Constraint and Integer Programming: Toward a Unified by Michela Milano

By Michela Milano

Constraint and Integer Programming provides many of the easy principles of constraint programming and mathematical programming, explores techniques to integration, brings us brand new on heuristic tools, and makes an attempt to determine destiny instructions during this fast-moving box.

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For instance, suppose there is a constraint and in our current solution at least one of ii, xi, x3 and x4 is fractional. Rather than branching on the one variable, it is possible to create five subproblems: one for each variable taking on the value 1, and one for havingall variables take on valueO. These subproblems completely cover the feasible solutions relative to this constraint, and can decrease the amount of branching needed relative to standard branching. Branching can even be used to model aspects that are difficult to embed in the integer programming formulation.

Enforcing arc consistency for global constraints by solving subproblems on the fly. In Proceedings of the International Conference on Principles and Practice of Constraint Programming, CP99. , and Wunderling, R. (2000) . MIP: Theory and practice - closing the gap. In Powell, M. , editors, System Modelling and Optimization: Methods, Theory and Applications. Kluwer. Caseau, Y. and Laburte, E (1997). Solving small TSPs with constraints. In Proceedings ofthe Fourteenth International Conference on Logic Programming -ICLP'97, pages 316-330.

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. Many logical constraints can be modeled through the use of binary integer variables: integer variables that can only take on the values 0 or 1. The binary variable Xj might be used to represent opening (Xj = 1) or not opening (Xj = 0) warehouse i. 17 Constraint and Integer Programming It is possible to combine binary variables into more complicated functions.

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