Most fuzzy controllers developed to date have been of the rule-based type. These controllers require considerable knowledge engineering to set up their rule base. An alternative approach is a fuzzy relational model-based controller (FRMBC), where a fuzzy relational model (FRM) of the process is imbedded into a conventional model-based controller. Constructing the FRM from a set of process data rather than from process knowledge reduces considerably the engineering effort of setting up a fuzzy controller. Several modelling methods to do so have been proposed in the literature. This paper looks at the multi-variable optimization methods of simulated annealing (SA), threshold accepting (TA) and iterative improvement for model formulation. Comparisons are made between the optimization methods described in the paper and more traditional methods of fuzzy model identification. The basis of the comparisons are the well known Box-Jenkins furnace data, and data from a simulated pH process. Amongst the things considered in the comparisons are model accuracy; the computational effort involved in identification; and the performance of the resulting models when included in a FRMBC. It was found that the multi-variable optimization methods described in this paper are far superior to traditional methods in terms of model accuracy, but are considerably slower.