Constraint Modeling in the Context of Academic Task Assignment

Abstract

We explore fundamental issues of the modeling, implementation, and processing of non-binary constraints. General techniques for reformulating non-binary constraints (i.e., hidden variable, dual graph) are not practical for high-arity constraints. In our study, we motivate our need to express practical requirements as non-binary constraints, then we explore reformulation methods to deal with them since the conventional methods become impractical. Our work builds on the work of Gent et al. (1999), while we motivate and anchor our investigations in the practical context of a real-world application. This is the assignment of graduate teaching assistants to courses in our department. This task is a critical responsibility that our department's administration has to drudge through every semester. The idea for this particular application is borrowed from Rina Dechter, at the UC Irvine. We model this application using 4 types of unary constraints, one type of binary constraint, and 3 types of non-binary constraints. Since in our application problems are over-constrained, a satisfactory assignment is one that maximizes the number of courses covered