Nested Interior–Exterior Optimisation for Explainable Autonomous Complex Systems Modelling Using Cross‐Clustered Migration and Cooperative Learning

ABSTRACT Accurate and explainable modelling of Autonomous Complex Systems (ACS) is vital for civil and military applications, requiring a balance between model performance and interpretability. This study proposes a nested interior–exterior optimisation approach for explainable ACS modelling, leveraging a cross‐clustered framework with migration and cooperative learning. For interior optimisation of the ACS model, a cross‐clustered migration mechanism is designed to incorporate pseudogenes to simultaneously optimise the structure and parameters, enabling compact yet accurate ACS models. For exterior optimisation of the ACS model, a cross‐clustered cooperative learning mechanism is designed to allocate additional resources to superior‐performing models and redistribute their optimal structures and parameters across different models in varied clusters. The belief rule base (BRB) is adopted as the baseline model, ensuring explainability and accessibility for decision‐makers. A case study on drone system modelling validates the approach's efficacy, demonstrating that: (1) cross‐clustered migration facilitates efficient simultaneous optimisation, producing compact ACS models with superior performance, that is, BRBs with seven and eight rules are identified as optimal ACS models for modelling two objectives; (2) cross‐clustered cooperative learning leverages multiple optimisation algorithms (e.g., GrEA, MOEA/D, SPEA2) to outperform single‐algorithm approaches and (3) comprehensive analysis of interior and exterior optimisation confirms the framework's robustness. Last but not least, optimal BRBs are fully explainability to ACS decision‐makers as it can provide completely transparent and accessible modelling procedures and inferencing interfaces.