Is (12!)*(9!)*(16!) too many configurations for a brute force solution?

Question

I am trying to optimise a system. Its a network. I will optimise it by swapping the positions of nodes. There are three regions where I can swap nodes (so that nodes can only be swapped with nodes in the same region). The region's have sizes of 12, 9, and 16. As far as I know, this means that I have (12!)(9!)(16!) possible configurations. My question then is, do I have too many possible solutions to just run through solutions on say, a Python program that just checks configurations against some cost function. My cost function is just summations and multiplications.

Answer 1

In 2013, the world's fastest supercomputer was performing 33 quadrillion operations per second, or $3.3\times 10^{13}$.

$12!9!16!$ is just a little over $3.3 \times 10^{27}$.

That means that, assuming each configuration only required a single operation, it would take over $10^{14}$ seconds to complete all configurations, over 3 million years.

So, unless you're VERY patient, you might want to find a way to reduce that number.