I came across Google OR-Tools which computes the TSP with reasonable approximations as discussed in this link. I am curious to know what specfic algorithm this tool uses for TSP. Does it have any specific optimizations (to the code) that make it perform well? (There are several approximate algorithms for the TSP, I am just curious to know if it uses a mix of multiple algorithms or which specific algorithm it uses).
See comment here:
https://github.com/google/or-tools/issues/920#issuecomment-435880431
it links to:
https://www.researchgate.net/publication/226021015_A_Constraint_Programming_Toolkit_for_Local_Search
which is a good starting point to understand the technology used.
Related
I'm working on project where I need to minimize functions by several variables like func(input_parameters, variable_parameters) -> min(variable_parameters).
I use optimizing functions from SciPy, so minimization process is a grey box: I can see the code on GitHub and read about used algorithms, but I'd like to think that it's okay and aim to testing of my own project.
Though, particular libraries shouldn't matter in this question.
At the moment I use few approaches:
Create simple examples and find global/local minima by hand and create test that performs optimization and compares its solution with the right one
If method needs gradients, compare analytically calculated gradients with their numerical approximation in tests
For iterative algorithms built upon ones provided by SciPy check that sequence of function values is monotonically nonincreasing in tests
Is there a book or an article about testing of mathematical optimization procedures?
P. S. I'm not talking about Test functions for optimization
, I'm asking about approaches used to test optimization procedure to find bugs faster.
I find the hypothesis library really useful for testing optimisation algorithms in development.
You can set it up to generate random test cases (functions, linear programs, etc) according to some specification. The idea is that you pass these to your algorithm and test for known invariants. For example you could have it throw random problems or subproblems at your algorithm and check that (for example):
Gradient descent methods produce a series of nonincreasing objectives
Local search finds a solution with no better neighbours
Heuristics maintain feasibility
There's a useful PyCon talk here explaining the idea of property based testing. It focuses more on testing APIs than algorithms, but I think the ideas transfer. I've found this approach does a pretty good job finding cases of unexpected behaviour as I'm writing a new algorithm.
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.
Are there any good libraries in c++ for sequential nonlinear optimization with constraints?
I am looking for inequality constraints and/or upper and lower bounds.
There is a stackoverflow question already for this but not all of them have constraints.
I know of NLopt, but it doesn't work well for my specific problem. Are there any others?
I finally found the solution that i was looking for if any one else is interested lpOpt
One SQP algorithm that you could try is DONLP2. It was originally written in Fortran 77 but there is an ANSI C version as well. It uses dense algebra, so it is primarily suitable for small to medium-sized problems. It is free for academic use. You need to request the code directly from the author, follow the instructions in the link.
UPDATE Sequential Quadratic Programming is only one approach to solving non-linear objective functions with constraints, there is also for example interior point methods. One very good large-scale open-source C++ alternative that applies the interior point approach is Ipopt (already mentioned in another answer). There is also for example the commercial package KNITRO. If you cannot or do not want to provide objective function and constraints gradients, you could also have a look at COBYLA2, of which a C version can be downloaded here.
For further inspiration, you could also consult the Decision Tree For Optimization Software, which lists different optimization codes suitable for a wide range of different problems.
I need to do analytical integration in C++. For example, I should integrate expressions like this: exp[I(x-y)], I is an imaginary number.
How can I do this in C++?
I tried GiNaC but it can just integrate polynomials. I also tried SymbolicC++. It can integrate functions like sine, cosine or exp(x) and ln(x), but it is not very powerful. For example, it can not integrate x*ln(x) which can be easily obtained by use of Mathematica or by integration by parts.
Are there any other tools or libraries which are able to do symbolic computation like analytical integration in C++?
If you need to do symbolic integration, then you're probably not going to get anything faster than running it in mathematica or maxima - they're already highly optimised. So unless your equations have a very specific formulae that you can exploit in a way that Mathematica or Maxima can not then you're probably out of luck -- and at very least you're not going to get that kind of custom manipulation from an off-the-shelf library.
You may be justified in writing your own code to get a speed boost if you needed to do numerical solutions. ( I know that I did for generating numerical solutions to PDEs).
The other C++ libraries I am aware of that do symbolic computation are
SymEngine (https://github.com/symengine/symengine)
Piranha (https://github.com/bluescarni/piranha)
If I am not mistaken, SymEngine does not yet support integration; however, Piranha does. The documentation for Piranha is somewhat limited at the moment and is under development, but you can see the integration function here. Note that the second link uses the syntax for the Python wrapper Piranha. However, Piranha "is a computer-algebra library for the symbolic manipulation of sparse multivariate polynomials and other closely-related symbolic objects (such as Poisson series)", so I do not think it can integrate the particular functions in which you may be interested.
Though it is not C++, you may also be interested in SymPy for Python, which can perform some of the more complicated symbolic integration you may be interested in. The documentation for SymPy's integrate is here.
A couple of days ago, I was searching for a symbolic math library like SymPy for C++, because I bedazzled by its speed comparing to Python or most of the other programming languages.
I found Vienna Math Library, an awesome library with very modern syntax, and SymPy's features to the best of my knowledge. This library also has an integral function that can be used for your problem.
It was good enough for solving IK (Inverse Kinematics) of 3 degrees of freedom articulated manipulator.
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?