A Brief Tour of Constraint Programming

A main motivation in constraint programming, especially in the constraint satisfaction problem, is to find a feasible solution to a stated set of constraints, or to prove that no such solution exists, hence it has a great deal of overlap with the subject of this book. Indeed, a main thrust of research on the constraint satisfaction problem is achieving a feasible solution as quickly as possible. As will be seen, a number of the techniques used in constraint programming are related to methods well known in optimization, yet others are novel. In recent years, constraint programming and mathematical programming (i.e. optimization) have begun to cross-fertilize, developing more capable hybrid methods along the way. See Chinneck (2002a) for example. For an excellent up-to-date summary of how optimization and constraint programming have merged, see the book Integrated Methods for Optimization by John Hooker (2007). Lustig and Puget (2001) also provide a concise explanation of the relationship between mathematical programming and constraint programming.

This chapter presents a very brief summary overview of constraint programming based on material by Bartak (1999), Kumar (1992), Dechter and Rossi (2002), Russell and Norvig (2002) and Miguel (2001), among others. References to the original publications on the techniques described herein can be found in those sources. This topic deserves an in-depth treatment in light of the subject of this book, possibly in a companion volume of about the same size, but that is a project for another time and an author more versed in the subject matter. The purpose of this brief tour is simply to make the reader aware of the rich body of algorithms relevant to issues of feasibility and infeasibility that is available in the constraint programming literature. The reader is urged to investigate further.