Extending a General-purpose Algebraic Modeling Language to Combinatorial Optimization: a Logic Programming Approach

General-purpose algebraic modeling languages are a central feature of popular computer systems for large-scale optimization. Languages such as AIMMS [2], AMPL [12, 13], GAMS [4, 5], LINGO [23] and MPL [18] allow people to develop and maintain diverse optimization models in their natural mathematical forms. The systems that process these languages convert automatically to and from the various data structures required by packages of optimizing algorithms (“solvers”), with only minimal assistance from users. Most phases of language translation remain independent of solver details, however, so that users can easily switch between many combinations of language and solver. Algebraic modeling languages have been applied most successfully in linear and smooth nonlinear optimization. They have been notably less successful in combinatorial or discrete optimization, however, for two interconnected reasons. First, modeling languages have lacked the kinds of expressions that are needed to describe combinatorial problems in natural and convenient ways. Indeed, only one feature of these languages has been of direct use for combinatorial optimization: the option to specify that certain variables must take integer values. Hence these languages have been useful mainly for combinatorial problems that have straightforward formu-