Guillaume Rochart

Explanations for global constraints

Numerous industrial problems can be modelled as constraint satisfaction problems: scheduling, call centers, television spots, etc. Constraint programming offers high-level modelling and reusable techniques for solving such problems. In order to provide efficient solvers and to better meet user needs, global constraints are often used. They model complex constraints over numerous variables: for instance, gcc, alldiff or stretch.

Explanations and numeric CSPs

Numerous industrial problems can be modelled as MINLP (Mixed Integer NonLinear Programming) problems combining both numeric and integer variables: design of water transmission networks, automobile, aircraft, etc. [1]. These problems are really hard to solve since they combine both the combinatorial nature of mixed integer programming and the intrinsic difficulty of nonlinear programs. Several methods were proposed to solve these problems: branch-and-bound, extended cutting plane methods, and generalised Benders decomposition, etc. But industrial applications need more than solving problems. Problems can be dynamic, this implies that constraints may be added or removed dynamically. Moreover, if no solution is found, the user often needs to know why the problem is over-constrained, or why the expected solution is inconsistent.