Extracting and Exploiting Bounds of Numeric Variables for Optimal Linear Numeric Planning

In numeric AI planning, a state is represented by propositions and numeric variables, actions change the values of numeric variables in addition to adding and deleting propositions, and goals and preconditions of actions may include conditions over numeric variables.  While domains of numeric variables are rational numbers in general, upper and lower bounds on variables affected only by constant increase and decrease can sometimes be determined and exploited by a heuristic function. In this paper, we generalize the existing method to variables that are changed by linear effects. We exploit the extracted bounds to improve the numeric LM-cut heuristic, a state-of-the-art admissible heuristic for linear numeric planning. Empirical evaluation shows that our method improves the performance of LM-cut in multiple domains. The proposed method can also detect unsolvability of some numeric tasks in polynomial time.