Integration of multi agent reinforcement learning with golden jackal optimization for predicting average localization error in wireless sensor networks

Wireless Sensor Networks (WSNs) used in modern applications like environmental monitoring, smart cities, and healthcare systems depend on accurate sensor node localization. However, attaining accurate localization is challenging due to dynamic environmental conditions. Varying network densities and the interdependence of parameters such as anchor ratio, transmission range, and node density increase the Average Localization Error (ALE) in WSNs. Existing methodologies, including regression-based models, heuristic approaches, and optimization-driven methods, struggle to generalize across dynamic environments due to their reliance on static parameter configurations. Machine learning-based approaches have improved localization accuracy but require extensive labeled datasets and often lack adaptability to real-time variations. Traditional optimization techniques tend to converge with local optima, limiting their effectiveness in dynamically changing network topologies. To overcome these limitations, a novel Multi-Agent Reinforcement Learning (MARL) algorithm is proposed in this research, combined with Golden Jackal Optimization (GJO). The proposed optimized MARL framework dynamically learns optimal parameter adjustments through a reward mechanism, minimizing localization error and its variability even under dynamic network conditions. The GJO algorithm fine-tunes the hyperparameters of MARL to improve generalization across different WSN configurations. The proposed model is evaluated using a benchmark dataset, and performance metrics such as Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Square Error (RMSE), R-squared (R²), and Mean Absolute Percentage Error (MAPE) are analyzed. Experimental results demonstrate that the proposed model significantly outperforms existing methods such as Grid Search RF, Bayesian Optimized RF, Gradient Boosting, and Deep Neural Networks. The proposed approach achieves an MSE of 0.02, MAE of 0.11, RMSE of 0.14, R² of 0.88, and MAPE of 2.5%, reflecting its ability to adapt dynamically and improve localization accuracy compared to static or heuristic models.