When planning for tasks that feature both state-dependent action costs and conditional effects using relaxation heuristics, the following problem appears: handling costs and effects separately leads to worse-than-necessary heuristic values, since we may get the more useful effect at the lower cost by choosing different values of a relaxed variable when determining relaxed costs and relaxed active effects. In this paper, we show how this issue can be avoided by representing state-dependent costs and conditional effects uniformly, both as edge-valued multi-valued decision diagrams (EVMDDs) over different sets of edge values, and then working with their product diagram. We develop a theory of EVMDDs that is general enough to encompass state-dependent action costs, conditional effects, and even their combination.We define relaxed effect semantics in the presence of state-dependent action costs and conditional effects, and describe how this semantics can be efficiently computed using product EVMDDs. This will form the foundation for informative relaxation heuristics in the setting with state-dependent costs and conditional effects combined.

Most work in planning focuses on tasks with state-independent or even uniform action costs. However, supporting state-dependent action costs admits a more compact representation of many tasks. We investigate how to solve such tasks using heuristic search, with a focus on delete-relaxation heuristics. We first define a generalization of the additive heuristic to such tasks and then discuss different ways of computing it via compilations to tasks with state-independent action costs and more directly by modifying the relaxed planning graph. We evaluate these approaches theoretically and present an implementation of the additive heuristic for planning with state-dependent action costs. To our knowledge, this gives rise to the first approach able to handle even the hardest instances of the combinatorial Academic Advising domain from the International Probabilistic Planning Competition (IPPC) 2014.

Supporting state-dependent action costs in planning admits a more compact representation of many tasks. We generalize the additive heuristic and compute it by embedding decision-diagram representations of action cost functions into the RPG. We give a theoretical evaluation and present an implementation of the generalized additive heuristic. This allows us to handle even the hardest instances of the combinatorial Academic Advising domain from the IPPC 2014.