... Do you have a set constraint programming solver that you always use, no matter which global constraint you actually need (implementing the needed global constraint yourself if needed)?
Find one that is well supported, that you understand to some extent, and that is powerful enough (speed and expressiveness) to suit your future needs. Invest your time in choosing a good tool and learning to use it well, then implementing constraints will be easier than struggling with a tool that is inadequate for the job.
There are online tools for linear optimization, constraint solving, even an extension for Microsoft Excel called OpenSolver which extends Excel’s built-in Solver with more powerful solvers. Constraint Logic Solvers are available which run on many different languages:
Which to choose is partly a function of many things. Different Contraint Programming Solvers perform better than others in benchmarks, speed and ability is one aspect to consider.
Focus on how easy is it to learn a system, and the modelling aspect. Consider the syntax, element constraint, reification and defining predicates (decompositions). Look for community support and the number of examples, documentation, etc.
You'll notice that Google's OR-Tools has a Stack Overflow tag for OR-Tools (as does Choco, on top of Java). OR-Tools is free, and placed well in the benchmarks:
"OR-Tools is an open source software suite for optimization, tuned for tackling the world's toughest problems in vehicle routing, flows, integer and linear programming, and constraint programming.
After modeling your problem in the programming language of your choice, you can use any of a half dozen solvers to solve it: commercial solvers such as Gurobi or CPLEX, or open-source solvers such as SCIP, GLPK, or Google's GLOP and award-winning CP-SAT.".
Further afield are proof solvers such as ACL2 (A Computational Logic for Applicative Common Lisp), an extension to Lisp which is itself an extensible theory in a first-order logic, and an automated theorem prover. It represents a difficult uphill climb, but it produces programs capable of proving themselves to be correct.
If you visit the GCC you'll notice that they describe the global contraints in Prolog (and XML) so if you want to rely on that reference it's helpful if your Constraint Logic Solver is written in (or accepts) Prolog (or that you are fluent in that language).
Constraint logic programming extends Prolog to include concepts from constraint satisfaction. A constraint logic program allows constraints in the body of clauses, such as: A(X,Y) :- X+Y>0. It is suited to large-scale combinatorial optimisation problems and is thus useful for applications in industrial settings, such as automated time-tabling and production scheduling. Most Prolog systems ship with at least one constraint solver for finite domains, and often also with solvers for other domains like rational numbers.".
There are global constraints in SICStus Prolog, and five libraries: Constraint Handling Rules, Constraint Logic Programming over Booleans (unsupported since release 4.0.7), Constraint Logic Programming over Finite Domains, Constraint Logic Programming over Rationals or Reals (unsupported), and a Finite Domain Constraint Debugger - it's quite a full featured version of Prolog, but it's not free.
B-Prolog is a fast alternative and while it does have a tag on SO there's barely a dozen uses of it. But if you look at Wikipedia's comparison of Prolog implementations you'll notice that it has a feature set comparable to SICStus.
So you should probably favor a Prolog implementation, but there's no reason why you couldn't use Haskell. Which underlying language is used to run whichever solver is very much a personal preference, but choosing one language and a solver framework with a large community and numerous libraries for different solvers (or the ability to output for a long list of separate solver executables) ensures that you'll always be able to progress forward rather than getting stuck implementing missing features or asking for assistance.
A good tool to compare some of the popular solvers is the Apache Software Foundation's Constraint Programming Solvers comparison tool. For example comparing Choco, Picat, and OR-Tools shows that OR-Tools requires quite a lengthy specification compared to Picat, while Choco is certainly more mature and supports more Global Constraints.
Hakan Kjellerstrand's webpage and blog on Constraint Programming while not updated in the past year has a decade of archives and (amongst numerous other pages) a webpage about Global Constraints, also one on Operations Research.
Wikipedia's has webpages on: Constraint Satisfaction and Hill Climbing (but nothing for Late Acceptance Hill Climbing (LAHC)). LAHC is one of the techniques employed by OptaPlanner, an AI constraint solver. Google returns over 70M results for "Late Acceptance Hill Climbing" - lesson: don't let one site's miss make you miss, check multiple sources. Another search term to use is "Late Acceptance Anytime Algorithm" (related to LAHC) which returns another 56M results.
Some of the newest directions have the least information available, it's important to do your own research and determine which direction you wish to go. Breakthroughs in AI and Neuromorphic Computing are frequent enough that best laid plans go awry a few years later; but as long as the legacy tools you have available are sufficiently capable and fast enough for your needs you shouldn't worry about bleeding edge too much, nor completely discount it either.
The website arXiv has 3761 results for "Constraint Programming" and is an excellent source for researching the latest techniques.
I would like to clarify that I am absolutely not an expert when it comes to constraint programming (I happen to use it when it seems to be the right tool for the right job).
A description of the bottom-up and top-down proof procedures used for searching the problem space gives some insight into choosing your tool and approach.