This paper describes a polynomially-solvable class of temporal planning problems. Polynomiality follows from two assumptions. Firstly, by supposing that each sub-goal fluent can be established by at most one action, we can quickly determine which actions are necessary in any plan. Secondly, the monotonicity of sub-goal fluents allows us to express planning as an instance of STP≠ (Simple Temporal Problem with difference constraints). This class includes temporally-expressive problems requiring the concurrent execution of actions, with potential applications in the chemical, pharmaceutical and construction industries.
We also show that any (temporal) planning problem has a monotone relaxation which can lead to the polynomial-time detection of its unsolvability in certain cases. Indeed we show that our relaxation is orthogonal to relaxations based on the ignore-deletes approach used in classical planning since it preserves deletes and can also exploit temporal information.
Constraint partitioning in penalty formulations for solving temporal planning problems