Integer Programming Models in AI Planning: Preliminary Experimental Results

As one of the challenges posed in their paper “Ten Challenges in Propositional Reasoning and Search,” Selman et al. (1997) mention the development of Integer Programming (IP) models and methods for propositional reasoning. Even though it is straightforward to formulate a satisfiability problem as an integer programming model, their concern is that the basic technique used to solve integer programs—that is, the linear (LP) relaxation of the problem—does not guide the selection of values in solving the the integer program. As a reason for this, they mention that the LP relaxation of the problem usually sets most values to 12 . Recently, we have begun to investigate the use of IP methods in the planning domain. Even though we are still in the early stages of our research, our preliminary experiments strongly suggest that IP methods do have something to offer for these problems. In particular, it appears that the LP relaxation of the problem does provide guidance in solving the IP. Below we briefly summarize the IP formulations and the results of our experiments.