Guided Archimedes Optimization Algorithm: A novel global–local fusion approach for robust engineering design problem solving

Abstract The Archimedes optimization algorithm (AOA) is a recently developed metaheuristic inspired by Archimedes’ principle, a fundamental law in physics. AOA has demonstrated impressive performance in solving complex optimization problems due to its simplicity and efficiency. Despite its popularity, AOA has some key limitations, such as a tendency to get stuck in local optima, weak exploitation capabilities, and difficulty balancing exploration (searching for new possibilities) and exploitation (optimizing known solutions). To address these shortcomings, this paper introduces the guided Archimedes optimization algorithm (GAOA), which incorporates a guiding vector based on the best solution and population mean. Additionally, it employs a neighbourhood-based strategy for better exploitation and a controlled random walk to prevent premature convergence. The performance of GAOA is evaluated against AOA, its variants, and other popular algorithms on the CEC’17 and CEC’22 test suites, as well as on real-world engineering problems. The results show that GAOA is a highly competitive optimizer, securing the top rank in 18 out of 29 functions on the CEC’17 (50D) benchmark suite and 11 out of 12 functions on the CEC’22 (20D) suite. These findings demonstrate that GAOA is a robust optimization tool that can adapt to a variety of complex challenges.