Interval Based Relaxation Heuristics for Numeric Planning with Action Costs

Abstract

Many real-world problems can be expressed in terms of states and actions that modify the world to reach a certain goal. Such problems can be solved by automated planning. Numeric planning supports numeric quantities such as resources or physical properties in addition to the propositional variables from classical planning. We approach numeric planning with heuristic search and introduce adaptations of the relaxation heuristics \(h_\text {max}\), \(h_\text {add}\) and \(h_{\text {FF}}\) to interval based relaxation frameworks. In contrast to previous approaches, the heuristics presented in this paper are not limited to fragments of numeric planning with instantaneous actions (such as linear or acyclic numeric planning tasks) and support action costs.