The idea of using metaheuristics algorithms to train a neural network (NN) has gained increasing interest in recent years. This paper investigates the limitation of standard backpropagation algorithms in optimizing a NN such as convergence problems and sensitivity to initial parameters and proposes a hybrid optimization method called Particle Swarm Optimization-Backpropagation-Differential Evolution-Feedforward Neural Network (PSO-BP-DE-FNN) to address these limitations for heart disease prediction. The methodology involves using an FNN architecture and training using BP, where the weights and biases are iteratively adjusted to minimize the loss function. The PSO and DE algorithms are used as global optimization techniques to explore the search space and improve the performance of the FNN. Our paper demonstrates the feasibility and effectiveness in terms of accuracy and loss score of the hybrid PSO-BP-DE-NN approach for heart disease prediction in comparison to three other approaches. It is shown that the suggested hybrid algorithm offers a promising approach for tackling complex prediction and classification tasks in healthcare.