Constraint Programming


Constraint Programming is a relatively new paradigm used to model and solve combinatorial optimization problems. It is most effective on highly combinatorial problem domains such as timetabling, sequencing, and resource-constrained scheduling. Successful industrial applications utilizing constraint programming technology include the gate allocation system at Hong Kong airport, the yard planning system at the port of Singapore, and the train timetable generation of Dutch Railways.

Constraint Programming in AIMMS

This chapter discusses the special identifier types and language constructs that AIMMS offers for formulating and solving constraint programming problems. We will see that constraint programming offers a much wider range of modeling constructs than, for example, integer linear programming or nonlinear programming. Different variable types can be used, while restrictions can be formed using arbitrary algebraic and logical expressions or by the use of special constraint types, such as alldifferent. In addition, AIMMS offers a specific syntax to express scheduling problems in an intuitive way, taking advantage of the algorithmic power that underlies constraint-based scheduling.

This chapter

In this chapter, the basic constraint programming concepts are first presented, including different variable types and restrictions in Constraint Programming Essentials. Scheduling Problems discusses the AIMMS syntax for modeling constraint-based scheduling problems. The final section of this chapter discusses issues related to modeling and solving constraint programs in AIMMS.


An in-depth discussion on constraint programming is given in [RBTW06] and more details on constraint-based scheduling can be found in [BPN01].

Online resources

First, the Association for Constraint Programming organizes an annual summer school, the material for which is posted online. This material can be accessed at The CPAIOR conference series organizes tutorials alongside each event, the materials of which are posted online. The CPAIOR 2009 tutorial provides an introduction to constraint programming and hybrid methods, and available online at