Control-based structural optimization for crashworthiness using adaptive hybrid cellular automata

The hybrid cellular automaton (HCA) algorithm is a control-based numerical method for generating conceptual designs of lightweight vehicle structures for crashworthiness. In the HCA framework, material distribution is governed by a closed-loop system of distributed proportional-integral-derivative (PID) controllers, where the final structure corresponds to the steady-state solution of the dynamic system. The algorithm's convergence rate depends on the tuning of controller gains, which are traditionally determined using heuristic approaches such as the Ziegler–Nichols method. While effective, these strategies are often conservative and may result in slow convergence. This work introduces an adaptive tuning strategy that dynamically adjusts controller gains to improve the convergence rate and numerical stability of the HCA algorithm. The proposed method also reduces dependence on manual parameter tuning and enhances performance consistency across diverse problem types. The effectiveness of the adaptive HCA algorithm is demonstrated through structural design problems involving both linear-static and nonlinear dynamic models.