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.
The electricity network balancing problem consists of ensuring that the electricity demands of the consumers are met by the committed supply. Constraints are imposed on the different elements of the network, so that damage to the equipment is prevented when transformers are stepped up or down, or generation is increased. We consider this problem within zones, which are sub-networks constructed using carefully chosen decomposition principles. The automation of decision making in electricity networks is a step forward in their management which is necessary for coping with the increase in power system complexity that we expect in the near term. In this paper we explore the deployment of planning techniques to solve the zone-balancing problem. Embedding electricity networks in a domain description presents new challenges for planning. The key point is that the propagation of information requires complex updates to the state when an action is applied. We have developed a method in which the computation of the critical numeric quantities is performed calling an external power flow equation solver, demonstrating a clean interface between the planner and this domain-specific computation. This solver allows us to move the power flow computations outside of the planning process and update the values efficiently. We also examine a second important feature of this problem, which is the interaction between exogenous events and constraints over the entire plan trajectory within a zone.
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.
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