André Grahl Pereira

Optimal Sokoban solving using pattern databases with specific domain knowledge

A pattern database (PDB) stores shortest distances from abstract states to a set of abstract goal states. For many search problems the best heuristic function is obtained using PDBs. We aim to find optimal solutions for Sokoban using PDBs. Due to the domain-specific characteristics of the goal states a straightforward application of PDBs in Sokoban results in an ineffective heuristic function. We propose an alternative approach, by introducing the idea of an instance decomposition to obtain an explicit intermediate goal state which allows an effective application of PDBs. We also propose a domain-specific tie breaking rule. When applied to the standard set of instances this approach improves heuristic values on initial states, detects considerable more deadlocks in random states, and doubles the number of optimally solved instances compared to previous methods.

Pull and PushPull are PSPACE-complete

We prove PSPACE-completeness of a broad class of moving-blocks problems similar to the well-known puzzle Sokoban. Several computational complexity results are known for moving-blocks problems. However, most of the literature is focused on problems with push moves and the complexity of many of them are still open. In this article, we study the computational complexity of moving-blocks problems with pull moves and problems with push and pull moves. Our reductions are from Nondeterministic Constraint Logic. We improve the known NP-hardness results of Pull problems to PSPACE-completeness results. We also were able to show that the whole class of PushPull problems is PSPACE-complete.

Data assimilation using NeuroEvolution of Augmenting Topologies

The use of numerical prediction models are essential to modern society. Data assimilation is a technique that aims to increase the prediction accuracy by combining a model output with observational data, resulting in a state that is closer to the true state of the problem. Depending on the size of the model output and the number of observations to assimilate, the combination of these two sources of information may require intensive computing and become a challenge, even for supercomputers used in this type of application. Thus neural networks have been proposed as an alternative to perform high quality data assimilation at lower computational cost. This paper investigates the use of NeuroEvolution of Augmenting Topologies (NEAT) in data assimilation. NEAT is capable of adapting the connections weights and the neural network topology using principles of evolutionary computation in a search for a minimum topology and best performance. In this work, two different models were used for testing: the Lorenz Attractor and Shallow Water model. The experiments compared the results obtained with NEAT and backpropagation neural networks, using as benchmark the Best Linear Unbiased Estimator (BLUE). In the experiment with the Lorenz Attractor, NEAT was able to emulate the data assimilation task with smaller error at lower computational cost. For the Shallow Water model, tested using different grid sizes, it was observed that the errors obtained with both neural networks were small, but NEAT showed high error values. On the other hand, NEAT always gets a topology with significantly fewer operations, and the computational cost difference increases with the grid size.

Analyzing Tie-Breaking Strategies for the A* Algorithm

For a given state space and admissible heuristic function h there is always a tie-breaking strategy for which A∗ expands the minimum number of states [Dechter and Pearl, 1985]. We say that these strategies have optimal expansion. Although such a strategy always exists it may depend on the instance, and we currently do not know a tie-breaker that always guarantees optimal expansion. In this paper, we study tie-breaking strategies for A∗. We analyze common strategies from the literature and prove that they do not have optimal expansion. We propose a novel tie-breaking strategy using cost adaptation that has always optimal expansion. We experimentally analyze the performance of A∗ using several tie-breaking strategies on domains from the IPC and zero-cost domains. Our best strategy solves significantly more instances than the standard method in the literature and more than the previous state-of-the-art strategy. Our analysis improves the understanding of how to develop effective tie-breaking strategies and our results also improve the state-of-the-art of tie-breaking strategies for A∗.

An approximate nearest neighbors search algorithm for low-dimensional grid locations

We propose a new algorithm for the problem of approximate nearest neighbors (ANN) search in a regularly spaced low-dimensional grid for interpolation applications. It associates every sampled point to its nearest interpolation location, and then expands its influence to neighborhood locations in the grid, until the desired number of sampled points is achieved on every grid location. Our approach makes use of knowledge on the regular grid spacing to avoid measuring the distance between sampled points and grid locations. We compared our approach with four different state-of-the-art ANN algorithms in a large set of computational experiments. In general, our approach requires low computational effort, especially for cases with high density of sampled points, while the observed error is not significantly different. At the end, a case study is shown, where the ionosphere dynamics is predicted daily using samples from a mathematical model, which runs in parallel at 56 different longitude coordinates, providing sampled points not well distributed that follow Earth’s magnetic field-lines. Our approach overcomes the comparative algorithms when the ratio between the number of sampled points and grid locations is over 2849:1.

Improved Airport Ground Traffic Control with Domain-Dependent Heuristics

In this paper we study the application of a domain-dependent heuristic to airport ground traffic control. We consider two variants of the problem. In the first, proposed for the International Planning Competition in 2004, the in-bound and out-bound airplanes have fixed parking and take-off positions. In the second, more realistic variant a controller can assign dynamically for each airplane the runway for take-off or the parking position, such that the total movement of planes at the airport is minimized. We are particularly interested in the second variant, which has an implicitly defined goal state where multiple states could satisfy the goal condition, and the impact of this fact on domain-independent and domain-dependent heuristics. We compare domain-independent heuristics in the Fast Downward planner on this domain to a domain-dependent heuristic.