Current Research

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Current Research

Current research in integrating constraint programming and integer programming is moving along several parallel paths. For example, the most straightforward approach is to simultaneously use both a constraint programming model and an integer programming model to represent complementary parts of a problem. Thus, each relevant constraint is included in whichever model it fits or, when feasible, in both models. As a constraint programming algorithm and an integer programming algorithm are applied to the respective models, information is passed back and forth to focus the search on the feasible solutions (those that satisfy the constraints of both models).

This kind of double modeling scheme can be implemented with the Optimization Programming Language (OPL) that is incorporated into the OPL-CPLEX Development System. After employing the OPL modeling language, the OPL-CPLEX Development System can invoke both a constraint programming algorithm (CP Optimizer) and a

mathematical programming solver (CPLEX) and then pass some information from one to the other.

Although double modeling is a good first step, the goal is to fully integrate constraint programming and integer programming so that a single hybrid model and a single algo- rithm can be used. It is this kind of seamless integration that will be able to fully provide the complementary strengths of both techniques. Although fully achieving this goal remains a formidable research challenge, good progress continues to be made in this direction. Selected Reference 5 describes the current state of the art in this area.

Even at this early stage, there already have been numerous successful applications of the merger of mathematical programming and constraint programming. The areas of application include network design, vehicle routing, crew rostering, the classical transportation problem with piecewise linear costs, inventory management, computer graphics, software engineering, databases, finance, engineering, and combinatorial optimization, among others. In addition, Selected Reference 3 describes how scheduling is proving to be a particularly fruitful area for the application of constraint programming. For example, because of the many complicated scheduling constraints involved, constraint programming has been used to determine the regular-season schedule for the National Football League in the United States.

These applications only begin to tap the potential of integrating constraint programming and integer programming. Further progress in completing this integration promises to open up many exciting new opportunities for important applications.

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