This paper describes an optimal generalized regression neural network (GRNN) in which training of the network is optimization of the smoothing factors. A eugenic evolution strategy genetic algorithm (EGA)

which integrates random evolution operation and deterministic optimization operation

is adopted in this paper to realize global optimization in high efficiency. The eugenic evolution strategies used in this paper include adding new deterministic Powell searching operation，improving crossover operation，modifying adaptive crossover probability and mutation probability

and others. The GRNN-EGA

which is based on EGA and provides powerful capacity in non-linear modeling and predicting

is applied to modeling delayed coking process to predict the productivity of coke. The GRNN-EGA prediction results are compared to those obtained with the radial basis function network（RBFN）and the GRNN-Powell

which is based on Powell optimization. The GRNN-EGA model has better prediction performance and stability as compared with the latter two models.