By Michela Milano

Constraint and Integer Programming provides the various simple rules of constraint programming and mathematical programming, explores techniques to integration, brings us brand new on heuristic equipment, and makes an attempt to figure destiny instructions during this fast-moving box.

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Which formulation should be used? Often, this is a computational issue: it is difficult to tell except by trying both . If the choice is between two formulations where one has a provably stronger relaxation (like our warehouse example), it is almost always better to go with the one with the stronger relaxation. There are tradeoffs, however. Many formulations with stronger relaxations are also larger in terms of the number variables and/or constraints. This makes the linear relaxation slower to solve.

1 Modeling While it seems that integer programming is quite restrictive, that is not the case. Many structures of practical interest can be modeled as linear constraints (though the model might not be immediately obvious). Here we outline some non-obvious uses of integer variables in modeling. For more examples, see the book by (Williams, 1999). 1 Logical Constraints. For many problems, it is important to identify when certain conditions occur. For instance, in a warehouse location problem, there may be a fixed cost incurred when a particular warehouse is opened.

The purpose of this chapter is to introduce the reader to CP and IP basic concepts used throughout the book. Clearly, this chapter is far from being comprehensive, but it provides some pointers to the literature that can be used for a deeper study. 3). 4. 2). 3. To conclude this overview, incomplete search is presented in Section 4. 2. CP(FD) Basic Concepts Constraint Programming on Finite Domain (referred to as CP(FD» has been recognized as a suitable modelling and solving tool to face combinatorial (optimization) problems.

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