What you describe falls under the general umbrella term of combinatorial optimization, of which Constraint Programming, Mixed Integer Programming, SAT, SMT, and

What you describe falls under the general umbrella term of combinatorial optimization, of which Constraint Programming, Mixed Integer Programming, SAT, SMT, and local search techniques can be said to fall under. Personally, I find the languages and methods used in constraint programming (CP) to define models the most clear, even though that is not always the best way to actaully solve the problems. To write CP models, the MiniZinc language is quite nice and has support for using many different solvers on the back end. The MiniZinc website (https://www.minizinc.org/ https://www.minizinc.org/) has quite a lot of documentation. For an outsider perspective, Hillel Wayne wrote an interesting blog post on using MiniZinc (https://hillelwayne.com/post/minizinc/ https://hillelwayne.com/post/minizinc/).