Multi-level optimisation divides a problem into sections such that each can be addressed using the most appropriate evaluation and optimisation processes. A methodology is proposed to address the design and operation of a building and its energy system, split into three levels: building design, system design and system operation. The optimisation techniques used are a multi-objective genetic algorithm (design) and mixed-integer linear programming (operation); the evaluation methods used are the building energy simulation program EnergyPlus (building level) and the ‘energy hub’ model (system level). The objective functions used here were annual carbon emissions and initial capital cost (for the multi-objective design problem) and annual running costs (for the single objective operational problem). The methods used are described in detail, and the proposed methodology is applied to a case study concerning an office building. The detailed results presented include the trade-off front of optimal design-level solutions, the convergence of the optimisation, trends in the associated design variable values, derived properties of each solution, the operational variable values, and the run-times of the operational optimisation. Conclusions are drawn regarding the case study and the overall approach, and future directions are suggested.