I am looking for solvers for mixed-integer nonlinear programs (MINLP). Are there solvers that instead of exact solutions, provide faster but approximate solutions with some error bound?
Hi, for mixed-integer nonlinear programming you have the following solvers:
NOMAD: https://www.gerad.ca/nomad/Project/Home.html
DFL: http://www.dis.uniroma1.it/~lucidi/DFL/
Hello,
Naturally smaller problems you can solve by Excel solver which has GRG and Evolutionary solving methods which both are appropriate for nonlinear problems (GRG for smooth and convex whereas Evolutionary for non-smooth and non-convex functions) . By installing the open-solver add-in you will have also access to the mentioned by Richard Epenoy NOMAD solver.
Regards,
I would look concorde. I has worked for other problem than the TSP.
Dear Mohammad,
Use AMPL environment and select Outer Approximation Algorithm. It will be very fast and produce the least error while solving MINLP problems even with a large number of variables and constraints.
Hi,
Almost all modern day optimization solvers that can provide exact solutions have provision to terminate the solution process as per your requirement. One can provide termination conditions based on the number of feasible solutions, optimality and feasibility tolerances, the number of iterations, total solving time, etc. Pick a solver and you can find these termination options in its manual. Following are few such solvers.
MINOTAUR: https://wiki.mcs.anl.gov/minotaur/index.php/MINOTAUR
NEOS server's list of solvers: https://neos-server.org/neos/solvers/index.html
Cheers!
Fairly certain Lingo can solve these problems. You might contact them (Lindo Systems) about a student version (6 month license) that accommodates unlimited variables and constraints.
The only way to get error bounds is through the use of deterministic solvers. Additionally, if the problem is nonconvex when integrality is relaxed, you will need a global MINLP solver for valid error bounds. There are several global MINLP solvers available nowadays; all are based on branch and bound technology. The global MINLP solvers BARON, ANTIGONE, SCIP, LINDOGLOBAL and COUENNE are all available under GAMS; some of them are available under AMPL and AIMMS. Some comparisons between these solvers are provided in Mittelmann's site at http://plato.asu.edu/ftp/minlp.html. BARON, in particular, is available for free through the NEOS server. It is also available in commercial forms from GAMS, AIMMS, AMPL and minlp.com. The minlp.com distribution can run under MATLAB, YALMIP, Pyomo and JuMP. The BARON option you can use for faster termination is called deltaTerm.
TOMLAB is the great package that works in MATLAB
In this package, there is a robust subroutine that solves mixed-integer nonlinear programming in MATLAB
Please see the following link:
http://tomopt.com/tomlab/
You could try Pyomo, which offers interfaces to several mixed-integer optimizers (both linear and non-linear). Take a look to this link (https://stackoverflow.com/questions/42391945/solving-minlp-with-pyomo-and-bonmin) and to Pyomo documentation. I have coded MILP programs myself, not MINLP, but I'm pretty sure the syntax and solver callings are pretty similar.
Good luck!!
If you're interested in good solutions which have no guarantee (meaning a local solver). You might want to check out: https://github.com/lanl-ansi/Juniper.jl
It works best if your problem is nonconvex (for convex other solvers are better) and you can run the branch and bound part easily in parallel.
Edit:
I didn't see your convex tag:
Check out: A Review and Comparison of Solvers for Convex MINLP http://www.optimization-online.org/DB_HTML/2018/06/6650.html
A heuristic MINLP solver is available here:
http://www.midaco-solver.com/
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