PDDL+ models are advanced models of hybrid systems and the resulting problems are notoriously difficult for planning engines to cope with. An additional limiting factor for the exploitation of PDDL+ approaches in real-world applications is the restricted number of domain-independent planning engines that can reason upon those models. With the aim of deepening the understanding of PDDL+ models, in this work, we study a novel mapping between a time discretisation of pddl+ and numeric planning as for PDDL2.1 (level 2). The proposed mapping not only clarifies the relationship between these two formalisms but also enables the use of a wider pool of engines, thus fostering the use of hybrid planning in real-world applications. Our experimental analysis shows the usefulness of the proposed translation and demonstrates the potential of the approach for improving the solvability of complex PDDL+ instances.

Admissible heuristics are essential for optimal planning in the context of search algorithms like A*, and they can also be used in the context of suboptimal planning in order to find quality-bounded solutions. In satisfacing planning, on the other hand, admissible heuristics are not exploited by the best-first search algorithms of existing planners even when a time window is available for improving the first solution found. For example, in the well-know planner LAMA, better solutions within such a time window are sought by restarting a Weighted-A* search guided by inadmissible heuristics, each time a better solution is found. In this paper, we investigate the use of admissible heuristics in the context of LAMA for pruning nodes that cannot lead to better solutions. The revised search of LAMA is experimentally evaluated using two alternative admissible heuristics for pruning and three types of problems: planning with soft goals, planning with action costs, and planning with both action costs and soft goals. Soft goals are compiled into hard goals following the approach of Keyder and Geffner. The empirical results show that the use of admissible heuristics in LAMA can be of great help to improve the planner performance.