  Many planning formalisms allow for mixing numeric with Boolean effects.
However, most of these formalisms are undecidable. In this paper, we will
analyze possible causes for this undecidability by studying the number of
different occurrences of actions, an approach that proved useful for metric
fluents before. We will start by reformulating a numeric planning problem known
as restricted tasks as a search problem. We will then show how an NP-complete
fragment of numeric planning can be found by using heuristics. To achieve this,
we will develop the idea of multi-valued partial order plans, a least
committing compact representation for (sequential and parallel) plans. Finally,
we will study optimization techniques for this representation to incorporate
soft preconditions.
