The generalised optimisation of a flotation network is studied by means of using variable connections (structural parameters) and variable enhancement factors which are used instead of a flotation model to describe the separation process. The enhancement factors are functions of variables affecting the flotation process. These functional relationship may be derived by means of using a flotation model. Bounds are placed on the enhancement factors by means of either using a flotation model or by inspection of existing pilot or commercial plant data. These bounds, together with external, system and mass balance constraints and an appropriate objective function, define the general optimisation problem for a flotation network. The optimisation problem above may be solved by non-linear programming methods, however, it is easily transformable into a Linear Programme which is easy to solve. The procedure has been applied to a flotation circuit comprising three banks of cells for which an optimal set of connections and enhancement factors has been computed for varying constraints. A simulation procedure based on a gamma flotation model has been applied to one of the optimal circuits so as to compute the flotation variables.