The Metric-FF Planning System: Translating "Ignoring Delete Lists" to Numeric State Variables

Planning with numeric state variables has been a challenge for many years, and was a part of the 3rd International Planning Competition (IPC-3). Currently one of the most popular and successful algorithmic techniques in STRIPS planning is to guide search by a heuristic function, where the heuristic is based on relaxing the planning task by ignoring the delete lists of the available actions. We present a natural extension of ``ignoring delete lists'' to numeric state variables, preserving the relevant theoretical properties of the STRIPS relaxation under the condition that the numeric task at hand is ``monotonic''. We then identify a subset of the numeric IPC-3 competition language, ``linear tasks'', where monotonicity can be achieved by pre-processing. Based on that, we extend the algorithms used in the heuristic planning system FF to linear tasks. The resulting system Metric-FF is, according to the IPC-3 results which we discuss, one of the two currently most efficient numeric planners

Many Particle Hardy-Inequalities

In this paper we prove three differenttypes of the so-called many-particle Hardy inequalities. One of them is a "classical type" which is valid in any dimesnion $d\neq 2$. The second type deals with two-dimensional magnetic Dirichlet forms where every particle is supplied with a soplenoid. Finally we show that Hardy inequalities for Fermions hold true in all dimensions.Comment: 20 page

Ordered Landmarks in Planning

Many known planning tasks have inherent constraints concerning the best order in which to achieve the goals. A number of research efforts have been made to detect such constraints and to use them for guiding search, in the hope of speeding up the planning process. We go beyond the previous approaches by considering ordering constraints not only over the (top-level) goals, but also over the sub-goals that will necessarily arise during planning. Landmarks are facts that must be true at some point in every valid solution plan. We extend Koehler and Hoffmann's definition of reasonable orders between top level goals to the more general case of landmarks. We show how landmarks can be found, how their reasonable orders can be approximated, and how this information can be used to decompose a given planning task into several smaller sub-tasks. Our methodology is completely domain- and planner-independent. The implementation demonstrates that the approach can yield significant runtime performance improvements when used as a control loop around state-of-the-art sub-optimal planning systems, as exemplified by FF and LPG

Multi-Lattice Kinetic Monte Carlo Simulations from First-Principles: Reduction of the Pd(100) Surface Oxide by CO

We present a multi-lattice kinetic Monte Carlo (kMC) approach that efficiently describes the atomistic dynamics of morphological transitions between commensurate structures at crystal surfaces. As an example we study the reduction of a $(\sqrt{5}\times \sqrt{5})R27^{\circ}$ PdO(101) overlayer on Pd(100) in a CO atmosphere. Extensive density-functional theory calculations are used to establish an atomistic pathway for the oxide reduction process. First-principles multi-lattice kMC simulations on the basis of this pathway fully reproduce the experimental temperature dependence of the reduction rate [Fernandes et al., Surf. Sci. 2014, 621, 31-39] and highlight the crucial role of elementary processes special to the boundary between oxide and metal domains.Comment: 19 pages, 10 figure