EXPERIMENTS WITH AN INTEGER PROGRAMMING FORMULATION OF AN EXPERT SYSTEM

Abstract

We present expert system (ES) and Integer Programming (IP) formulations of an NP-complete constraint satisfaction problem (CSP). The problem involves generating a plan for assigning faculty to courses given a variety of constraints and preferences and other tentative data. The expert system consists of a heuristic rule-based problem solver and a truth maintenance system. The IP model consists of about 700 zero-one decision variables and 300 constraints. We describe and contrast the expert system and IP models in terms of behavior, quality of results, and computational performance. We find that the expressiveness of the IP model is hampered by its single objective function, inability to encode various types of complex preferences, the lack of useful output when it fails to find a feasible solution, and a general lack of control over inference. It is also difficult to make incremental revisions to the plan produced by the IP model. In contrast, the truth maintenance system maintains justifications for assignments, which makes it possible to reason about incremental modifications to a plan. In terms of performance, we found that whenever the IP approach finds a solution, it does so quickly using the Pivot and Complement heuristic of Balas and Martin (1980). The branch and bound always failed to find a feasible integer solution when the heuristic failed to find one.