Enhanced Global Optimization Using a Novel Hybrid Sine Cosine-Gazelle Algorithm with Brownian Motion and Lévy Flight Mechanisms

Abstract Metaheuristic algorithms are crucial for solving intricate optimization problems in diverse fields. The Sine Cosine Algorithm (SCA), known for its efficiency and simplicity in global search, sometimes struggles with premature convergence and inadequate exploitation. To address these challenges, this study introduces a novel hybrid SCA-Gazelle Optimisation Algorithm (HSCAGOA) by integrating the Gazelle Optimisation Algorithm’s (GOA) exploitation strategy. Inspired by gazelle behaviour, GOA enhances local search capabilities, improving the balance between the exploration and exploitation phases. Additionally, HSCAGOA incorporates Brownian motion and Lévy flight mechanisms to further enhance exploration capabilities. This research rigorously evaluates HSCAGOA through extensive computational experiments on 33 benchmark test problems and six engineering design challenges. Comparisons with classical SCA and various state-of-the-art optimisation algorithms show that HSCAGOA consistently achieves faster convergence and higher solution quality across diverse optimisation landscapes. To validate these results, ranking analysis is conducted using the Wilcoxon rank-sum test and the Wilcoxon signed-rank test, confirming the efficacy of HSCAGOA. Furthermore, employing the Combined Compromise Solution (CoCoSo) method for multi-criteria decision-making enables systematic ranking and comparison of HSCAGOA’s performance against other algorithms. Additionally, a comparative analysis was conducted against renowned CEC competition winners, including LSHADEcnEpSin, LSHADESPACMA, and CMA-ES. HSCAGOA is evaluated through extensive computational experiments involving CEC 2017 benchmark test functions. Moreover, sensitivity analysis is performed to assess the robustness of HSCAGOA under varying configurations, including different population sizes and maximum iteration counts on CEC 2022 benchmark test functions. The findings highlight the algorithm’s adaptability and reliability in addressing complex optimization challenges. In summary, this study introduces HSCAGOA as a robust optimisation framework that mitigates the limitations of traditional SCA. It provides an effective solution for addressing complex real-world optimisation problems across different domains.