JuMP extensions for constraint programming.

These extensions rely on ConstraintProgrammingExtensions, an extension for MathOptInterface.jl providing several constraint-programming-oriented sets. There is already one solver providing some of these new sets: CPLEXCP.jl.

For now, the new syntax can only be used with a patch applied on top of JuMP: PR 2241.

The goal of these series of packages is to provide access to constraint programming (CP) within Julia, considering that CP is barely unavailable in the ecosystem, the exception being ConstraintSolver.jl.

The CP environment is very different from the mathematical programming one (and it is not related to the lack of dual variables in CP solvers): the functionalities provided by the solvers do not easily match (some provide reified constraints, others equivalence constraints; some solvers provide specific expressions like count(…), that may be then used in the objective function, others only support constraints like x <= count(…) or x == count(…)). You can express the same constraints with all solvers, but not always in the same way. Moreover, solvers tend not to provide callable libraries, unlike optimisation solvers: they provide higher-level APIs, usually in languages such as C++ or Java. This means that, for closed-source solvers, there is no access to the solver, only to a modelling layer (like CPLEX CP Optimizer). Similarly, many solvers are written in Java, and thus require an access to the JVM to be run.

Due to these differences, the rationale behind the sets provided by ConstraintProgrammingExtensions.jl is to propose all new elements as constraints, and not functions. Solvers only supporting the constraint count(…) in the form x == count(…) directly match these definitions (for instance, Gecode). Others provide expressions for this constraints (like CPLEX CP Optimizer), but they can be used in constraints to match the same semantics. In other words, the goal is to provide a set of "flat" primitives that is supported by a large number of solvers.

This is similar to what MiniZinc provides, except JuCP & co. work on the code level. MiniZinc is a common descriptive language for CP that is independently implemented by several solvers (like Gecode, JaCoP, Choco). Under the hood, MiniZinc transforms the input file in FlatZinc, a lower-level programming language (a kind of intermediate representation), which the solver then reads. This is similar to AMPL's NL format (in time, maybe AmplNLWriter.jl should be extended to handle CP extensions). Savile Row and Conjure are similar in principle to MiniZinc, with the definition of a high-level language to describe the models (Essence), which is lowered by Conjure (Essence'); these two pieces of software also optimise the models, which is not, currently, a goal of JuCP & co.; again, communication is mostly made through files. On the other hand, JuCP & co. work by directly using the solvers' API, similarly to how other solvers work with JuMP/MOI. This approach has also been chosen by ECLiPSe, for instance to communicate with Gecode.

In the specific case of CPLEX CP Optimizer, albeit the solver itself is written in C++ and available through a C++ API, this way has not been chosen. Actually, the C++ library that IBM gives is only a static library, which is a nightmare to convert into a standard dynamic library. Furthermore, this process requires many platform-specific tools to do so (mostly, the linker and many .lib library files for the dependencies: Clang.jl does not provide access to the linker, the dependencies require a core Visual C++ installation; these dependencies are heavier than the JVM). Another solution would have been to write a callable library on top of CPLEX Concert, which was deemed too heavy for a prototype (maybe IBM may help on this side?).

In approximate order of importance:

• Have PR 2051 merged into JuMP to allow more syntax extensions.
• Complete the solver wrapper CPLEXCP.jl. This means (again, in approximate order of importance):
  • improving the test suite (see the next point)
  • adding the missing constraints
  • wrap the missing parts, especially tuning the search phase
  • study how to integrate it more with Julia, for instance callbacks
• Decide what to do for testing the wrappers. Many tests in MathOptInterface.jl do not apply, as the solvers are severely limited when it comes to continuous problems; also, they don't provide dual values. Changing variable types is often not possible, which implies that variables must be created with their constraint (add_constrained_variable instead of add_variable plus add_constraint). This probably calls for simplifying methods in ConstraintProgrammingExtensions.jl to only call the relevant tests in MathOptInterface.jl, plus providing a lot of new tests.
• Determine how to expose more basic functionalities from solvers, like interval variables.
• Determine how to expose more advanced functionalities from solvers, like custom propagators, custom constraints, custom search techniques. Search Combinators can be a good start.
• Write wrappers for more solvers. The major ones are:
  • Gecode. In C++, models must inherit the Script class; have a look at their FlatZinc implementation, more precisely ParserState?
  • JaCoP. Highly similar to CPLEX CP in Java, [no need to inherit from a given class](https://github.com/radsz/jacop/blob/develop/src/main/java/org/jacop/examples/fd/ExampleFD.java.
  • Choco, mostly the same.