Many remote sensing applications encountered in astronomy and space science involve the solution of nonlinear inverse problems. These are often difficult to solve because of nonlinearities, ill-behaved integration kernels, and amplification of data noise associated with the inversion of the integral operator. In some cases these difficulties are severe enough to warrant repeated evaluations of the forward problem as an alternate approach to formal inversion. Because a forward approach is intrinsically repetitive and time consuming, an efficient and flexible forward technique is required for this avenue to be practical. We show how a forward technique based on a genetic algorithm allows us to fit magnetostatic models of the solar minimum corona to observations in white light to a degree that would otherwise have been computationally prohibitive. In addition, and perhaps equally important, the method also allows the determination of global error estimates on the model parameters defining the best fit solution. ¿ 1998 American Geophysical Union