The pursuit of sustainable aviation has driven the development of Large Aspect Ratio Wings (LARWs), which offer enhanced aircraft operational efficiency and reduced environmental impact. Their pronounced flexibility, however, introduces significant design challenges, as performance optimisation must account for flexibility-induced load variations and potential aeroelastic instabilities. Traditional design methods, particularly those relying on low-fidelity models, risk yielding suboptimal and non-robust designs. This work presents a high-fidelity, fully Algorithmic-Differentiation (AD)-based aeroelastic optimisation framework capable of capturing both structural (geometric) and aerodynamic (CFD-based) nonlinearities to accurately predict aerostructural responses. The framework integrates gradient-based optimisation, adjoint method and parallel computing to efficiently address large-scale wing models with thousands of design variables and millions of degrees of freedom. The main novelty of the framework lies in its augmentation with AD-based evaluation of buckling and modal constraints, in addition to stress-based strength constraints commonly adopted in the literature, thereby enabling realistic aerostructural optimisation scenarios. Industrially relevant test cases, including the NASA Common Research Model and the High-Fidelity Aeroelastic optimisation Benchmark, are tested enforcing single or combined constraints, while capturing large structural deflections and geometric nonlinearities typical of LARW designs. Overall, this work significantly advances high-fidelity optimisation of LARWs assessing their performance and emission-reduction potential, while providing a meaningful contribution to Multidisciplinary Design Optimization (MDO) research.