Handling Stagnation in Differential Evolution Using Elitism Centroid-Based Operations

Differential evolution (DE) algorithms are simple and efffcient evolutionary algorithmsthat perform well in various optimization problems. Unfortunately, they inevitably stagnate when differential evolutionary algorithms are used to solve complex problems (e.g., real-world artiffcial neural network (ANN) training problems). To resolve this issue, this paper proposes a framework based on an efffcient elite centroid operator. It continuously monitors the current state of the population. Once stagnation is detected, two dedicated operators, centroid-based mutation (CM) and centroid-based crossover (CX), are executed to replace the classical mutation and binomial crossover operations in DE. CM and CX are centred on the elite centroid composed of multiple elite individuals, constituting a framework consisting of elitism centroid-based operations (CMX) to improve the performance of the individuals who fall into stagnation. In CM, elite centroid provide evolutionary direction for stagnant individuals, and in CX, elite plasmoids address the limitation that stagnant individuals can only obtain limited information about the population. TTe CMX framework is simple enough to easily incorporate into both classically well-known DEs with constant population sizes and state-of-the-art DEs with varying populations. Numerical experiments on benchmark functions show that the proposed CMX method can signiffcantly enhance the classical DE algorithm and its advanced variants in solving the stagnation problem and improving performance.