I think the reason why these tools are not accessible as they could be is because the vast majority of solvers are MIPs (Mixed Integer Programming) based, meaning the domain need to be written down using mathematical equations. This in turn means a user would need to be familiar with both the domain and mathematics in order to correctly write constraints.

That being said, MIPs are not the only kind of solvers. There are also "local search" based constraint solvers, which does not have the restriction that each constraint must be modelled as a relation or equation of integer variables. In local search solvers, the constraints are mostly treated as a black box that tells how good a particular solution is. As a consequent, local search solvers are typically unable to find the optimal solution (since it would require testing all possible solutions because the constraint is treated as a black box), but rather finds a "near-optimal" solution in reasonable time.

One local search based solver is Timefold Solver. In it, users annotate their domain so the solver knows what are the variables and possible values. This means instead of your constraints dealing with `int`, it would deal with `Shift` and `Employee`, and can access any of their methods.

Disclosure: I work on Timefold Solver

You totally nailed it. The actual syntax / API of constraint solvers are so simple they can be learned in no time at all. What actually takes time and expertise is modelling problems in this fashion and there are almost 0 real world (in size and complexity) examples out there for others to reference.

I have about 5 years of experience in MiniZinc solving scheduling problems but sadly all that code is locked behind closed doors never to be open sourced. I would love put together some fully worked constraint programming examples complete with containerisation / visualisation/ modeling etc but the barrier to doing so is finding problems that are actually worth solving and have open source data to work on.

I agree, the theory isn't nearly as difficult as the reductions. Dennis Yurichev's "SAT/SMT by Example" (https://smt.st/) is a great resource on this topic, although pretty intimidating.

> Most of the material you can find is how to solve sudoku (the hello world of the space) or highly technical primary research literate meant exclusively for domain experts

Exactly. I was looking at using a sat solver for a rules engine and couldn't make heads or tails how to use it. After alot of deduction, got a basic POC working, but couldn't extend it to what was actually needed. But the gulf between toy implementations and anything more substantial was very large.

I’m a long time coder but a bit rusty now. Last year I built a football team optimiser using Google’s OR tools (various optional constraints like being with friends and trying to balance skill levels across teams). LLM’s can go quite far in terms of getting you into the approximately correct direction fairly quickly. They fail right now at really getting it right but I was far enough that I could then take it the rest of the way.

Do you have a link to the Coursera course?

yep, once you have the data, constraints, and utility functions properly* in the system you can brute force your way to many good enough solutions very quickly.

I coach a basketball league that has 8 periods. No player can play 2 more periods that any other player. The number of possible line-ups per game while still hitting the playing time contraint is astronomical. Very easy to find a series line-ups that fits the constraint, but very hard to find an optimal or near-optimal series of line-ups. It gets even more fun when you have to adjust for late arrivals or unannounced no-shows.

* not always completely doable

I can guarantee you a blog post detailing how to do this would go triple platinum

It's quite niche but it exists: https://en.wikipedia.org/wiki/Geometric_constraint_solving

A whole bunch of problems can be set up either way. MILP always has an objective, and the constraints are always linear combinations of the decisions. Gurobi is so incredibly fast that it might be worth contorting your problem into a MILP just so you can get solutions at all.

CP-SAT is integer only, so I'm guessing for physics it's not great (you can scale your reals but that's not as good as working with floating point directly).

The advantage of CP-SAT is that it handles boolean and integer variables and constraints much more efficiently than a MIP solver, specially higher-level constraints like all_different.

I would assume largely similarly? https://www.amazon.com/gp/product/1107658799/ is the book I last went through on this and it covers a lot of the same ideas. In particular, I'm assuming the section of this post that aims to minimize some value are directly using the same stuff.

I'm intrigued by bits like Outside Margin Comments[1] - `$onMargin minCol 20 maxCol 45` - text before column 20 and after column 45 is treated as a comment - 1970s.

[1] https://www.gams.com/latest/docs/UG_GAMSPrograms.html#UG_GAM...

Another "friendly syntax, multi-solver" approach is MiniZinc.org.

Indeed, it seems like an obvious thing to do. But just as you noted, it's not very clear LLMs really can improve over Prolog in terms of expressiveness and practicality given that Prolog already was designed for natural language parsing and is a concise formalism based on predicate logic (and ultimately propositional and first order logic) with constraint domain theory embeddings such as for arithmetic. Prolog syntax is also the starting point for most constraint solvers, and Prolog evaluation is also often referred to as basis for generalization into constraint solving. Though I'm not sure this generalization bears much value tbh when the break-through successes in constraint solving were particular domain-specific techniques (SAT solvers, interval propagation, arc consisteny/finite domain propagation, etc).

They're already very good at it—I myself have been using OR-Tools's CP-SAT solver for a large bin packing problem at work (via https://github.com/ankane/or-tools-ruby) & Chat-GPT was a big help working out the details of some of the constraints and objectives.

It is indeed a very good fit. There is some cool research about it: https://github.com/skadio/ner4opt

I think that I would. Using natural language to describe the problem and constraints would be much better than figuring out mid project that the variable structure I've chosen does not allow to express a particular constraint. Defining the right structure is just Art at this point.