At Octeract, we use Deterministic Global Optimisation (DGO) to guarantee global optimality for general non-convex, mixed-integer optimisation problems.
The mathematics of DGO provide this guarantee because they allow us to perform calculations over entire regions of space, as opposed to isolated points (conventional optimisation methods).
This information is then used to derive rigorous bounds over the entire region: a best-case and a worst-case scenario. This procedure is repeated for increasingly smaller regions of space, and the math guarantees that the bounds are guaranteed to approach each other as the regions become smaller.
Eventually, this allows us to locate a small region where we can guarantee global optimality.
Unfortunately, the guarantee comes at great computational cost (the problem is NP-Hard after all), which makes the solving of large-scale industrial problems impossible a lot of the time.
Our DGO engine is the first of its kind which is able to harness the power of distributed computing to accelerate DGO methods - thus allowing us to guarantee global optimality for much larger problems than previously thought possible.