what is the stack you use ? especially for the algorithm hotpath ?
I'm not sure if you are using libraries like Gurobi or CPLEX.
The JIT compiler works pretty well, and with tools like JITWatch, Honest Profiler and the -XX:+LogCompilation -XX:+PrintAssembly options you can understand how the hot paths are running in a lot of detail.
For our current operation, the optimisers' servers run Ubuntu on bare metal in our own data centres. Of course, like in any large organisation we make plenty of use of virtualization and EC2 - just not for our optimisers at this point in time.
So no, we haven't yet tested using GPUs.
edit: Can you provide insight?
It is a local search algorithm that probably has simulated annealing or tabu search as a metaheuristic.
Although, they probably segment the deliveries to some common starting points and the problem size is reduced significantly - maybe to around thousand orders per starting point.
Research can easily optimize thousands of deliveries very effectively.
With ASP (answer-set-programming) you can also avoid the specificity of modeling-language DSLs and instead focus on formalization.