Training of a neural network is a real-valued optimization problem, and can not be solved with standard ant algorithms (such as Ant System and Ant Colony Optimization), and you need to use the Ant Colony Optimization for Continuous Domains (ACOR).
Ant implementation of ACOR is available to download in the following link:
To train an artificial neural network using a metaheuristic (like ACOR), you need to define an objective function, which gets the decision variables (parameters of the networks), sets the parameters in the structure of the networks equal to these values, evaluate the network for the train set of data, and finally calculate an index of performance (e.g. RMS of error), and return this value. This is used as objective function for the optimization function and can be used with any intelligent optimization algorithm.
A similar work, is performed for training of an ANFIS (Adaptive Neuro-Fuzzy Inference System) structure, using PSO and GA, and the related source code is available to download, in the following link: