Partial redundant modeling

Abstract

Redundant modeling combines different models of the same problem using channeling constraints [1]. Channeling constraints allow different formulations of a problem to interact, propagating the constraints between different formulations. This can result in a significant improvement in performance. Originally, work on redundant modeling assumed that redundant models must fully characterize the problem [1]. Later, Smith argued that only the primal model need fully characterize the problem, while the dual model need only have all the dual variables and channeling constraints between the two models (a minimal combined model) [2]. This paper proposes partial redundant modeling, an extension of the minimal combined model that encourages more than two models, omits some dual variables and omits all the dual constraints. Partial redundant models originate in problems with a categorical structure, where the variables may be subdivided into categories. Often these categories can be identified as groups of variables that fall under n-ary constraints that partition the variables into disjoint sets. Real world problems, such as scheduling and rostering, may also have categorical structure. Logic puzzles are a class of problems with a simplified version of categorical structure. A logic puzzle consists of a set of objects, a set of categories (same-size disjoint subsets of those objects) that must take on different values, and a set of semantic relations, which specify the relationships that hold between the categories. In a logic puzzle, each category can be viewed as a subset of CSP variables under an all-diff constraint. Different CSP models can be obtained by selecting the objects in a different category as the domain values, taking all other objects in the other categories to be the variables. We propose to maintain multiple partial redundant models of problems with categorical structure, adding channeling constraints between the n-ary constraints in the redundant partial models. These channeling constraints make certain that value assignments under an n-ary constraint in one partial model are reflected under that n-ary constraint in some other partial model. We call these categorical channeling constraints. © Springer-Verlag Berlin Heidelberg 2005.