A new algorithm developed to perform autonomous fitting of gravitational microlensing light curves is presented. The new algorithm is conceptually simple, versatile and robust, and parallelizes trivially; it combines features of extant evolutionary algorithms with some novel ones, and fares well on the problem of fitting binary-lens microlensing light curves, as well as on a number of other difficult optimization problems. Success rates in excess of 90 per cent are achieved when fitting synthetic though noisy binary-lens light curves, allowing no more than 20 min per fit on a desktop computer; this success rate is shown to compare very favourably with that of both a conventional (iterated simplex) algorithm, and a more state-of-the-art, artificial neural network based approach. As such, this work provides proof of concept for the use of an evolutionary algorithm as the basis for real-time, autonomous modelling of microlensing events. Further work is required to investigate how the algorithm will fare when faced with more complex and realistic microlensing modelling problems; it is, however, argued here that the use of parallel computing platforms, such as inexpensive graphics processing units, should allow fitting times to be constrained to under an hour, even when dealing with complicated microlensing models. In any event, it is hoped that this work might stimulate some interest in evolutionary algorithms, and that the algorithm described here might prove useful for solving microlensing and/or more general model-fitting problems.