The use of Digital Twins (DTs) for continuously optimising manufacturing systems under a constant stream of changes, also known as ”online optimisation”, is taken for granted by many authors but rarely demonstrated possible given the challenges in keeping a DT synchronised with its real system whilst using it to run look-ahead simulations. This research addresses this gap by demonstrating that online optimisation is achievable alongside real-time look-ahead simulation in DTs, even under constant changes in the system being modelled. The main enabling factor is a proposed architecture which can underpin a Digital Twin with Adaptive capabilities, or Adaptive Digital Twin (ADT). The capabilities include Real-time Simulation, Online Optimisation, and Adaptivity (RSO2A). The proposed ADT architecture is suitable for constantly changing production environments with unpredictable demands, for example, those envisioned to deliver the concept of mass personalisation, allowing customers to co-create and co-design products based on personal preferences. To demonstrate and validate the support of the ADT architecture for RSO2A, an Adaptive Manufacturing System (AMS) for mass personalisation is developed in silico. The AMS is underpinned by the proposed ADT architecture and simulated its operation and adaptation using realistic shoe personalisation scenarios. The simulation output demonstrates how the proposed architecture and the ADT built with it enable the AMS to maintain continuous production of personalised shoes and continuously re-configure its layout to adapt to new changes in the production environment. •The development of Adaptive Digital Twins architecture with appropriate abstractions for real-time simulation, online optimisation, and adaptivity.•The development of Adaptive Manufacturing System for mass personalisation production environment.•Real-time layout optimisation capability enabled by Adaptive Digital Twins architecture.