Hybrid Nelder–Mead Algorithm and Dragonfly Algorithm for Function Optimization and the Training of a Multilayer Perceptron

Dragonfly algorithm (DA) is a new optimization technique based on swarm intelligence. DA simulates the static and dynamic swarming behaviors of dragonflies in nature. The search pattern of DA consists of two essential phases: exploration and exploitation that are inspired by the survival rule of dragonflies in navigating, searching for food and fleeing enemies when dynamically or statistically swarming. This method is straightforward to implement and is efficient in solving real-world problems. However, an excessive number of social interactions in DA may result in low solution accuracy, easy stagnation at local optima and an imbalance between exploration and exploitation. To overcome these deficiencies, an improved Nelder–Mead algorithm is added to the conventional DA (INMDA) to strengthen its local explorative capability and avoid the possibility of falling into local optima. Simulation experiments were conducted on several well-known benchmark functions with different dimensions. In addition, the three classic classification problems are utilized to benchmark the performance of the proposed algorithm in training a multilayer perceptron. The experimental results and statistical significance show that the performance of the proposed INMDA is superior to that of the other algorithms.