The Potential of Constraint Programming

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The Potential of Constraint Programming

In the 1990s, constraint programming features, including powerful constraint-solving algorithms, were successfully incorporated into a number of general-purpose programming languages, as well as several special-purpose programming languages. This brought computer science closer and closer to the Holy Grail of computer programming, namely, allowing the user to simply state the problem and then the computer will solve it.

As word of this exciting development began to spread beyond the computer science community, researchers in operations research began to realize the great potential of integrating constraint programming with the traditional techniques of integer programming (and other areas of mathematical programming as well). The much greater flexibility in expressing the constraints of the problem should greatly increase the ability to formulate valid models for complex problems. It also should lead to much more compact and straight- forward formulations. In addition, by reducing the size of the feasible region that needs to be considered while efficiently finding solutions within this region, the constraint-solving algorithms of constraint programming might help accelerate the progress of integer programming algorithms in finding an optimal solution.

Because of their substantial differences, integrating constraint programming with integer programming is a very difficult task. Since integer programming does not recognize most of the constraints of constraint programming, this requires developing computer- implemented procedures for translating from the language of constraint programming to the language of integer programming and vice versa. Good progress is being made, but this undoubtedly will continue to be one of the most active areas of OR research for some years to come.

To illustrate the way in which constraint programming can greatly simplify the formulation of integer programming models, we now will introduce two of the most important “global constraints” of constraint programming. A global constraint is a constraint that succinctly expresses a global pattern in the allowable relationship between multiple variables. Therefore, a single global constraint often can replace what used to require a large number of traditional integer programming constraints while also making the model considerably more readable. To clarify the presentation, we will use very simple examples that don’t require the use of constraint programming to illustrate global constraints, but these same types of constraints also can readily be used for some much more complicated problems.

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