Constrained Hybrid Metaheuristic Algorithm for Probabilistic Neural Networks learning

This study investigates the potential of hybrid metaheuristic algorithms to enhance the training of Probabilistic Neural Networks (PNNs) by leveraging the complementary strengths of multiple optimisation strategies . Traditional learning methods, such as gradient-based approaches, often struggle to optimise high-dimensional and uncertain environments, while single-method metaheuristics may fail to exploit the solution space fully. To address these challenges, we propose the constrained Hybrid Metaheuristic (cHM) algorithm, a novel approach that combines multiple population-based optimisation techniques into a unified framework. The proposed procedure operates in two phases: an initial probing phase evaluates multiple metaheuristics to identify the best-performing one based on the error rate, followed by a fitting phase where the selected metaheuristic refines the PNN to achieve optimal smoothing parameters. This iterative process ensures efficient exploration and convergence, enhancing the network's generalisation and classification accuracy . cHM integrates several popular metaheuristics, such as BAT, Simulated Annealing, Flower Pollination Algorithm , Bacterial Foraging Optimisation, and Particle Swarm Optimisation as internal optimisers. To evaluate cHM performance, experiments were conducted on 16 datasets with varying characteristics, including binary and multiclass classification tasks, balanced and imbalanced class distributions, and diverse feature dimensions. In the experimental evaluation, CHM outperforms individual metaheuristics by a large margin in all the metrics tested. Specifically, the average test accuracy metric is ranked first in 10 out of 16 datasets, with the runner-up method scoring only 3 wins. Similarly, in the average test precision metric, cHM is the winning method for 9 datasets, with the second method securing 3 wins. Finally, in the average test recall metric, the respective figures are 8 wins for CHM and 5 for the second-best method. At the same time, due to its composite nature, CHM's average training fit time is about 2-3 times greater than the average time for the competing single metaheuristics. Overall, the results demonstrate that cHM effectively combines the strengths of individual metaheuristics, leading to faster convergence and more robust learning. The proposed method improves classification performance across diverse datasets by optimising the smoothing parameters of PNNs, proving its application flexibility and efficiency. • Proposes a hybrid metaheuristic for Probabilistic Neural Networks . • Combines swarm-based methods to enhance accuracy and convergence. • Optimises smoothing factors through adaptive space exploration. • Tests the algorithm on 16 diverse datasets. • Ensures efficient and reproducible training procedures.