You might be interested by Comet, by Pascal van Hentenryck, since (I think) it is a good compromise, offering a high-level language but also an easy integration with mainstream languages (mainly Java).

Thanks a lot for your response! I will have a closer look at Comet. The fact that Comet is distributed commercially may hamper its more widespread adaption (at least there is a free academic license).

You might want to have a look at Google's or-tools. The library is written in C++ hence is fast, but it has a nice interface to python, hence making it very easy to write models. One negative aspect is that the number of global constraints currently implemented is limited.

Gecode is a very fast and well maintained library written in C++. This

A more general tool to write models are the zinc (and minizinc) languages of the G12 group. They have backends for a number of solvers, including Google's and Gecode. So, if you can model in minizinc, you can then run the models through various solvers.

I use ILOG CP Optimizer. It has several options - Java, C++, and the OPL format. There are special constructs for scheduling. Extremely useful for 'model-and-run' scenarios where you focus only on modeling using available constructs and solving is taken care by the solver. I am using it for both industry level applications and academic type research.

In terms of languages, have a look at MiniZinc (with its high level "sibling" Zinc and low level one FlatZinc; check http://www.minizinc.org/). For solvers I would have a look at Gecode and for platforms at G12.

I see a lot of people suggesting Gecode; any idea how it compares to Gurobi for convex optimization problems?

I am agree flatzinc is supported by many solvers. Gecode, but also the solvers that participate to the minizinc Challenge. You can find the complete list and results of the last challenge here : http://www.g12.cs.mu.oz.au/minizinc/challenge2012/results2012.html. I have to say that i do not particularly like flatzinc, but it is widely used...

@Brandon, It is difficult to answer to the question Mathematical programming versus Constraint programming because :

1- Some constraint programming solver uses a mathematical programming solver in certain cases (you can find in the previous link that gecode proposes a version that use the gurobi solver, Or-tools uses glpk).

2- Some mathematical programming solvers has integrated some constraint programming technique to reduce the variables domains (some preprocessing techniques used in MP ressemble to techniques proposed and used in CP.

3- It depends on the problem. The two sets of solvers do not attack the problem by the same side. MP attacks a problem by the cost of the objective function although CP attacks the problems by the variable domains, the feasibility.

My meaning is : If you have a very constrained problem, or a problem where the constraint are quite difficult to be expressed by linear programming, use CP. If your problem has a quite huge feasible domain, and you expect that there are many solutions, use MP.

I would suggest GAMS and MATLAB, but see what you are more familiar with.

I have herd that CP is powerful, but not used it yet.

What about AIMMS? I heard they already are CP compliant.

For an opensource solution, try using SCIP.

However, SCIP is implemented for C&C++ .

I meanwhile started writing a MiniZinc interface for Clojure. That will combine access to a range of state-of-the-art solvers, the rich world of Java libraries, and a very high-level language (Clojure). An early sketch is available at https://github.com/tanders/clojure2minizinc

For me AIMMS, since (1) it supports a big number of solvers for different problems. (2) very nice interface for importing multi-dimensional parameters (3) very nice model output interface (4) easy to understand and easy to follow.

Constraint programming solvers are made available thanks to library. There is a difference between the language in which there are written and the API of the library. You should consider more the API than the programming language. So this is a matter of taste. For instance I don't like minizinc but this just a personal opinion. If you are mainly focused on the modeling part of the problem then try to use an API which is simple. You could use or-tools in this case or Oscar (solver based on Scala). If you want to play with low level functions of a CP solver then you can use another solver which give you the possibility to interact with low level features like choco or Gecode. Gecode is fast but it is also complex sometimes (and easy to use for some other aspects). Try to have a look at the API and use only API stuff;

> For my purposes (focus on modelling of complex CSPs) I would ideally like some mainstream language that is at the same time rather high level. So, I am currently looking at the constraint programming libraries for Python.  

It makes sense. You can consider using the 'docplex' package in PyPI (https://pypi.python.org/pypi/docplex/1.0.455). It contains the CP Optimizer modeling for Python from IBM (http://www-01.ibm.com/software/commerce/optimization/cplex-cp-optimizer/). Then you can solve your problems either on the cloud or locally on your machine (CP Optimizer is free of charge for academics: https://www-304.ibm.com/ibm/university/academic/pub/jsps/assetredirector.jsp?asset_id=1070).

OptaPlanner (open source, apache license, pure Java) is used across the globe:  https://www.optaplanner.org/

It's very different from other constraint solves in the sense that it works with an input/output of rich domain classes that can make use of all OO techniques such as polymorphism and in the sense that the constraints are expressed as DRL patterns (which can call custom code) instead of mathmetical equations.

It has surprising little academic uptake, but it dominates the professional enterprise open source scene.

I recommend using minizinc to model the problem.