I have to make extensive use of Linear Programming & Mixed-Integer Linear Programming in my day job. This all runs on CPLEX. It would be really cool to do that sort of thing in Prolog, but I doubt it could handle massive models. Anyway you could explain what combinatorial optimization is for and how it differs from the things commonly seen in operations research?
For solving linear programs and mixed-integer linear programs with Prolog, I recommend the CLP(Q) and CLP(R) libraries of SICStus Prolog. See for example:
For discrete optimization tasks, also check out the integer constraint solver that ships with SICStus Prolog. See especially the combinatorial constraints:
As to the relation between Prolog and operations research: Prolog systems internally use methods from operations research to efficiently solve optimization tasks; in addition to that, you can of course also implement every OR algorithm in Prolog.
For many commercial users of SICStus Prolog, the efficiency of its constraint solvers are an important reason for buying a licence.
