DEA (Differential Evolution Algorithm) is a heuristic method for optimizing non-linear and non-differentiable continuous space functions. Hence it can be applied to global searches within the weight space of a typical neural network.
Differential Evolution is a nature inspired population based global search mechanisam. Which mainly employ mutation, crossover and selection. Its applicable to both constrained and unconstrained problems.
This entirely different from Differential evolution - an optimization algorithm. This algorithm is popularly known as DE.
Hence, you gave scope for confusion for different answers. DEA is based on linear programming concepts and DE is an evolutionary optimization technique. Study your problem thoroughly and decide which is appropriate for you