Abstract An Enhanced Simulated Annealing Algorithm, adapted to continuous variables problems, has been previously elaborated. Variables discretization has received special attention and several complementary stopping criteria have been developed and implemented to reduce the computational cost. This method, coupled with an ‘open” circuit simulator — SPICE PAC — has been used for minimizing objective functions which describe circuit performance optimization problems or component model fitting to experimental data. In the same way synaptic coefficients of analogue multilayer neural networks have also been determined. In the paper, various parameters of a non-linear general purpose GaAs FET model are directly determined by our Enhanced Simulated Annealing. We minimize an objective function of several continuous variables — model parameters — based on the relative and absolute least squares errors between a measured drain current/voltage characteristics data set and computed model responses. The model is described by fairly simple explicit expressions and, hence, can be easily implemented in programs of computer-aided analysis and design of circuits with GaAs FETs. Our optimization procedure, which does not require heavy and inaccurate derivatives computations, reaches, in a reasonable time, a good accuracy for representing complex GaAs MESFET transistor behaviour.