Generalizing the Relaxed Planning Heuristic to Non-linear Tasks

The relaxed planning heuristic is a prominent state-to-goal estimator function for domain-independent forward-chaining heuristic search and local search planning. It enriches the state-space traversal of almost all currently available suboptimal state-of-the-art planning systems.While current domain description languages allow general arithmetic expressions in precondition and effect lists, the heuristic has been devised for propositional, restricted, and linear tasks only. On the other hand, generalizations of the heuristic to non-linear tasks are of apparent need for modelling complex planning problems and a true necessity to validate software. Subsequently, this work proposes a solid extension to the estimate that can deal with non-linear preconditions and effects. It is derived based on an approximated plan construction with respect to intervals for variable assignments. For plan extraction, weakest preconditions are computed according to the assignment rule in Hoare’s calculus.