I want to model an optimization problem that contains quite some bilinear terms. As such, I want to make use of the functionality of Gurobi 9.0 to solve bilinear problems. Clearly, I can use the GurobiPy API. However, I might want to compare other solvers (like BARON). So, I wonder whether it is possible to use Pyomo to formulate the problem and then solve it using Gurobi? Will there be any problems?
As far as I can tell, there should not be a problem. The same Gurobi solver will be used. Your problem will just be modelled in a somewhat different syntax (PYOMO) which is easily portable for solving with a wider range of solvers.
If still in doubt, I suggest you try a very simple problem with a bilinear term.
Note however that BARON requires a commercial license unlike Gurobi which offers free academic licenses.
Best of luck!
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What is the best online solution to solve a linear programming problem?
I heard about several like Gurobi.
One thing I especially want is the possibility to get an approximate solution when the exact resolution takes too long.
The most comprehensive online optimization system is NEOS. It takes models in a variety of input formats and has a wide range of solvers.
Many solvers have settings to allow them to terminate early, even before optimality is reached, if you want an approximate and quick solution. But often your best bet in that case is to use a heuristic algorithm designed specifically for your problem.
There is boost 1.53 out and OdeInt in it. It has a range of numerical ode solvers in it. Yet I wonder if there is lsode analog in it - for cases when you have garanteed analitical solution?
I don't fully understand your question. LSODE solves any generic ODE of the form dx/dt = f(x,t) [1], just like the methods in odeint. However, LSODE checks for stiffness of the problem and chooses the right scheme (predictor corrector for non-stiff, and backward differentiation for stiff problems). odeint does not provide this automatic selection, but rather relies on the user to choose the right scheme for the problem. None of the two implementations use a possible existing analytical solution, as far as I know.
[1] https://computation.llnl.gov/casc/odepack/odepack_home.html
Most ODE solvers does imply some kind of restrictions over original LSODE (the Fortran implementation). The closest alternative I know is Octave from GNU for now.
I have a set of problems (sets of equations and inequalities) for which I know that all variables have to be integers, and have finitely many solutions. I know that if I take any random objective function and let an lp or mip solver onto it, it finds a solution, however I want all solutions to the problem, and of course, as efficiently as possible. I don't really care about optimizing anything, but apparently most of the software that deals with it does. Is there any solver that can do that? If so, which one is the best/simplest one, or which one would you recommend? At best one that can be used as a C/C++ library.
There is a nice blog post by Paul Rubin on how to find K best solutions, which can be easily generalized to get all the solutions. As Ali suggested one of the approaches is to use a solution pool. Two other approaches are:
Use an incumbent callback to track and reject solutions.
Use an incumbent callback with solution injection.
See the blog post for details.
IBM ILOG CPLEX has a solution pool feature and it's free for academic purposes.
I guess you can probably get all solution if you set the maximum pool size sufficiently large. I don't know for sure, never tried.
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?
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).
If you would like to get a feasibel integer solution fast and if you don't need the optimal solution, you can try
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.
Try different values for solver parameters concerning MIP heuristics.
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.
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.
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.
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.
I am newbie for integer linear programming.
I plan to use a integer linear programming solver to solve my combinatorial optimization problem.
I am more familiar with C++/object oriented programming on an IDE.
Now I am using NetBeans with Cygwin to write my applications most of time.
May I ask if there is an easy use ILP solver for me?
Or it depends on the problem I want to solve ? I am trying to do some resources mapping optimization. Please let me know if any further information is required.
Thank you very much, Cassie.
If what you want is linear mixed integer programming, then I would point to Coin-OR (and specifically to the module CBC). It's Free software (as speech)
You can either use it with a specific language, or use C++.
Use C++ if you data requires lots of preprocessing, or if you want to put your hands into the solver (choosing pivot points, column generation, adding cuts and so on...).
Use the integrated language if you want to use the solver as a black box (you're just interested in the result and the problem is easy or classic enough to be solved without tweaking).
But in the tags you mention genetic algorithms and graphs algorithms. Maybe you should start by better defing your problem...
For graphs I like a lot Boost::Graph
I have used lp_solve ( http://lpsolve.sourceforge.net/5.5/ ) on a couple of occasions with success. It is mature, feature rich and is extremely well documented with lots of good advice if your linear programming skills are rusty. The integer linear programming is not a just an add on but is strongly emphasized with this package.
Just noticed that you say you are a 'newbie' at this. Well, then I strongly recommend this package since the documentation is full of examples and gentle tutorials. Other packages I have tried tend to assume a lot of the user.
For large problems, you might look at AMPL, which is an optimization interpreter with many backend solvers available. It runs as a separate process; C++ would be used to write out the input data.
Then you could try various state-of-the-art solvers.
Look into GLPK. Comes with a few examples, and works with a subset of AMPL, although IMHO works best when you stick to C/C++ for model setup. Copes with pretty big models too.
Linear Programming from Wikipedia covers a few different algorithms that you could do some digging into to see which may work best for you. Does that help or were you wanting something more specific?