Levi H. S. Lelis

Semi-supervised Density-Based Clustering

Most of the effort in the semi-supervised clustering literature was devoted to variations of the K-means algorithm. In this paper we show how background knowledge can be used to bias a partitional density-based clustering algorithm. Our work describes how labeled objects can be used to help the algorithm detecting suitable density parameters for the algorithm to extract density-based clusters in specific parts of the feature space. Considering the set of constraints estabilished by the labeled dataset we show that our algorithm, called SSDBSCAN, automatically finds density parameters for each natural cluster in a dataset. Four of the most interesting characteristics of SSDBSCAN are that (1) it only requires a single, robust input parameter, (2) it does not need any user intervention, (3) it automaticaly finds the noise objects according to the density of the natural clusters and (4) it is able to find the natural cluster structure even when the density among clusters vary widely. The algorithm presented in this paper is evaluated with artificial and real-world datasets, demonstrating better results when compared to other unsupervised and semi-supervised density-based approaches.

Predicting the size of IDA*'s search tree

Korf, Reid and Edelkamp initiated a line of research for developing methods (KRE and later CDP) that predict the number of nodes expanded by IDA* for a given start state and cost bound. Independently, Chen developed a method (SS) that can also be used to predict the number of nodes expanded by IDA*. In this paper we improve both of these prediction methods. First, we present @e-truncation, a method that acts as a preprocessing step and improves CDP@?s prediction accuracy. Second and orthogonally to @e-truncation, we present a variant of CDP that can be orders of magnitude faster than CDP while producing exactly the same predictions. Third, we show how ideas developed in the KRE line of research can be used to improve the predictions produced by SS. Finally, we make an empirical comparison between our new enhanced versions of CDP and SS. Our experimental results suggest that CDP is suitable for applications that require less accurate but fast predictions, while SS is suitable for applications that require more accurate predictions but can afford more computation time.

Memory-Efficient Tree Size Prediction for Depth-First Search in Graphical Models

We address the problem of predicting the size of the search tree explored by Depth-First Branch and Bound (DFBnB) while solving optimization problems over graphical models. Building upon methodology introduced by Knuth and his student Chen, this paper presents a memory-efficient scheme called Retentive Stratified Sampling (RSS). Through empirical evaluation on probabilistic graphical models from various problem domains we show impressive prediction power that is far superior to recent competing schemes.

Human computation for procedural content generation in platform games

One of the major challenges in procedural content generation in computer games is to automatically evaluate whether the generated content has good quality. In this paper we describe a system which uses human computation to evaluate small portions of levels generated by an existing system for the game of Infinite Mario Bros. Several such evaluated portions are then combined into a full level of the game. The composition of the small portions into a full level is done by accounting for the human-annotated information and the mathematical model of tension arcs used in interactive drama and storytelling. We tested our system with human subjects and the results show that our approach is able to generate levels with better visual aesthetics and that are more enjoyable to play than other existing approaches.

Learning to Speed Up Evolutionary Content Generation in Physics-Based Puzzle Games

Procedural content generation (PCG) systems are designed to automatically generate content for video games. PCG for physics-based puzzles requires one to simulate the game to ensure feasibility and stability of the objects composing the puzzle. The major drawback of this simulation-based approach is the overall running time of the PCG process, as the simulations can be computationally expensive. This paper introduces a method that uses machine learning to reduce the number of simulations performed by an evolutionary approach while generating levels of Angry Birds, a physics-based puzzle game. Our method uses classifiers to verify the stability and feasibility of the levels considered during search. The fitness function is computed only for levels that are classified as stable and feasible. An approximation of the fitness that does not require simulations is used for levels that are deemed as unstable or unfeasible by the classifiers. Our experiments show that naively approximating the fitness values can lead to poor solutions. We then introduce an approach in which the fitness values are approximated with the average fitness value of the levels parents added to a penalty value. This approximation scheme allows the search procedure to find good-quality solutions much more quickly than a competing approach—we reduce from 43 to 25 minutes the running time required to generate one level of Angry Birds.

Predicting optimal solution cost with conditional probabilities

Heuristic search algorithms are designed to return an optimal path from a start state to a goal state. They find the optimal solution cost as a side effect. However, there are applications in which all one wants to know is an estimate of the optimal solution cost. The actual path from start to goal is not initially needed. For instance, one might be interested in quickly assessing the monetary cost of a project for bidding purposes. In such cases only the cost of executing the project is required. The actual construction plan could be formulated later, after bidding. In this paper we propose an algorithm, named Solution Cost Predictor (SCP), that accurately and efficiently predicts the optimal solution cost of a problem instance without finding the actual solution. While SCP can be viewed as a heuristic function, it differs from a heuristic conceptually in that: 1) SCP is not required to be fast enough to guide search algorithms; 2) SCP is not required to be admissible; 3) our measure of effectiveness is the prediction accuracy, which is in contrast to the solution quality and number of nodes expanded used to measure the effectiveness of heuristic functions. We show empirically that SCP makes accurate predictions on several heuristic search benchmarks.

Stratified Sampling for Even Workload Partitioning Applied to IDA* and Delaunay Algorithms

This work presents Workload Partitioning and Scheduling (WPS), a novel algorithm for evenly partitioning the computational workload of large implicitly-defined work-list-based applications on distributed/shared-memory systems. In WPS, a stratified sampling technique estimates the number of work items that will be processed in each step of the target application. Then WPS uses this estimation to evenly partition and distribute the computational workload. An empirical evaluation on large applications -- Iterative-Deepening A* (IDA*) applied to (4 × 4)- and (5 × 5)-Sliding-Tile Puzzles, Delaunay Mesh Generation, and Delaunay Mesh Refinement -- shows that WPS is applicable to a range of applications. A coordination between WPS and existing work-stealing schedulers for intra-node load balancing yields additional speedups in the range of 18% to 40% compared to that achieved with the existing work-stealing schedulers alone. Such a coordination also outperforms an existing workload-partitioning scheme intended specifically for IDA* algorithms by 17% to 36%.

On creating complementary pattern databases

A pattern database (PDB) for a planning task is a heuristic function in the form of a lookup table that contains optimal solution costs of a simplified version of the task. In this paper we introduce a method that sequentially creates multiple PDBs which are later combined into a single heuristic function. At a given iteration, our method uses estimates of the A* running time to create a PDB that complements the strengths of the PDBs created in previous iterations. We evaluate our algorithm using explicit and symbolic PDBs. Our results show that the heuristics produced by our approach are able to outperform existing schemes, and that our method is able to create PDBs that complement the strengths of other existing heuristics such as a symbolic perimeter heuristic.

Predicting optimal solution costs with bidirectional stratified sampling in regular search spaces

Optimal planning and heuristic search systems solve state-space search problems by finding a least-cost path from start to goal. As a byproduct of having an optimal path they also determine the optimal solution cost. In this paper we focus on the problem of determining the optimal solution cost for a state-space search problem directly, i.e., without actually finding a solution path of that cost. We present an algorithm, BiSS, which is a hybrid of bidirectional search and stratified sampling that produces accurate estimates of the optimal solution cost. BiSS is guaranteed to return the optimal solution cost in the limit as the sample size goes to infinity. We show empirically that BiSS produces accurate predictions in several domains. In addition, we show that BiSS scales to state spaces much larger than can be solved optimally. In particular, we estimate the average solution cost for the 6 × 6 , 7 × 7 , and 8 × 8 Sliding-Tile puzzle and provide indirect evidence that these estimates are accurate. As a practical application of BiSS, we show how to use its predictions to reduce the time required by another system to learn strong heuristic functions from days to minutes in the domains tested.

Stratified Strategy Selection for Unit Control in Real-Time Strategy Games.

In this paper we introduce Stratified Strategy Selection (SSS), a novel search algorithm for micromanaging units in real-time strategy (RTS) games. SSS uses a type system to partition the player’s units into types and assumes that units of the same type must follow the same strategy. SSS searches in the state space induced by the type system to select, from a pool of options, a strategy for each unit. Empirical results on a simulator of an RTS game shows that SSS employing either fixed or adaptive type systems is able to substantially outperform stateof-the-art search-based algorithms in combat scenarios with up to 100 units.