HSMAOA: An enhanced arithmetic optimization algorithm with an adaptive hierarchical structure for its solution analysis and application in optimization problems

The Arithmetic Optimization Algorithm (AOA) has recently gained significant attention as a novel meta-heuristic algorithm. However, it faces challenges such as premature convergence and entrapment in local optima when addressing complex optimization problems. To overcome these limitations, this paper proposes an enhanced AOA, termed the Self-Adaptive Hierarchical Arithmetic Optimization Algorithm (HSMAOA). The proposed method integrates three key strategies: Firstly, a spiral-guided random walk mechanism is introduced to improve global search ability. Secondly, a novel adaptive hierarchy leader and follower mechanism is proposed, which establishes a complete multi-branch tree hierarchy with decreasing branching degrees within the population, thereby increasing information exchange among population individuals to escape local optima. Finally, a differential mutation strategy based on ranked selection is introduced to enhance candidate solution quality. HSMAOAʼs performance was evaluated on the CEC2022 test suite against some state-of-the-art algorithms. Results, including optimization accuracy analysis, convergence curves, and various statistical tests, demonstrate HSMAOAʼs superior optimization capability and robustness. In addition, tests on eight engineering structure optimization problems, including the pressure vessel design problem, the multiple disk clutch brake design problem, and the step-cone pulley problem, and so forth, further validate its effectiveness. Thus, HSMAOA shows strong competitiveness in complex optimization tasks and potential for a wide range of applications, and is an advantageous and promising alternative solution for optimization problems.