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I have an integer linear optimisation problem and I'm interested in feasible, good solutions. As far as I know, for example the Gnu Linear Programming Kit only returns the optimal solution (given it exists). This takes endless time and is not exactly what I'm looking for: I would be happy with any good solution, not only the optimal one.

So a LP-Solver that e.g. stops after some time and returns the best solution he found so far, would do the job.

Is there any such software? It would be great if that software was open source or at least free as in beer.

Alternatively: Is there any other way that usually speeds up Integer LP problems? Is this the right place to ask?

Turion
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5 Answers5

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Many solvers provide a time limit parameter; if you set the time limit parameter, they will stop once the time limit is reached. If an integer feasible solution has been found, it will return the best feasible solution found to that point.

As you may know, integer programming is NP-hard, and there is a real art to finding optimal solutions as well as good feasible solutions quickly. To compare the different solvers, see Prof. Hans Mittelmann's Benchmarks for Optimization Software. The MILP benchmarks - particularly MIPLIB2010 and the Feasibility Benchmark should be most relevant.

In addition to selecting a good solver, there are many things that can be done to improve solve times including tuning the parameters of the solver and model reformulation. Many people in research and industry - including myself - spend our careers working on improving the solve times of MIP models, both in general and for specific models.

If you are an academic user, note that the top commercial systems like CPLEX and Gurobi are free for academic use. See the respective websites for details.

Finally, you may want to look at OR-Exchange, a sister site to Stack Overflow that focuses on the field of operations research.

(Disclaimer: I currently work for Gurobi Optimization and formerly worked for ILOG, which provided CPLEX).

Greg Glockner
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  • The Benchmark link was quite useful. I found, that COIN is an open source operations research project that has LP solvers, e.g. https://projects.coin-or.org/Clp and MILP solvers, see https://projects.coin-or.org/SYMPHONY. They did not as well as Gurobi and CPLEX in the benchmarks, but they work. – Turion Oct 08 '11 at 15:53
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    In my experience it's quite difficult to improve the performance of Gurobi or Cplex by tuning their parameters manually. Not that this is a bad thing - the algorithms work incredibly well without user intervention. – user327301 Feb 04 '13 at 19:13
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If you would like to get a feasibel integer solution fast and if you don't need the optimal solution, you can try

  1. Increase the relative or absolute Gap. Usually solvers have small gaps of say 0.0001% for relative gap. This means that the solver will continue searching for MIP solutions until it the MIP solution is not farther than 0.0001% away from the optimal solution. Increase this gab to e.g. 1%., So you get good solution, but the solver will not spent a long time in proving optimality.

  2. Try different values for solver parameters concerning MIP heuristics.

  3. CPLEX and GUROBI have parameters to control, MIP emphasis. This means that the solver will put more emphasis on looking for feasible solutions or on proving optimality. Set emphasis to feasible MIP solutions.

Most solvers like CPLEX, Gurobi, MOPS or GLPK have settings for gap and heuristics. MIP emphasis can be set - as far as I know - only in CPLEX and Gurobi.

Knasterbax
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As far as I know CPLEX can. It can return the solution pool which contains primal feasible solutions in the search, and if you specify the search focus on feasibility rather on optimality, more faesible solutions can be generated. At the end you can just export the pool. You can use the pool to do a hot start so it's pretty up to you. CPlex is free now at least in my country as you can sign up as a researcher.

jc W
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  • Thanks, CPLEX has already been mentioned. Is it possible to set a minimum required efficiency, like for example at lest n % of the non-integer solution? – Turion Aug 04 '12 at 14:56
  • When you way non-integer you mean infeasible one? – jc W Aug 05 '12 at 08:53
  • I don't know, I'm not really into the vocabulary of these optimisation algorithms. I just know that the simplex algorithm first approximates something like an optimal floating point solution. It's efficiency therefore must be an upper bound for the efficiency of any integer solution. – Turion Aug 06 '12 at 09:14
  • enn, why you want to set % of non-integer as the measure of "efficiency"? % is refering to what? the number of integer & non-integer solutions? But for me non-integer one is not actually a valid solution. – jc W Aug 07 '12 at 02:30
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    As far as I know, cplex can be stoped on the following conditions: (1) time is out (2) has populated n integer solutions (3) a predefiend gap is reached (like current lower bound and upper bound is close as some value or some %, 0 means optimality) (4) enough nodes in the tree have been processed. – jc W Aug 07 '12 at 02:41
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A usual approach for solving ILP is branch-and-bound. This utilized the solution of many sub-LP (without-I). The finally optimal result is the best of all sub-LP. As at least one solution is found you could stop anytime and would have a best-so-far.

One package that could do it, is the free lpsolve. Look there at set_timeout for giving a time limit, and when it is ILP the solve function can return in SUPOPTIMAL the best_so_far value.

flolo
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Could you take into account Microsoft Solver Foundation? The only restriction is technology stack that you prefer and here you should use, as you guess, Microsoft technologies: C#, vb.net, etc. Here is example how to use it with Excel: http://channel9.msdn.com/posts/Modeling-with-Solver-Foundation-30 .

Regarding to your question it is possible to have not a fully optimized solutions if you set efficiency (for example 85% or 0.85). In outcome you can see all possible solutions for such restriction.

apros
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