I got an email last week from a PR firm asking whether I would be willing to talk to some ILOG people about the upcoming release of CPLEX 11. Made me feel like a real journalist! Since I am unfortunately missing the Seattle INFORMS (the 12 hour flights from Auckland to LA are killing!), I was going to miss my normal chats with Irv Lustig and the gang, so I did talk with them a few days ago by phone.

You can read the press release about CPLEX 11. Since I have a few sports scheduling problems that are just not solving under CPLEX 10 (or anything else I have tried), I am looking forward to seeing if things are better under 11.

There were three things that struck me when talking to the CPLEX folks:

- Pretty well all of the improvements are in the integer programming parts, not the linear programming parts. This is in keeping with Bob Bixby’s talk at EURO (you can see a version of the talk in Seattle, too) where he said that LP improvements were enormous from 1996-2003 but not much has happened in the last few years.
- The improvements in mixed integer programming in this version are coming from improved search. This contrasts with previous improvements that came from better cuts. So, when CPLEX went from version 6 to 6.5, there was a huge improvement in speed due to the addition of Gomory cuts. I would guess that in the academic world, search has received about 1% of the attention that cuts have gotten. There is a well defined theory of facets, cut generation, and so on, and very little general insight into search. CPLEX 11 uses something ILOG calls “dynamic search”. If you use dynamic search, you have to give up all the callbacks that are normally used to provide user-defined search, so you are accepting the ILOG “black box” on search. This should lead to some pretty interesting testing: can problem-dependent search do better than the general search approach? The constraint programmers have always had search as a key component to their systems; it is about time integer programmers spent more time thinking about it. Is it possible to put search on the same solid foundation that cut generation is? Or will search end up being just a bunch of heuristics that happen to work well on many instances?
- Parallel is getting more attention (and parallel linear programming may be the step that makes LP faster). But it is clear at this point that having 8 cores (as I do!) won’t result in 8 times speedup. First, the root node isn’t parallel, so anything with an expensive root node won’t see much improvement at all. Later, once the branch-and-bound search tree is in full swing, the amount of memory access needed is large, so the bottleneck occurs in the pipe to the memory. I got the impression that this is something they are working on, which is good: lots of the upcoming speed improvements are going to be in parallel computing rather than higher clock speeds.

There are other new aspects to CPLEX 11 on the usability front, most notably the ability to generate all optimal solutions, not just one, which seems like a useful feature.

ILOG has put together some forums on optimization and constraint programming. If you hurry, you can be the first to post to them!

## { 4 } Comments

Do you have sports scheduling problems that are too hard for CPLEX 10 that you can share?

I’d love to see one.

–Abie

The easiest to generate are based on the Traveling Tournament Problem http://mat.tepper.cmu.edu/TOURN . Generate all trips for the 8 team problem (so team 4 seeing teams 2, 5, and 6 starting in slot 7 is one trip) along with all home stands (2 at home for team 3 starting in slot 1). Cost for a trip is the distance traveled. Constraints are “no home after home”, “no away after away”, and “if A at B, then B home”. The 8 team problem is not huge enormous, but the IP doesn’t solve very well at all.

“There are other new aspects to CPLEX 11 on the usability front, most notably the ability to generate all optimal solutions, not just one, which seems like a useful feature.”

Still, CPLEX 11 will not generate all the optimal solutions; it will try to populate more feasible solutions in the neighbourhood, but there is no guarantee that it will find all the optimal solutions.

When I was testing the 4-thread parallel CPLEX MIP solver, I also observed that the root node is not parallel.

I thought it should be easy to solve. Just at the beginning, half split the feasible region of the root node into 4 parts, then each thread solves one part. It is kind of skip the root node and branch into 4 nodes directly. I called it dynamic Branch-and-Bound and will appear in my paper soon.

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