The self-adaptive Cuckoo genetic algorithm for echo state networks optimization

This paper introduces the Self-Adaptive Cuckoo Genetic Algorithm (SACGA) for Echo State Network (ESN) optimization. Traditional Genetic Algorithms (GAs) of- ten simplify the search space or focus solely on error minimization, overlooking key factors such as the reservoir quality of ESN. The proposed SACGA addresses these limitations by optimizing all hyperparameters across the entire search space and incorporating the concept of separation, as a reservoir quality metric, in the fit- ness evaluation alongside the standard predictive error minimization criterion. The SACGA features a novel design that integrates a self-adaptive mutation mechanism and Cuckoo-inspired offsprings within a traditional GA framework, for an opti- mal balance between exploration and exploitation. The self-adaptive mechanism dynamically adjusts the mutation rates, affecting both the crossover and mutation processes. The Cuckoo-inspired offsprings, generated via the Lévy flight mecha- nism, explore the search space’s boundaries. The SACGA outperforms baseline GAs (with fixed mutation rates of 10% and 1%, and a deterministic mutation rate scheme) in Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) metrics on benchmark datasets (Multiple Superimposed Oscillator, Mackey-Glass, Nonlinear Auto-Regressive Moving Aver- age). Results show faster convergence to lower error rates highlighting its efficiency in ESN optimization for time series prediction.