Could someone maybe give a high-level explanation into why commercial ILP solvers (e.g. Gurobi) are that much better than free/open-source ones? Is it because ILP is inherently that difficult to solve (I know it's NP-hard), that the best solvers are just a large ensemble of heuristics for very specific sub-problems and thus no general "good" strategy has made it's way into the public domain?
It’s mostly that they work closely with clients in a very hands on way to implement problem-specific speedups. And they’ve been doing this for 10-20 years. In the MILP world this means good heuristics (to find good starting points for branch & bound, and to effectively prune the B&B tree), as well as custom cuts (to cut off fractional solutions in a way that effectively improves the objective and solution integrality).
It’s common that when researchers in Operations Research pick a problem, they can often beat Gurobi and other solvers pretty easily by writing their own cuts & heuristics. The solver companies just do this consistently (by hiring teams of PhDs and researchers) and have a battery of client problems to track improvements and watch for regressions.
> the best solvers are just a large ensemble of heuristics for very specific sub-problems
The big commercial solvers have the resources (and the clients interested in helping) to have invested a lot of time in tuning everything in their solves to real-world problems. Heuristics are part of that; recognizing simpler sub-problems or approximations that can be fed back into the full problem is also part.
I think a big part is that the OSS solvers are somewhat hamstrung by the combination of several issues: (1) the barrier to entry in SoTA optimizer development is very high, meaning that there are very few researchers/developers capable of usefully contributing both the mathematical and programming needed in the first place, (2) if you are capable of (1), the career paths that make lots money lead you away from OSS contribution, and (3) the nature of OSS projects means that "customers" are unlikely to contribute back to kind of examples, performance data, and/or profiling that is really needed to improve the solvers.
There are some exceptions to (2), although being outside of traditional commercial solver development doesn't guarantee being OSS (e.g. SNOPT, developed at Stanford, is still commercially licensed). A lot of academic solver work happens in the context of particular applications (e.g. Clarabel) and so tends to be more narrowly focused on particular problem classes. A lot of other fields have gotten past this bottleneck by having a large tech company acquire an existing commercial project (e.g. Mujoco) or fund an OSS project as a means of undercutting competitors. There are narrow examples of this for solvers (e.g. Ceres) but I suspect the investment to develop an entire general-purpose solver stack from scratch has been considered prohibitive.
Commercial solvers have a huge bag of tricks & good pattern detection mechanisms to detect which tricks will likely help the problem at hand.
If you know your problem structure then you can exploit it and it is possible to surpass commercial solver performance. But for a random problem, we stand 0 chance.
NP-hard is really hard, but it is hard for (a) polynomial running time, (b) for exact solutions, (c) on worst case problems.
One might suspect that fast enough on specific problems for approximate solutions that still make/save a lot of money might also be welcome. Ah, perhaps not!
E.g., in NYC, two guys had a marketing resource allocation problem, tried simulated annealing, and ran for days before giving up.
They sent me the problem statement via email, and in one week I had the software written and in the next week used the IBM OSL (Optimization Subroutine Library) and some Lagrangian relaxation. In 500 primal-dual iterations with
600,000 variables
40,000 constraints
found a feasible solution within 0.025% of
optimality.
So, I'd solved their problem (for practical purposes, the 0.025% has to count as a solving) for free.
They were so embarrassed they wanted nothing to do with me. We never got to where I set a price for my work.
The problem those two guys had was likely that, if they worked with me, then I would understand their customers and, then, beat the guys and take their customers. There in NYC, that happened a second time.
If a guy is in, say, the auto business, and needs a lawyer, the guy might want the best lawyer but will not fear that the lawyer will enter the auto business as a powerful competitor. Similarly for a good medical doctor.
For an optimization guy saving, say, 5% of the operating costs of a big business, say, $billion in revenue a year, all the management suite will be afraid of the guy getting too much power and work to get him out -- Goal Subordination 101 or just fighting to retain position in the tribe.
After having some grand successes in applied math where other people had the problem but then being afraid that I would be too powerful, I formulated:
If some technical, computing, math, etc. idea you have is so valuable, then start your own business exploiting that idea -- of course, need a suitable business for the idea to be powerful.
scale and speed. for example, most quant trading firms run huge optimizations as often as possible. open-source solver often cannot even solve the problems (OOM exceptions, etc)
In most MILP domains, the underlying engineering know-how is more critical than mathematical formulations or CS coding: (that's why most OR groups operate independently of math or CS departments).
OSS never took off among professional engineers because they've have "skin in the game", unlike math and CS folks who just reboot, and pretend nothing is wrong.
I vaguely recall building a resource allocation tool using IBM's "ILOG" mixed integer linear programming library and we realised that if we'd built the tool about 20 years earlier it would have still been running for the same problems we were now solving within 5 minutes.
As I recall it the raw computer power had increased by a factor of around a thousand and the algorithms had improved by about the same, giving us a factor of a million improvement.
Worth pondering when trying to predict the future!
The "resources" in question were diamonds by the way...
Can anyone share how this is used in practice? Somehow I imagine implementing numerical optimization often fails due to the usual problems with data-driven approaches (trust, bad data, etc.) and ultimately someone important just decides how things are going to be done based on stomach feel.
We use solvers throughout the stack at work: solvers to schedule home batteries and EVs in peoples homes optimally, solvers to schedule hundreds of thousands of those homes optimally as portfolios, solvers to trade that portfolio optimally.
The EU electricity spot price is set each day in a single giant solver run, look up Euphemia for some write ups of how that works.
Most any field where there is a clear goal to optimise and real money on the line will be riddled with solvers
I can't share pricing details since they are confidential but if you just want to play with MIP you don't need to buy one of the big three (XPRESS, Gurobi, CPLEX) which are all very expensive but usually available for free for students. There are at least two good open source / free for non-commercial use MIP solvers available:
You can get a temporary free license for Gurobi. You are limited to a 1000 node problem size, but you can learn how to use the tool and set up your problem.
If you have a problem that needs Gurobi, it’s worth paying for it. Talk with their sales team. They are happy to help you get started. They know once you know how to use it, and how it can solve problems you will be inclined to use it in the future.
Their price list wasn't that confidential last I spoke with the sales team. It depends on the license type. Last I heard, it's around $15k/year for a standard subscription license. You can probably trial it for free, or be a student and have longer free access.
What I've heard - and obviously I can't confirm this - is that their only pricing tier is "call us" - at which point they try to figure out how much money you're making and ask for a slice of it.
Heh, given all of the whispering, I was imagining something 10x the price. I am a nobody and have at least one license to a different product that is some $13k annual.
It’s much cheaper than making suboptimal decisions slowly. Free solvers are fine for small problems (GLPK, for example), but lots of business problems are pretty much impossible to solve in the timeframe required unless you fork over cash for a premium solver (Gurobi being the best).
The last time I checked about a decade ago, a full license with multiple users and on a server was around 100k USD. I don't recall exact number of seats or server count restrictions.
I want to add that, for many in the industry, it is well worth the price.
The best MIP solvers (CPLEX, GUROBI, FICO) are all extremely expensive unless you're an academic. The free ones are fine for smaller problems. Some like Mosek are quite affordable and a good middle ground. To most organizations, the cost is reasonable for what they're getting.
It's not cheap but actually quite reasonable and the quality is very good vs free solvers. If you are building a product that needs MILP it's worth it.
I remember implementing some version of Gomory cutting hyperplanes back in the 1990s in Maple (for learning, not for production.) Looks like the field has progressed...
> if we needed two months of running time to solve an LP in the early 1990s, we would need less than one second today. Recently, Bixby compared the machine-independent performance of two MILP solvers, CPLEX and Gurobi, between 1990 and 2020 and reported speed-ups of almost 4×10^6.
It feels like there’s a significant lack of “ML/AI” based approaches applied to these kinds of problems. I’ve seen a lot of example of RL/GNN papers that do attempt to solve smaller problems but it always feels like the best option is to just pay for a gurobi license and have at it. I’ve been doing some scheduling optimisation recently (close to job shop scheduling) and while there’s some examples of using RL they just don’t seem to cut it. I’ve resorted to evolutionary algorithms to get reasonable solutions to some big problems. Maybe it’s just always more efficient to using OR type approaches when you can formulate the problem well.
It depends on the problem. The security contained unit commitment problem (how you figure out which power plants to turn on when) is an unbelievably complex problem that MILP solvers like Gurobi can find globally optimal solutions (within the bounds of the MIP gap) quickly. Sure you could create a genetic algorithm, but there is no guarantee it will give you an answer that isn't stuck in a local minima. That is assuming you can make it run fast. Neural networks are also going to be sub optimal.
SAT is a standard GOFAI problem and you can of course use any programming language in the ML family to write a SAT solver. Thus I'd say that "ML/AI" approaches are, if anything, quite applicable!
"... between 1988 and 2004, hardware got 1600 times faster, and LP solvers got 3300 times faster, allowing for a cumulative speed-up factor higher than 5 × 106, and that was already 20 years ago!"
"The authors observed a speedup of 1000 between [the commercial MILP solvers of] 2001 and 2020 (50 due to algorithms, 20 due to faster computers)."
I wonder if we can collect these speedup factors across computing subfields, decomposed by the contribution of algorithmic improvements, and faster computers.
In compilers, there's "Proebsting's Law": compiler advances double computing power every 18 years.
Unless the OP meant to post specifically the abstract, which I very much doubt, the content submitted is the PDF linked. That said, if that's how the [pdf] tag is meant to be used on this forum, I could understand. Would just also leave me moderately annoyed & wondering why the tag isn't automated then, since that'd be automatable.
Readit News
It’s common that when researchers in Operations Research pick a problem, they can often beat Gurobi and other solvers pretty easily by writing their own cuts & heuristics. The solver companies just do this consistently (by hiring teams of PhDs and researchers) and have a battery of client problems to track improvements and watch for regressions.
The big commercial solvers have the resources (and the clients interested in helping) to have invested a lot of time in tuning everything in their solves to real-world problems. Heuristics are part of that; recognizing simpler sub-problems or approximations that can be fed back into the full problem is also part.
I think a big part is that the OSS solvers are somewhat hamstrung by the combination of several issues: (1) the barrier to entry in SoTA optimizer development is very high, meaning that there are very few researchers/developers capable of usefully contributing both the mathematical and programming needed in the first place, (2) if you are capable of (1), the career paths that make lots money lead you away from OSS contribution, and (3) the nature of OSS projects means that "customers" are unlikely to contribute back to kind of examples, performance data, and/or profiling that is really needed to improve the solvers.
There are some exceptions to (2), although being outside of traditional commercial solver development doesn't guarantee being OSS (e.g. SNOPT, developed at Stanford, is still commercially licensed). A lot of academic solver work happens in the context of particular applications (e.g. Clarabel) and so tends to be more narrowly focused on particular problem classes. A lot of other fields have gotten past this bottleneck by having a large tech company acquire an existing commercial project (e.g. Mujoco) or fund an OSS project as a means of undercutting competitors. There are narrow examples of this for solvers (e.g. Ceres) but I suspect the investment to develop an entire general-purpose solver stack from scratch has been considered prohibitive.
If you know your problem structure then you can exploit it and it is possible to surpass commercial solver performance. But for a random problem, we stand 0 chance.
Isn't that statement trivially applicable to anything NP-Hard (which ILP is, since it's equivalent to SAT)?
One might suspect that fast enough on specific problems for approximate solutions that still make/save a lot of money might also be welcome. Ah, perhaps not!
E.g., in NYC, two guys had a marketing resource allocation problem, tried simulated annealing, and ran for days before giving up.
They sent me the problem statement via email, and in one week I had the software written and in the next week used the IBM OSL (Optimization Subroutine Library) and some Lagrangian relaxation. In 500 primal-dual iterations with
600,000 variables
40,000 constraints
found a feasible solution within 0.025% of optimality.
So, I'd solved their problem (for practical purposes, the 0.025% has to count as a solving) for free.
They were so embarrassed they wanted nothing to do with me. We never got to where I set a price for my work.
The problem those two guys had was likely that, if they worked with me, then I would understand their customers and, then, beat the guys and take their customers. There in NYC, that happened a second time.
If a guy is in, say, the auto business, and needs a lawyer, the guy might want the best lawyer but will not fear that the lawyer will enter the auto business as a powerful competitor. Similarly for a good medical doctor.
For an optimization guy saving, say, 5% of the operating costs of a big business, say, $billion in revenue a year, all the management suite will be afraid of the guy getting too much power and work to get him out -- Goal Subordination 101 or just fighting to retain position in the tribe.
After having some grand successes in applied math where other people had the problem but then being afraid that I would be too powerful, I formulated:
If some technical, computing, math, etc. idea you have is so valuable, then start your own business exploiting that idea -- of course, need a suitable business for the idea to be powerful.
Modern SAT solvers are a good example of this. CDCL is elegant.
OSS never took off among professional engineers because they've have "skin in the game", unlike math and CS folks who just reboot, and pretend nothing is wrong.
As I recall it the raw computer power had increased by a factor of around a thousand and the algorithms had improved by about the same, giving us a factor of a million improvement.
Worth pondering when trying to predict the future!
The "resources" in question were diamonds by the way...
The EU electricity spot price is set each day in a single giant solver run, look up Euphemia for some write ups of how that works.
Most any field where there is a clear goal to optimise and real money on the line will be riddled with solvers
1. Salesman & delivery travel plan
2. Machine, Human and material resource scheduling for production
3. Inventory level for warehouse distribution center. This one isn't fully automatic because demand forecasting is hard
gurobi case studies: https://www.gurobi.com/case_studies/
some cplex case studies: https://www.ibm.com/products/ilog-cplex-optimization-studio/...
hexaly (formerly localsolver) case studies: https://www.hexaly.com/customers
https://highs.dev/https://www.scipopt.org/
If you have a problem that needs Gurobi, it’s worth paying for it. Talk with their sales team. They are happy to help you get started. They know once you know how to use it, and how it can solve problems you will be inclined to use it in the future.
- Timefold Solver (not MIP, focussed on vehicle routing, job scheduling, shift rostering, etc): http://solver.timefold.ai
- Several solvers at COIN-OR: https://www.coin-or.org/
- Choco
I want to add that, for many in the industry, it is well worth the price.
Rather: if you are building a product that will for sure make a lot of money, and needs MILP, it's worth it.
A lot of product concepts that nerds create are very innovate, but are often some private side projects.
> if we needed two months of running time to solve an LP in the early 1990s, we would need less than one second today. Recently, Bixby compared the machine-independent performance of two MILP solvers, CPLEX and Gurobi, between 1990 and 2020 and reported speed-ups of almost 4×10^6.
"The authors observed a speedup of 1000 between [the commercial MILP solvers of] 2001 and 2020 (50 due to algorithms, 20 due to faster computers)."
I wonder if we can collect these speedup factors across computing subfields, decomposed by the contribution of algorithmic improvements, and faster computers.
In compilers, there's "Proebsting's Law": compiler advances double computing power every 18 years.