Training feedforward neural networks (FFNN) is a complex process that requires determining the right weights and biases, crucial parameters that largely dictate the FFNN’s effectiveness. Traditional methods like gradient descent are common in FFNN training but have limitations, including the risk of becoming trapped in local minima. Evolutionary algorithms present a solution to bypass these issues. This study takes into consideration the effectiveness of three differential evolution variations in FFNN training: the conventional DE, an opposition-based DE, and a novel centroid-based DE. The most successful among these, the centroid-based DE algorithm, called CQODTA, integrates a centroid-based method and dynamic opposition-based learning with differential evolution. The centroid method uses the centre point of the top-performing individuals as a reference for population updates, while the rest are adjusted using the usual crossover and mutation techniques. This method effectively affects the search space due to its reliance on the leading individuals. Simultaneously, the opposition-based learning concept, which takes the opposite of an existing solution, bolsters the algorithm’s ability to search broadly. We compare our trio of DE-based training methods against 14 other variants. Our thorough testing demonstrates the DE-based trainers’ adeptness at tackling various complex tasks.