RGN: A Triple Hybrid Algorithm for Multi-level Image Segmentation with Type II Fuzzy Sets

This paper presents a study focused on enhancing the effectiveness of cuckoo search (CS). The goal is to improve its performance in avoiding local optima, improve the exploration and exploit potentially new solutions. To achieve this, we incorporate three additional algorithms – grey wolf optimizer (GWO), red panda optimization (RPO), and naked mole rat algorithm (NMRA) – into the basic CS framework to strengthen its exploration and exploitation capabilities. The resulting hybrid algorithm is named RGN, standing for red panda, grey wolf and naked mole-rat. To make the parameters of the RGN algorithm adaptable, six new mutation operators and inertia weights are added to the proposed RGN algorithm. The proposed algorithm is tested on CEC 2005, CEC 2014, and CEC 2022 benchmark problems to prove its effectiveness. Friedman test and Wilcoxon rank-sum tests, are done to analyse the significance of the proposed RGN algorithm statistically. It has been found that the proposed RGN is significantly better with respect to LSHADE-SPACMA, SaDE, SHADE, CMA-ES, extended GWO, hierarchical learning particle swarm optimization (FHPSO), Kepler optimization algorithm (KOA), improved chef-based optimization algorithm (CBOADP), improved symbiotic herding optimization (IMEHO), blended-biogeography based optimization (B-BBO), and Laplacian BBO (LX-BBO), among others. Application of the proposed algorithm RGN for Multilevel Image Thresholding with Type II Fuzzy Sets, shows that it is better than other algorithms over various performance matrices including mean squared error (MSE), peak signal-to-noise ratio (PSNR), and structural similitude index (SSIM). Experimentally and statistically, it has been proved that the proposed RGN algorithm can be considered as a better alternative for optimization research.