An Enhanced Hierarchical Hybrid Algorithm: In Galactic Swarm Optimization and Gravitational Search Algorithm

Abstract

This paper presents a hierarchical hybrid metaheuristic combining Galactic Swarm Optimization GSO and the Gravitational Search Algorithm GSA using dynamic parameter adaptation strategies The first strategy FHGSO applies fuzzy logic exclusively to the GSO component it dynamically adapts the Level 2 cognitive and social coefficients of the intersubpopulation interaction using the FGSO inference system The second strategy FHGSA applies fuzzy logic exclusively to the GSA component it dynamically adjusts the gravitational descent coefficient α and the Kbest selection ratio using the FGSA inference system Both strategies use the normalized current iteration as the sole input producing smooth transitions between exploration and exploitation The theoretical foundation integrates classical Type1 fuzzy set theory including formal definitions of fuzzy sets membership functions linguistic variables and fuzzy logic operations with practical fuzzy inference system design using Mamdani methodology This integration provides a mathematically rigorous approach to handling parameter uncertainty throughout algorithm execution Three algorithm variants were systematically evaluated I HGSO the base hybrid without fuzzy adaptation II FHGSO the hybrid with FGSO adapting only the GSO Level 2 coefficients and III FHGSA the hybrid with FGSA adapting only the GSA parameters α and Kbest Experiments were conducted on seven classical benchmark functions at 10 30 and 50 dimensions and on the 12 IEEE CEC 2022 benchmark functions at 2 10 and 20 dimensions Results demonstrate that each fuzzy variant improves over the base HGSO on different problem types FHGSO benefits functions sensitive to Level 2 diversity while FHGSA excels on composite and highdimensional problems where gravitational dynamics are the limiting factor