is critical for developing an understanding of symbolic entities, such as objects [13]. Inadequacies in this area limit generalization capabilities and decision-making consistency. Addressing these limitations requires frameworks that combine segregation, representation, and composition of information [14].  
Parallel and distributed computing systems (DCSs) have emerged as a transformative solution to manage the escalating computational demands of ANNs. By leveraging parallelism, distributed systems divide large-scale computational tasks into smaller, more manageable subtasks, which are then processed concurrently [15]. This approach not only improves computational efficiency but also enables scalable solutions for resource-intensive applications [16]. Furthermore, distributed evolutionary algorithms offer advantages over traditional sequential methods, particularly in optimizing ANN architectures [17].  
This study presents a novel, integrated framework that combines RBCs with DCSs for energy-efficient and performance-optimized training of ANNs. Unlike prior works that apply traditional optimization methods in static or homogeneous computing environments [18; 19; 20], this approach introduces the use of parallel GAs specifically adapted to heterogeneous and dynamically reconfigurable DCS architectures. The framework uniquely incorporates the following:  
* Custom mathematical models for evaluating both performance and availability metrics of DCS nodes, enabling precise matching between computational tasks and resource profiles.
* A multi-objective optimization scheme that leverages Pareto-front analysis to jointly optimize energy consumption, computational latency, and system reliability--parameters that are rarely optimized in combination in the related literature.
* A GA-based decision-support system, which does not merely optimize ANN hyperparameters but also orchestrates resource allocation strategies across distributed nodes, adapting in real time to system feedback and load conditions.