Evolving Distributed Algorithms with Genetic Programming

Distributed systems are one of the most vital components of the economy. The most prominent example is probably the internet, a constituent element of our knowledge society. During the recent years, the number of novel network types has steadily increased. Amongst others, sensor networks, distributed systems composed of tiny computational devices with scarce resources, have emerged. The further development and heterogeneous connection of such systems imposes new requirements on the software development process. Mobile and wireless networks, for instance, have to organize themselves autonomously and must be able to react to changes in the environment and to failing nodes alike. Researching new approaches for the design of distributed algorithms may lead to methods with which these requirements can be met efficiently. In this thesis, one such method is developed, tested, and discussed in respect of its practical utility. Our new design approach for distributed algorithms is based on Genetic Programming, a member of the family of evolutionary algorithms. Evolutionary algorithms are metaheuristic optimization methods which copy principles from natural evolution. They use a population of solution candidates which they try to refine step by step in order to attain optimal values for predefined objective functions. The synthesis of an algorithm with our approach starts with an analysis step in which the wanted global behavior of the distributed system is specified. From this specification, objective functions are derived which steer a Genetic Programming process where the solution candidates are distributed programs. The objective functions rate how close these programs approximate the goal behavior in multiple randomized network simulations. The evolutionary process step by step selects the most promising solution candidates and modifies and combines them with mutation and crossover operators. This way, a description of the global behavior of a distributed system is translated automatically to programs which, if executed locally on the nodes of the system, exhibit this behavior. In our work, we test six different ways for representing distributed programs, comprising adaptations and extensions of well-known Genetic Programming methods (SGP, eSGP, and LGP), one bio-inspired approach (Fraglets), and two new program representations called Rule-based Genetic Programming (RBGP, eRBGP) designed by us. We breed programs in these representations for three well-known example problems in distributed systems: election algorithms, the distributed mutual exclusion at a critical section, and the distributed computation of the greatest common divisor of a set of numbers. Synthesizing distributed programs the evolutionary way does not necessarily lead to the envisaged results. In a detailed analysis, we discuss the problematic features which make this form of Genetic Programming particularly hard. The two Rule-based Genetic Programming approaches have been developed especially in order to mitigate these difficulties. In our experiments, at least one of them (eRBGP) turned out to be a very efficient approach and in most cases, was superior to the other representations.

An O(N) Algorithm for Three-Dimensional N-Body Simulations

We develop an algorithm that computes the gravitational potentials and forces on N point-masses interacting in three-dimensional space. The algorithm, based on analytical techniques developed by Rokhlin and Greengard, runs in order N time. In contrast to other fast N-body methods such as tree codes, which only approximate the interaction potentials and forces, this method is exact ?? computes the potentials and forces to within any prespecified tolerance up to machine precision. We present an implementation of the algorithm for a sequential machine. We numerically verify the algorithm, and compare its speed with that of an O(N2) direct force computation. We also describe a parallel version of the algorithm that runs on the Connection Machine in order 0(logN) time. We compare experimental results with those of the sequential implementation and discuss how to minimize communication overhead on the parallel machine.

Statistical Object Recognition

Two formulations of model-based object recognition are described. MAP Model Matching evaluates joint hypotheses of match and pose, while Posterior Marginal Pose Estimation evaluates the pose only. Local search in pose space is carried out with the Expectation--Maximization (EM) algorithm. Recognition experiments are described where the EM algorithm is used to refine and evaluate pose hypotheses in 2D and 3D. Initial hypotheses for the 2D experiments were generated by a simple indexing method: Angle Pair Indexing. The Linear Combination of Views method of Ullman and Basri is employed as the projection model in the 3D experiments.

Model-Based Matching of Line Drawings by Linear Combinations of Prototypes

We describe a technique for finding pixelwise correspondences between two images by using models of objects of the same class to guide the search. The object models are 'learned' from example images (also called prototypes) of an object class. The models consist of a linear combination ofsprototypes. The flow fields giving pixelwise correspondences between a base prototype and each of the other prototypes must be given. A novel image of an object of the same class is matched to a model by minimizing an error between the novel image and the current guess for the closest modelsimage. Currently, the algorithm applies to line drawings of objects. An extension to real grey level images is discussed.

On Convergence Properties of the EM Algorithm for Gaussian Mixtures

"Expectation-Maximization'' (EM) algorithm and gradient-based approaches for maximum likelihood learning of finite Gaussian mixtures. We show that the EM step in parameter space is obtained from the gradient via a projection matrix $P$, and we provide an explicit expression for the matrix. We then analyze the convergence of EM in terms of special properties of $P$ and provide new results analyzing the effect that $P$ has on the likelihood surface. Based on these mathematical results, we present a comparative discussion of the advantages and disadvantages of EM and other algorithms for the learning of Gaussian mixture models.

Fast Object Recognition in Noisy Images Using Simulated Annealing

A fast simulated annealing algorithm is developed for automatic object recognition. The normalized correlation coefficient is used as a measure of the match between a hypothesized object and an image. Templates are generated on-line during the search by transforming model images. Simulated annealing reduces the search time by orders of magnitude with respect to an exhaustive search. The algorithm is applied to the problem of how landmarks, for example, traffic signs, can be recognized by an autonomous vehicle or a navigating robot. The algorithm works well in noisy, real-world images of complicated scenes for model images with high information content.

Hierarchical Mixtures of Experts and the EM Algorithm

We present a tree-structured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM's). Learning is treated as a maximum likelihood problem; in particular, we present an Expectation-Maximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an on-line learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain.

Uncertainty Propagation in Model-Based Recognition

Building robust recognition systems requires a careful understanding of the effects of error in sensed features. Error in these image features results in a region of uncertainty in the possible image location of each additional model feature. We present an accurate, analytic approximation for this uncertainty region when model poses are based on matching three image and model points, for both Gaussian and bounded error in the detection of image points, and for both scaled-orthographic and perspective projection models. This result applies to objects that are fully three- dimensional, where past results considered only two-dimensional objects. Further, we introduce a linear programming algorithm to compute the uncertainty region when poses are based on any number of initial matches. Finally, we use these results to extend, from two-dimensional to three- dimensional objects, robust implementations of alignmentt interpretation- tree search, and ransformation clustering.

Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID���. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

A Conservative Front Tracking Algorithm

The discontinuities in the solutions of systems of conservation laws are widely considered as one of the difficulties in numerical simulation. A numerical method is proposed for solving these partial differential equations with discontinuities in the solution. The method is able to track these sharp discontinuities or interfaces while still fully maintain the conservation property. The motion of the front is obtained by solving a Riemann problem based on the state values at its both sides which are reconstructed by using weighted essentially non oscillatory (WENO) scheme. The propagation of the front is coupled with the evaluation of "dynamic" numerical fluxes. Some numerical tests in 1D and preliminary results in 2D are presented.

A concurrent region growing algorithm guided by circumscribed contours

Image segmentation of natural scenes constitutes a major problem in machine vision. This paper presents a new proposal for the image segmentation problem which has been based on the integration of edge and region information. This approach begins by detecting the main contours of the scene which are later used to guide a concurrent set of growing processes. A previous analysis of the seed pixels permits adjustment of the homogeneity criterion to the region's characteristics during the growing process. Since the high variability of regions representing outdoor scenes makes the classical homogeneity criteria useless, a new homogeneity criterion based on clustering analysis and convex hull construction is proposed. Experimental results have proven the reliability of the proposed approach

Autonomous underwater vehicle control using reinforcement learning policy search methods

Autonomous underwater vehicles (AUV) represent a challenging control problem with complex, noisy, dynamics. Nowadays, not only the continuous scientific advances in underwater robotics but the increasing number of subsea missions and its complexity ask for an automatization of submarine processes. This paper proposes a high-level control system for solving the action selection problem of an autonomous robot. The system is characterized by the use of reinforcement learning direct policy search methods (RLDPS) for learning the internal state/action mapping of some behaviors. We demonstrate its feasibility with simulated experiments using the model of our underwater robot URIS in a target following task

Proposal of a parallel architecture for a motion detection algorithm

This paper proposes a parallel architecture for estimation of the motion of an underwater robot. It is well known that image processing requires a huge amount of computation, mainly at low-level processing where the algorithms are dealing with a great number of data. In a motion estimation algorithm, correspondences between two images have to be solved at the low level. In the underwater imaging, normalised correlation can be a solution in the presence of non-uniform illumination. Due to its regular processing scheme, parallel implementation of the correspondence problem can be an adequate approach to reduce the computation time. Taking into consideration the complexity of the normalised correlation criteria, a new approach using parallel organisation of every processor from the architecture is proposed

Pose-based SLAM with probabilistic scan matching algorithm using a mechanical scanned imaging sonar

This paper proposes a pose-based algorithm to solve the full SLAM problem for an autonomous underwater vehicle (AUV), navigating in an unknown and possibly unstructured environment. The technique incorporate probabilistic scan matching with range scans gathered from a mechanical scanning imaging sonar (MSIS) and the robot dead-reckoning displacements estimated from a Doppler velocity log (DVL) and a motion reference unit (MRU). The proposed method utilizes two extended Kalman filters (EKF). The first, estimates the local path travelled by the robot while grabbing the scan as well as its uncertainty and provides position estimates for correcting the distortions that the vehicle motion produces in the acoustic images. The second is an augment state EKF that estimates and keeps the registered scans poses. The raw data from the sensors are processed and fused in-line. No priory structural information or initial pose are considered. The algorithm has been tested on an AUV guided along a 600 m path within a marina environment, showing the viability of the proposed approach