Multilayer neural networks are commonly and frequently used technique for mapping complex nonlinear input-output relationship. However, they add more computational cost due to structural complexity in architecture. This chapter presents different functional link networks (FLN), a class of higher order neural network (HONN). FLNs are capable to handle linearly non-separable classes by increasing the dimensionality of the input space by using nonlinear combinations of input signals. Usually such network is trained with gradient descent based back propagation technique, but it suffers from many drawbacks. To overcome the drawback, here a natural chemical reaction inspired metaheuristic technique called as artificial chemical reaction optimization (ACRO) is used to train the network. As a case study, forecasting of the stock index prices of different stock markets such as BSE, NASDAQ, TAIEX, and FTSE are considered here to compare and analyze the performance gain over the traditional techniques.