Can a trained neural network replace optimization algorithms?

I am curious if that is possible maybe we can train neural networks once and use it instead of solving an optimization problem in every operation window of a system.

Edit

I am dealing with a resource allocation problem that I solve using an evolutionary optimization approach (every 5 minutes). It takes quite some time to reach a solution. I am sure there may better algorithms to reduce this time and complexity.

But, here I am curious if we train a neural network somehow to replace my resource allocation optimization algorithm? The purpose is to reduce complexity.

If it is possible, can you please refer to some literature or some specific technique.

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