Constraint Programming

Abstract

In contrast to mathematical programming, which has its roots in the Operations Research community, constraint programming has its origins in the Artificial Intelligence and Computer Science communities. Constraint programming can be traced back to the constraint satisfaction problems studied in the 1970s. A constraint satisfaction problem requires a search for a feasible solution that satisfies all given constraints. To facilitate the search for a solution to such a problem various special purpose languages have been developed, e.g., Prolog. However, during the last decade of the twentieth century, constraint programming has not only been used for solving feasibility problems, but also for solving optimization problems. Several approaches have been developed that facilitate the application of constraint programming to optimization problems. One such approach is via the Optimization Programming Language (OPL), which was designed for modeling and solving optimization problems through both constraint programming techniques and mathematical programming procedures