High-Flyer is pretty damn rich actually. Someone did some calculation and it turns out they are spending ~$200m (somewhere in that range) on 150 employee compensation alone.
Movement of the chips to China is under restriction too.
However, neither access to the chips via cloud compute providers or Chinese nationals working in the US or other countries on clusters powered by the chips is restricted.
Thank you. Your comment makes me check if there's anything like Brave for Firefox. And here it is: cachyos-v4/cachy-browser 130.0-2 (Firefox is at 131.0.2-1 now).
I was on CPLEX team for a few years. Core developers are all PhDs from Stanford/MIT and etc. So it's very hardcore stuff, no less than AI research.
Completely agree that size is not a good proxy for estimating MIP difficulties. Internally we colllected a bunch of very hard problems to sovle from different domains. Some are actually pretty small, say a few thousand variables/constraints. IMHO what made hard problems difficult to solve is actually the 'intneral structure' of the problems. And modern industry solvers all have a lot of built-in heurstics to take advantages of the structures, i.e., what kind of cuts, presolve/diving/branching strategy to apply, how to get the bounds ASAP.
Interestinglly at some point some folks even tried using machine learning to predict strategies. Didn't work quite well back then (10+ years ago). There was some work of using seq2seq for MIP (pointer network, I think) a few years ago; worked OK. So I'm really looking forward to some breakthroughs by LLM.
It's a shame that after IBM aquired ILOG (which owns CPLEX), most of the ppl left for Gurobi.
> IMHO what made hard problems difficult to solve is actually the 'intneral structure' of the problems.
20 years ago I wrote a master’s thesis in computer vision. The stereo matching algorithm I developed could be expressed as a big integer linear program. But after pondering it for some time I realized it could also be expressed as a dynamic programming problem, with tiny integer linear programs as subproblems. Reduced the runtime by like a factor of 1000x, or more.
I feel most of those big search problems could be solved much easier and quicker with some form of annealing/tree search/dynamic or greedy algorithms with results very close to the theoretical linear optimum
> with results very close to the theoretical linear optimum
In this case I could prove it was the globally optimal solution.
But this was only possible of course due to the internal structure of the problem: it was in effect a simpler problem hiding within a linear integer program. Standard solvers couldn’t find this structure, but it was possible to do by hand.
What's the situation with CPLEX these days? Is IBM still investing any serious resources into it? Gurobi keeps getting massively better (either in performance or expressiveness) every release.
CPlex has shown no progression in the benchmarks in the past years, so it is safe to assume that the number of developers they have employed is either 0 or maybe 1.
Not the same person but maybe "Mixed-Integer Nonlinear Programming: A Survey of Algorithms and Applications" could be a good start? I haven't read it yet.
I am an academic in the field. A good starting point would be Tobias Achterberg's PhD thesis:
"Constraint Integer Programming"
It details the implementation of SCIP, which is one of the leading open source solvers, and explains some of the most important tricks.
That said, there is a lot of literature out there; if you're interested in a particular aspect like e.g. presolving or cutting planes, then feel free to ask me further questions. It is worth noting that the implementation specifics are hidden by the top commercial solvers, so these are difficult to find anywhere
