Extending an algebraic modeling language to support constraint programming

Although algebraic modeling languages are widely used in linear and nonlinear programming applications, their use for combinatorial or discrete optimization has largely been limited to developing integer linear programming models for solution by branch-and-bound procedures. Yet much of a modeling language's underlying structure for expressing integer programs is equally useful for describing more general combinatorial optimization constructs. Constraint programming solvers offer an alternative approach to solving combinatorial optimization problems, in which natural combinatorial constructs are addressed directly within the solution procedure. Hence the growing popularity of constraint programming motivates a variety of extensions to algebraic modeling languages for the purpose of describing combinatorial problems and conveying them to solvers. We examine some of these language extensions along with the significant changes in solver interface design that they require. In particular, we describe how several useful combinatorial features have been added to the AMPL modeling language and how AMPL's general-purpose solver interface has been adapted accordingly. As an illustration of a solver connection, we provide examples from an AMPL driver for ILOG Solver.