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I need to solve an under-determined linear system of equations and constraints, then find the particular solution that minimises a cost function. This needs to be done in purely portable managed code that will run in .NET and Mono. What freely available libraries are there that I can use to implement this?

All of the optimisation algorithms provided by free libraries I have found only support interval constraints on single variables, e.g. 0 < x < 1, not constraints like x + 2y < 4. I have also found that often the linear equations solvers only support linear systems with one solution.

The closest I have found so far is DotNumerics, which includes Singular Value Decomposition for solving under-determined linear systems, but its optimisation algorithms only support single-variable constraints (as far as I can tell).

There are several other questions asking about linear programming, but my key requirements are multi-variable constraints and solving under-determined systems. I have yet to find a free library that supports multi-variable constraints.

Dylan
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  • have you tried alglib? – Marc Gravell May 09 '13 at 13:03
  • @MarcGravell After closer inspection, it does look like this fits my requirements. Thank you very much. Put that in an answer and I'll accept. I don't know how I did not spot it before. – Dylan May 09 '13 at 13:18

4 Answers4

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If you are developing for .NET (i.e. not Windows Store, Windows Phone or Silverlight), then I would definitely recommend that you take a look at lpsolve, that is suitable for large LP and/or MILP problems. Download the x86 or x64 development archives that contain the respective lpsolve DLL:s, and then download the .NET API archive that contains a C# file with P/Invoke calls to all relevant functions in the lpsolve API.

Another alternative is to use the CLP solver from the COIN-OR projects, via the CoinMP precompiled binaries. There is a C# wrapper DLL available here.

If you do require purely managed code, ALGLIB is probably your best bet (as suggested by Marc Gravell above), but be aware that the ALGLIB open-source license uses GPL. If you want to use ALGLIB in your own code without disclosing it to the open-source community, you would need to purchase a commercial ALGLIB license.

A quick Internet search also reveals a pure C# implementation of the Simplex LP algorithm here. I cannot identify the author, and I have no idea whether this implementation is correct or of any quality. The code does seem highly portable though, even in terms of Windows Store, Windows Phone, Silverlight and Mono contexts.

Anders Gustafsson
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  • I would have used lpsolve if native code was allowed, but as specified in my question the solution needs to be purely managed to ensure portability. So thanks, but no thanks. – Dylan May 10 '13 at 10:45
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    @Dylan Not sure why you think I deserved a downvote, it is not like my answer is misleading. Granted, you mention in passing that you require a managed solution, but it is not obvious from your question why this is such a deal breaker. More often than not, people ask for managed solutions when a P/Invoke solution would fit just fine (as in this case where *lpsolve* works perfectly under both .NET and Mono). Marc's answer is obviously the most relevant in your case, but be aware that *ALGLIB* is GPL licensed; if you want to use it commercially you have to purchase a commercial *ALGLIB* license. – Anders Gustafsson May 10 '13 at 17:52
  • Maybe the downvote was a bit hasty, but the guideline is to downvote if the answer is not useful. I can undo it if you edit the answer in some way. – Dylan May 10 '13 at 18:14
  • My answer contains a clear indication in what situations the solution is applicable, and it provides relevant references to the libraries and source code that are required to implement the solution. If you despite this don't think the answer is of any use to you or another SO reader with similar issues, then just keep the downvote. – Anders Gustafsson May 10 '13 at 18:26
  • But I can't undo the downvote unless you change something - it won't let me upvote it unless it is edited. – Dylan May 10 '13 at 18:32
  • I don't mean edit your answer to change its meaning. It is just a formality. – Dylan May 10 '13 at 18:34
  • Right, I see what you mean, sorry. I'll make some changes. – Anders Gustafsson May 10 '13 at 18:37
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    Sorry about the confusion, and the downvote, which is now rectified. – Dylan May 10 '13 at 18:45
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    Here, have an upvote. I am sure the answer will be useful to others without my requirement. – Dylan May 10 '13 at 18:51
  • @Anders: Unfortunately the code at "pastebin" doesn't mention whether it's public domain, or even much about its author. – Peter O. May 10 '13 at 23:22
  • @PeterO. You are right. I have removed the "public domain" statement from my answer. Nevertheless, there are no explicit copyright claims associated with the code and no author has revealed his- or herself, so in practice the code is there for anyone to use for whatever purpose. But as I mentioned, I have not verified its validity myself, I only included the link as a tip for others. – Anders Gustafsson May 11 '13 at 09:30
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ALGLIB is the usual go-to library for things like linear solvers. I would give that a good look before despairing.

Marc Gravell
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    For those looking, Google has released their or-tools https://developers.google.com/optimization/ I was able to hook this up in .NET quickly and it supports what the OP is looking for. – randomsolutions Mar 08 '16 at 02:13
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Linear programming is intended for doing exactly what you are asking. Multi-variable constraints are absolutely normal in linear programming. Look for free solvers like lpsolve (http://sourceforge.net/projects/lpsolve/), glpk (http://www.gnu.org/software/glpk/) or CBC (https://projects.coin-or.org/Cbc) for example.

I accept that the above suggestions are not in C# and not managed .net assemblies out-of-the-box. If that is a deal breaker for you, then maybe you can try building a version yourself from the source code of one of these libraries. Might require quite a bit of work though - I haven't tried it.

It is also unclear from your original question how big or complex a problem you are trying to solve. If you have variables that must take discrete values, then you would need a solver library that will do branch and bound or similar, otherwise if its purely linear and continuous then you can just use a simplex algorithm. Its in lots of textbooks if you can't find a pre-built version.

If its a really tiny problem (tens of variables and constraints) or just linear and continuous then you may be able to get away with your own fresh (portable, pure managed code) implementation, but if you have thousands of constraints and variables, you may struggle to get the performance you need. If you have a big and complex problem you may be out of luck as you may need a commercial solver to get the answers you need.

TimChippingtonDerrick
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no one mentioned solver foundation. It is a good option.

Naresh
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    A good one, with a few examples explained. Express (free) license allows to execute problems with up to 1000 decision variables. Given link is broken, but if you are interested, you can find it [here](http://msdn.microsoft.com/en-us/library/ff524509(v=vs.93).aspx) – krzychu Jun 06 '14 at 21:23
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    For exponential problems this is very limiting, and I would not consider it even remotely free. Something like a TSP is limited to 45 points, for example. – Max Izrin Apr 29 '17 at 11:40