The simultaneous optimization of building’s fabric construction, the size of heating, ventilating and air conditioning (HVAC) system, and the HVAC system supervisory control strategy, would auto- matically account for the thermal coupling between these building design elements. This paper describes the formulation of such an optimization problem for a single air conditioned zone. The problem formulation is described in terms of the optimization problem variables, the design con- straints, and the design objective function. The optimization problem has been solved using a Genetic Algorithm (GA) search method. It is concluded that the GA is able to find a feasible so- lution and it exhibits an exponential convergence on a solution. The solutions obtained are near- optimal, the lack of final convergence being re- lated to variables having a secondary effect on the energy cost objective function. Further research is required to investigate methods for improving the handling of equality constraints and to reduce the number of control variables (which will also improve the robustness of the algorithm).