The LM-cut heuristic, both alone and as part of the operator counting framework, represents one of the most successful heuristics for classical planning. In this paper, we generalize LM-cut and its use in operator counting to optimal numeric planning with simple conditions and simple numeric effects, i.e., linear expressions over numeric state variables and actions that increase or decrease such variables by constant quantities. We introduce a variant of hmaxhbd (a previously proposed numeric hmax heuristic) based on the delete-relaxed version of such planning tasks and show that, although inadmissible by itself, our variant yields a numeric version of the classical LM-cut heuristic which is admissible. We classify the three existing families of heuristics for this class of numeric planning tasks and introduce the LM-cut family, proving dominance or incomparability between all pairs of existing max and LM-cut heuristics for numeric planning with simple conditions. Our extensive empirical evaluation shows that the new LM-cut heuristic, both on its own and as part of the operator counting framework, is the state-of-the-art for this class of numeric planning problem.

Search and tracking is the problem of locating a moving target and following it to its destination. In this work, we consider a scenario in which the target moves across a large geographical area by following a road network and the search is performed by a team of unmanned aerial vehicles (UAVs). We formulate search and tracking as a combinatorial optimization problem and prove that the objective function is submodular. We exploit this property to devise a greedy algorithm. Although this algorithm does not offer strong theoretical guarantees because of the presence of temporal constraints that limit the feasibility of the solutions, it presents remarkably good performance, especially when several UAVs are available for the mission. As the greedy algorithm suffers when resources are scarce, we investigate two alternative optimization techniques: Constraint Programming (CP) and AI planning. Both approaches struggle to cope with large problems, and so we strengthen them by leveraging the greedy algorithm. We use the greedy solution to warm start the CP model and to devise a domain-dependent heuristic for planning. Our extensive experimental evaluation studies the scalability of the different techniques and identifies the conditions under which one approach becomes preferable to the others.

Compilation techniques in planning reformulate a problem into an alternative encoding for which efficient, off-the-shelf solvers are available. In this work, we present a novel mixed-integer linear programming (MILP) compilation for cost-optimal numeric planning with instantaneous actions. While recent works on the problem are restricted to actions that modify variables present in simple numeric conditions, our MILP formulation, in addition, handles linear conditions and linear action effects on numeric state variables. Such problems are particularly challenging due to the state-dependency of the action effects. Experiments show that our approach, in addition to being the state of the art for the more general problem class, is competitive with heuristic search-based planners on domains with only simple numeric conditions.

Linear programming has been successfully used to compute admissible heuristics for cost-optimal classical planning. Although one of the strengths of linear programming is the ability to express and reason about numeric variables and constraints, their use in numeric planning is limited. In this work, we extend linear programming-based heuristics for classical planning to support numeric state variables. In particular, we propose a model for the interval relaxation, coupled with landmarks and state equation constraints. We consider both linear programming models and their harder-to-solve, yet more informative, integer programming versions. Our experimental analysis shows that considering an NP-Hard heuristic often pays off and that A* search using our integer programming heuristics establishes a new state of the art in cost-optimal numeric planning.

Several advanced applications of autonomous aerial vehicles in civilian and military contexts involve a searching agent with imperfect sensors that seeks to locate a mobile target in a given region. Effectively managing uncertainty is key to solving the related search problem, which is why all methods devised so far hinge on a probabilistic formulation of the problem and solve it through branch-and-bound algorithms, Bayesian filtering or POMDP solvers. In this paper, we consider a class of hard search tasks involving a target that exhibits an intentional evasive behaviour and moves over a large geographical area, i.e., a target that is particularly difficult to track down and uncertain to locate. We show that, even for such a complex problem, it is advantageous to compile its probabilistic structure into a deterministic model and use standard deterministic solvers to find solutions. In particular, we formulate the search problem for our uncooperative target both as a deterministic automated planning task and as a constraint programming task and show that in both cases our solution outperforms POMDPs methods.

Numeric Timed Initial Fluents represent a new feature in PDDL that extends the concept of Timed Initial Literals to numeric fluents. They are particularly useful to model independent functions that change through time and influence the actions to be applied. Although they are very useful to model real world problems, they are not systematically defined in the family of PDDL languages and they are not implemented in any generic PDDL planner, except for POPF2 and UPMurphi. In this paper we present an extension of the planner POPF2 (POPF-TIF) to handle problems with numeric Timed Initial Fluents. We propose and evaluate two contributions: the first is based on improvements of the heuristic evaluation, while the second considers alternative search algorithms based on a mixture of Enforced Hill Climbing and Best First Search.