<p>Multi-objective optimisation in material design often involves conflicting objectives, leading to a set of Pareto-optimal solutions. However, practical applications typically require selecting a single optimal solution, a process that can be computationally impractical, especially in high-dimensional problems with several objectives. Traditional methods that compute the entire Pareto front exacerbate this challenge. Alternatively, solving the scalarised problem using, for instance, the Tchebycheff scalarisation function, can be an efficient approach to obtain a single Pareto optimal solution. Driven by the recent developments in smooth approximations of the Tchebycheff function and in the composite Bayesian optimisation framework, this work combines these techniques to solve the scalarised multi-objective optimisation problem. By exploiting the compositional structure of the scalarised objective function, we enhance the sampling efficiency of Bayesian optimisation, allowing for a faster convergence to a single Pareto optimal solution. Additionally, when the individual objective functions exhibit a compositional nature themselves, a double-nested compositional objective function arises. With this in mind, we explore the integration of a recently proposed composite Bayesian optimisation framework for structural analyses with the scalarisation framework to further improve the optimisation process; a full composite Bayesian optimisation framework is established for scalarised problems. Benchmarking against traditional Bayesian optimisation confirms the superior sample efficiency of our approach. By integrating smooth scalarisation with composite Bayesian optimisation, we provide a robust and computationally efficient alternative for solving scalarised multi-objective optimisation problems.</p>