i have a MILP with ~3000 binaries, 300000 continuous variables and ~1MM constraints. I am trying to solve this on the VM how long could it potentially take on a 16 core 128 gig machine? also what are the general limits of creating problems using pulp that cplex solver can handle on such a machine? any insights would be appreciated
The solution time is not just a function of the number of variables and equations. Basically, you just have to try it out. No one can predict how much time is needed to solve your problem.
It is impossible to answer either question sensibly. There are some problems with only a few thousand variables that are still unsolved 'hard' problems and others with millions of variables that can be solved quite easily. Solution time depends hugely on the structure and numerical details of your problem and many other non-trivial factors.
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I need to run a model, where I optimise a diet within a set of constraints and call all integer solutions in the end. I have found a diet example matching almost what I need here: hakank.org. However, in my case, my variables take continuous values, so in the examples this would be all the nutritional values and the cost, while only x take integer. However, it seems like I can only define either 'intvar' or 'boolvar' when defining by variables with this model. Is there a way to overcome this? Other would there be other more suitable models with examples that I can read online?
I'm new to constraint programming, so any help would be appreaciated!
Thanks.
Most Constraint Programming tools and solvers only work with integers. That is where their strength is. If you have a mixture of continuous and discrete variables, it is a good idea to have a look at Mixed Integer Programming. MIP tools and solvers are widely available.
The diet model is a classic example of an LP (Linear Programming) Model. When adding integer restrictions, you end up with a MIP model.
To answer your question: CPMpy does not support float variables (and I'm not sure that it's in the pipeline for future extensions).
Another take - than using MIP solvers as Erwin suggest - would be to write a MiniZinc (https://www.minizinc.org/) model of the problem and use some of its solvers. See my MiniZinc version of the diet problem: http://hakank.org/minizinc/diet1.mzn. And see the MiniZinc version of Stigler's Diet problem though it's float vars only: http://hakank.org/minizinc/stigler.mzn.
There are some MiniZinc CP solvers that also supports float variables, e.g. Gecode, JaCoP, and OptimathSAT. However, depending on the exact constraints - such as the relation with the float vars and the integer vars - they might struggle to find solutions fast. In contrast to some MIP solvers, generating all solutions is one of the general features of CP solvers.
Perhaps all these diverse suggestions more confuse than help you. Sorry about that. It might help if you give some more details about your problem.
So I want to try to solve my optimization problem using particle swarm optimiztion algorithm. As I comoratable with python I was looking into PySwarms toolkit. The issue is I am not really experienced in this field and don't really know how to account for integrality constraints of my problem. I was looking for advice on what are some approches to dealing with integral variables in PSO. And maybe some examples with PySwarms or any good alternative packages?
You can try pymoo module, which is an excellent multi-objective optimization tool. It can also solve mixed variable problems. Despite pymoo is first of all designed to solve such problems using genetic algorithms, there is an implementation of PSO (single-objective with continuous variables). Maybe you'll find it useful to try to solve your mixed variable problem using genetic algorithm or one of its modifications (e.g. NSGAII).
Gurobi and CPLEX are solvers that have been very popular in recent years. CPLEX is easier for academics in terms of the license. It is also said to be very high in performance. But Gurobi is claimed to be the fastest solver in recent years, with continuous improvements. However, it is said that its performance decreases when the number of constraints increases.
In terms of speed and performance, which solver is generally recommended specifically for large-scale problems with the quadratic objective function, which have not too many constraints?
Will their use within Python affect their performance?
Math programming is inherently hard and there will likely always be instances where one solver is faster than another. Often, problems are solved quickly just because some heuristic was "lucky".
Also, the size of a problem alone is not a reliable measure for its difficulty. There are tiny instances that are still unsolved while we can solve instances with millions of constraints in a very short amount of time.
When you're looking for the best performance, you should analyze the solver's behavior by inspecting the log file and then try to adjust parameters accordingly. If you have the opportunity to test out different solvers you should just go for it to have even more options available. You should be careful about recommendations for either of the established, state-of-the-art solvers - especially without hands-on computational experiments.
You also need to consider the difficulty of the modeling environment/language and how much time you might need to finish the modeling part.
To answer your question concerning Gurobi's Python interface: this is a very performant and popular tool for all kinds of applications and is most likely not going to impact the overall solving time. In the majority of cases, the actual solving time is still the dominant factor while the model construction time is negligible.
As mattmilten already said, if you compare the performance of the major commercial solvers on a range of problems you will find instances where one is clearly better than the others. However that will depend on many details that might seem irrelevant. We did a side-by-side comparison on our own collection of problem instances (saved as MPS files) that were all generated from the same C++ code on different sub-problems of a large optimisation problem. So they were essentially just different sets of data in the same model and we still found big variations across the solvers. It really does depend on the details of your specific problem.
I use python for scientific applications, esp. for solving differential equations. I´ve already used the odeint function successfully on simple equation systems.
Right now my goal is to solve a rather complex system of over 300 equations. At this point the odeint functions give me reasonable results as long as the time steps in the t-array are equal or smaller than 1e-3. But I need bigger time steps since the system has to be integrated over several thousand seconds. Bigger time steps yield the "excess work done.." error.
Does anyone have experience with odeint and can tell me, why this is the case, although the odeint function seems to choose its time steps automatically and then displays the results that match the time steps given by me?
I simply don´t understand why this happens. I think I can work around the problem by integrating multiple times, but maybe someone knows a better solution. I apologize in advance in the case there already is a solution elsewhere and I haven´t seen it.
I want to solve an optimisation problem using PuLP library in python. My optimisation problem has >10000 variables and lot of constraints. It takes very long time for PuLP to solve such big problems. Is there any way we can implement multi threading and gain speed ?
Any other solution/library for such big optimisation problems?
Linear programming has not been very amenable to paralelisation, so your best bet to make the problem faster is either to use a different solver or to reformulate your problem.
You can get a feel for the speed at which other solvers can solve your problem by generating an MPS file (using the writeMPS() method on your propblem variable) and submitting it to NeOS.