Generating Set Search method are one of the few alternatives for optimising high fidelity functions with numerical noise. These methods are usually only efficient when the number of variables is relatively small. This paper presents a modification to an existing Generating Set Search method; which makes it aware of the sparsity structure of the Hessian. The aim is to enable the efficient optimisation of functions with a relatively large number of variables. Numerical results show a decrease in the number function evaluation it takes to reach the optimal solution; sometimes by significant margins; on noisy as well as smooth problems; for a modest as well as relatively large number of variables.