Recent research in the area of hybrid optimization shows that the right combination of different technologies, which exploits their complementary strengths, simplifies modeling and speeds up computation significantly. A substantial share of these computational gains comes from better communicating problem structure to solvers. Metaconstraints, which can be simple (e.g. linear) or complex (e.g. global) constraints endowed with extra behavioral parameters, allow for such richer representation of problem structure. They do, nevertheless, come with their own share of complicating issues, one of which is the identification of relationships between auxiliary variables of distinct constraint relaxations. We propose the use of additional semantic information in the declaration of decision variables as a generic solution to this issue. We present a series of examples to illustrate our ideas over a wide variety of applications. Key words: modeling; hybrid methods; metaconstraints; semantics 1.

Recent research in hybrid optimization shows that a combination of technologies that exploits their complementary strengths can significantly speed up computation. The use of high-level metaconstraints in the problem formulation can achieve a substantial share of these computational gains by better communicating problem structure to the solver. During the solution process, however, metaconstraints give rise to reformulations or relaxations that introduce auxiliary variables, and some of the variables in one metaconstraint’s reformulation may be functionally the same as or related to variables in another metaconstraint’s reformulation. These relationships must be recognized to obtain a tight overall relaxation. We propose a modeling scheme based on semantic typing that systematically addresses this problem while providing simpler, self-documenting models. It organizes the model around predicates and declares variables by associating each with a predicate through a keyword that is analogous to a database query. We present a series of examples to illustrate this idea over a wide variety of applications. Key words: modeling; hybrid methods; metaconstraints; semantics 1.