Advancing hierarchical optimization: A-Cubed algorithm for adaptive agent collaboration

Over the past decade, metaheuristic optimization has garnered substantial attention. Nonetheless, the application of hierarchical strategies to augment the optimization process and enhance adaptability across various problem domains, particularly through the utilization of particle-specific characteristics, remains inadequately explored. This study presents the Agent Assembly Algorithm (A-Cubed), a novel meta-heuristic optimization algorithm inspired by the evolutionary strategies of elite adaptive societies and the collective adaptation of agents. A-Cubed introduces an innovative hierarchical assembly framework that distinctly organizes agent search behavior based on fitness and spatial proximity, marking a departure from conventional meta-heuristics that depend on static or predefined strategies. This framework facilitates dynamic, level-specific control over search behaviors. To bolster this approach, a time-distance adjustment mechanism progressively refines agent movement, thereby promoting an effective balance between global exploration and local exploitation. The efficacy of A-Cubed has been substantiated through four rigorous evaluations: (1) performance testing on 50 mathematical benchmark functions, in comparison with 12 leading meta-heuristic algorithms; (2) assessment on 12 benchmark functions from the IEEE CEC 2022 competition; (3) evaluation of its practicability in three scenarios of truss structure optimization to minimize weights; and (4) application in two topology optimization scenarios aimed at minimizing compliance. A-Cubed has exhibited consistent effectiveness in identifying optimal solutions, managing complex problems with stability, and adapting to diverse numerical optimization challenges. In engineering applications, it has excelled by achieving optimal results with fewer objective function evaluations and a high convergence rate, thereby establishing itself as a highly promising metaheuristic algorithm for optimization tasks. A-Cubed emerges as an efficient technique for addressing a wide array of problems, particularly in complex structural design, due to its ease of implementation and robust adaptability to varying problem characteristics.