Hybrid Physics-Machine Learning Framework for Multi-Objective Design Optimisation of Carbon/Glass Hybrid Composite Laminates under Bending

Hybrid carbon/glass fibre reinforced polymer composites offer attractive opportunities for balancing structural performance, weight, and material cost in bending-dominated applications. However, the design of such laminates is challenging due to the mixed discrete–continuous nature of the design variables, comprising stacking sequence and fibre volume fraction, and the highly nonlinear influence of these variables on flexural strength. This study proposes a physics-informed machine learning framework for the multi-objective optimisation of hybrid composite laminates subjected to three-point bending. A finite element dataset consisting of 240 laminate configurations was generated to characterise the relationship between laminate architecture and flexural strength. Three ensemble learning algorithms, namely Random Forest, Extra Trees, and GB Regression, were evaluated as surrogate models. Among these, GB achieved the highest predictive performance, yielding a five-fold cross-validation coefficient of determination of (R2 = 0.899 ± 0.027) and an independent test-set coefficient of determination of (R2 = 0.946), with a root mean square error of 44.8 MPa. Unlike fully data-driven optimisation approaches, machine learning was employed exclusively for flexural strength prediction, while laminate cost and weight were evaluated analytically using rule-of-mixtures formulations derived from constituent properties. The surrogate model was integrated into a Pareto-based optimisation framework and applied to evaluate 500,000 candidate laminate configurations under minimum flexural strength requirements of 1000 MPa and 1300 MPa. The optimisation identified 236,692 and 29,982 feasible laminate configurations for the respective strength constraints and revealed clear trade-offs between structural weight and material cost. The results further demonstrated that hybrid laminate architectures provide cost-effective solutions at moderate strength requirements, whereas increasingly carbon-dominant designs become necessary as strength demands increase. The proposed framework combines the predictive capability of machine learning with the transparency of physics-based modelling, providing an efficient and interpretable tool for hybrid composite laminate design. The methodology offers practical guidance for balancing performance, weight, and cost and can be readily extended to incorporate additional performance criteria, manufacturing constraints, and sustainability objectives.