Heuristics for Numeric Planning via Subgoaling

The paper presents a new relaxation for hybrid planning with continuous numeric and propositional state variables based on subgoaling, generalising the subgoaling principle underlying the hmax and hadd heuristics to such problems. Our relaxation improves on existing interval-based relaxations by taking into account some negative interactions between effects when achieving a subgoal, resulting in better estimates. We show conditions on the planning model ensuring that this new relaxation leads to tractable, and, for the hmax version, admissible, heuristics. The new relaxation can be combined with the interval-based relaxation, to derive heuristics applicable to general numeric planning, while still providing more informed estimates for the subgoals that meet these conditions. Experiments show the effectiveness of its inadmissible and admissible version on satisficing and optimal numeric planning, respectively. As far as we know, this is the first admissible heuristic enabling cost-optimal numeric planning.