Great question — answering as the UphillTech team:
Particle Swarm Optimization can be used to optimize a neural network with more than one hidden layer. Instead of optimizing a single weight matrix, and two bias vectors, you are just optimizing more of them. However, PSO is not often used for larger neural networks, because, particle swarm optimization is not all that efficient at working with a large amount of data, which you need to train larger neural networks. Particle Swarm Optimization involves taking many particles, and evaluating the fitness in all of them. If you have, let's say, 1,000,000 training examples, you are doing a lot more error calculations, even if you used a small batch size, than if you used another technique lake...
Full answer by Aiden Grossman: https://ai.stackexchange.com/a/10985 (CC BY-SA 4.0).
Need it done for your business? UphillTech.