## 3 Problem Statement  
ANNs are currently recognized as powerful tools for addressing a wide range of complex scientific and technical challenges. However, the lack of a standardized approach for structuring and synthesizing the parameters of ANN models significantly impedes their practical application. Additionally, the computational demands of evolutionary algorithms often require substantial hardware resources, making their execution difficult on conventional personal computers. To mitigate this issue, the use of parallel evolutionary algorithms or DCSs can significantly reduce computational time. Parallel execution allows for the simultaneous processing of calculations, a feature that sequential programming cannot offer. Distributed computing networks (CNs) provide the necessary hardware infrastructure for parallel processing, offering a promising solution to the computational challenges of ANN-based models. Advancements in network information technology and the availability of high-performance personal computers have greatly expanded access to computational resources, enabling more efficient solutions to complex problems. The capability of leveraging portable networks further enhances the computational potential of these systems. In tackling complex scientific and technical problems through computing, it is essential to develop formal methodologies that optimize network models, ultimately resulting in hardware-software systems capable of performing primary functions. The application of a Decision Support System (DSS) during the early stages of CN design or when modifying existing networks is vital. These systems are typically tailored to address intricate problems, driving technological advancements based on expert knowledge. DCSs are characterized by the spatial separation of their components and subsystems, which may arise due to size, environmental constraints, or specific functions. Among the most commonly used DCSs are centralized CNs, and this study focuses on their functional capabilities in addressing complex challenges. The choice of the GA as the core optimization method in this study is grounded in several methodological and practical considerations. First and foremost, GAs exhibit a well-established capacity for handling complex, multi-modal, and high-dimensional optimization tasks, which are characteristic of resource allocation and control in heterogeneous DCSs [33; 34]. Second, the inherently population-based structure of GAs maps naturally onto DCSs: each subpopulation (or \"island\") can be assigned to a different compute node, enabling concurrent evaluation and recombination with minimal synchronization overhead [35]. This island-model parallelism both accelerates convergence and enhances solution diversity in spaces such as those arising in ANN hyperparameter tuning and resource allocation. In contrast, PSO's update uses a swarm-wide global best:  
\[v_{i}^{t+1}=wv_{i}^{t}+c_{1}r_{1}(pbest_{i}-x_{i}^{t})+c_{2}r_{2}(gbest-x_{i}^ {t}),\]  
which explicitly depends on the global best position [36]. Maintaining this global information, each iteration across nodes incurs significant synchronization. DE's standard mutation also often uses global best or random pairs, which, similarly, can need coordination. The Spark PSO study highlights this: synchronous PSO had large idle times from global sync, while an asynchronous variant removed this overhead [37]. By contrast, GA can run fully asynchronously; for example, one distributed GA algorithm is reported to effectively use all CPU cores with multilevel parallelism [38]. Moreover, GA's operators (bit/string crossover and mutation) are simple and local, which suits resource-limited nodes. Taken together, GA's natural parallelism and lack of global dependencies make it compatible with heterogeneous or bandwidth-limited networks.