Fitness Uniform Optimization

In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient optimization progress on the one hand and in preserving genetic diversity to be able to escape from local optima on the other hand. Motivated by a universal similarity relation on the individuals, we propose a new selection scheme, which is uniform in the fitness values. It generates selection pressure toward sparsely populated fitness regions, not necessarily toward higher fitness, as is the case for all other selection schemes. We show analytically on a simple example that the new selection scheme can be much more effective than standard selection schemes. We also propose a new deletion scheme which achieves a similar result via deletion and show how such a scheme preserves genetic diversity more effectively than standard approaches. We compare the performance of the new schemes to tournament selection and random deletion on an artificial deceptive problem and a range of NP-hard problems: traveling salesman, set covering and satisfiability.Comment: 25 double-column pages, 12 figure

Finding long cycles in graphs

We analyze the problem of discovering long cycles inside a graph. We propose and test two algorithms for this task. The first one is based on recent advances in statistical mechanics and relies on a message passing procedure. The second follows a more standard Monte Carlo Markov Chain strategy. Special attention is devoted to Hamiltonian cycles of (non-regular) random graphs of minimal connectivity equal to three

A Memetic Algorithm for whole test suite generation

The generation of unit-level test cases for structural code coverage is a task well-suited to Genetic Algorithms. Method call sequences must be created that construct objects, put them into the right state and then execute uncovered code. However, the generation of primitive values, such as integers and doubles, characters that appear in strings, and arrays of primitive values, are not so straightforward. Often, small local changes are required to drive the value toward the one needed to execute some target structure. However, global searches like Genetic Algorithms tend to make larger changes that are not concentrated on any particular aspect of a test case. In this paper, we extend the Genetic Algorithm behind the EvoSuiTE test generation tool into a Memetic Algorithm, by equipping it with several local search operators. These operators are designed to efficiently optimize primitive values and other aspects of a test suite that allow the search for test cases to function more effectively. We evaluate our operators using a rigorous experimental methodology on over 12,000 Java classes, comprising open source classes of various different kinds, including numerical applications and text processors. Our study shows that increases in branch coverage of up to 53% are possible for an individual class in practice

AccuSyn: Using Simulated Annealing to Declutter Genome Visualizations

We apply Simulated Annealing, a well-known metaheuristic for obtaining near-optimal solutions to optimization problems, to discover conserved synteny relations (similar features) in genomes. The analysis of synteny gives biologists insights into the evolutionary history of species and the functional relationships between genes. However, as even simple organisms have huge numbers of genomic features, syntenic plots initially present an enormous clutter of connections, making the structure difficult to understand. We address this problem by using Simulated Annealing to minimize link crossings. Our interactive web-based synteny browser, AccuSyn, visualizes syntenic relations with circular plots of chromosomes and draws links between similar blocks of genes. It also brings together a huge amount of genomic data by integrating an adjacent view and additional tracks, to visualize the details of the blocks and accompanying genomic data, respectively. Our work shows multiple ways to manually declutter a synteny plot and then thoroughly explains how we integrated Simulated Annealing, along with human interventions as a human-in-the-loop approach, to achieve an accurate representation of conserved synteny relations for any genome. The goal of AccuSyn was to make a fairly complete tool combining ideas from four major areas: genetics, information visualization, heuristic search, and human-in-the-loop. Our results contribute to a better understanding of synteny plots and show the potential that decluttering algorithms have for syntenic analysis, adding more clues for evolutionary development. At this writing, AccuSyn is already actively used in the research being done at the University of Saskatchewan and has already produced a visualization of the recently-sequenced Wheat genome

Iterative Solvers for Physics-based Simulations and Displays

La génération d’images et de simulations réalistes requiert des modèles complexes pour capturer tous les détails d’un phénomène physique. Les équations mathématiques qui composent ces modèles sont compliquées et ne peuvent pas être résolues analytiquement. Des procédures numériques doivent donc être employées pour obtenir des solutions approximatives à ces modèles. Ces procédures sont souvent des algorithmes itératifs, qui calculent une suite convergente vers la solution désirée à partir d’un essai initial. Ces méthodes sont une façon pratique et efficace de calculer des solutions à des systèmes complexes, et sont au coeur de la plupart des méthodes de simulation modernes. Dans cette thèse par article, nous présentons trois projets où les algorithmes itératifs jouent un rôle majeur dans une méthode de simulation ou de rendu. Premièrement, nous présentons une méthode pour améliorer la qualité visuelle de simulations fluides. En créant une surface de haute résolution autour d’une simulation existante, stabilisée par une méthode itérative, nous ajoutons des détails additionels à la simulation. Deuxièmement, nous décrivons une méthode de simulation fluide basée sur la réduction de modèle. En construisant une nouvelle base de champ de vecteurs pour représenter la vélocité d’un fluide, nous obtenons une méthode spécifiquement adaptée pour améliorer les composantes itératives de la simulation. Finalement, nous présentons un algorithme pour générer des images de haute qualité sur des écrans multicouches dans un contexte de réalité virtuelle. Présenter des images sur plusieurs couches demande des calculs additionels à coût élevé, mais nous formulons le problème de décomposition des images afin de le résoudre efficacement avec une méthode itérative simple.Realistic computer-generated images and simulations require complex models to properly capture the many subtle behaviors of each physical phenomenon. The mathematical equations underlying these models are complicated, and cannot be solved analytically. Numerical procedures must thus be used to obtain approximate solutions. These procedures are often iterative algorithms, where an initial guess is progressively improved to converge to a desired solution. Iterative methods are a convenient and efficient way to compute solutions to complex systems, and are at the core of most modern simulation methods. In this thesis by publication, we present three papers where iterative algorithms play a major role in a simulation or rendering method. First, we propose a method to improve the visual quality of fluid simulations. By creating a high-resolution surface representation around an input fluid simulation, stabilized with iterative methods, we introduce additional details atop of the simulation. Second, we describe a method to compute fluid simulations using model reduction. We design a novel vector field basis to represent fluid velocity, creating a method specifically tailored to improve all iterative components of the simulation. Finally, we present an algorithm to compute high-quality images for multifocal displays in a virtual reality context. Displaying images on multiple display layers incurs significant additional costs, but we formulate the image decomposition problem so as to allow an efficient solution using a simple iterative algorithm

The geometry of dynamical triangulations

We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil

Analysis of combinatorial search spaces for a class of NP-hard problems, An

2011 Spring.Includes bibliographical references.Given a finite but very large set of states X and a real-valued objective function ƒ defined on X, combinatorial optimization refers to the problem of finding elements of X that maximize (or minimize) ƒ. Many combinatorial search algorithms employ some perturbation operator to hill-climb in the search space. Such perturbative local search algorithms are state of the art for many classes of NP-hard combinatorial optimization problems such as maximum k-satisfiability, scheduling, and problems of graph theory. In this thesis we analyze combinatorial search spaces by expanding the objective function into a (sparse) series of basis functions. While most analyses of the distribution of function values in the search space must rely on empirical sampling, the basis function expansion allows us to directly study the distribution of function values across regions of states for combinatorial problems without the need for sampling. We concentrate on objective functions that can be expressed as bounded pseudo-Boolean functions which are NP-hard to solve in general. We use the basis expansion to construct a polynomial-time algorithm for exactly computing constant-degree moments of the objective function ƒ over arbitrarily large regions of the search space. On functions with restricted codomains, these moments are related to the true distribution by a system of linear equations. Given low moments supplied by our algorithm, we construct bounds of the true distribution of ƒ over regions of the space using a linear programming approach. A straightforward relaxation allows us to efficiently approximate the distribution and hence quickly estimate the count of states in a given region that have certain values under the objective function. The analysis is also useful for characterizing properties of specific combinatorial problems. For instance, by connecting search space analysis to the theory of inapproximability, we prove that the bound specified by Grover's maximum principle for the Max-Ek-Lin-2 problem is sharp. Moreover, we use the framework to prove certain configurations are forbidden in regions of the Max-3-Sat search space, supplying the first theoretical confirmation of empirical results by others. Finally, we show that theoretical results can be used to drive the design of algorithms in a principled manner by using the search space analysis developed in this thesis in algorithmic applications. First, information obtained from our moment retrieving algorithm can be used to direct a hill-climbing search across plateaus in the Max-k-Sat search space. Second, the analysis can be used to control the mutation rate on a (1+1) evolutionary algorithm on bounded pseudo-Boolean functions so that the offspring of each search point is maximized in expectation. For these applications, knowledge of the search space structure supplied by the analysis translates to significant gains in the performance of search

Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

Multiscale Markov Decision Problems: Compression, Solution, and Transfer Learning

Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure, particularly beyond a single level of abstraction, has remained a longstanding challenge. We describe a fast multiscale procedure for repeatedly compressing, or homogenizing, Markov decision processes (MDPs), wherein a hierarchy of sub-problems at different scales is automatically determined. Coarsened MDPs are themselves independent, deterministic MDPs, and may be solved using existing algorithms. The multiscale representation delivered by this procedure decouples sub-tasks from each other and can lead to substantial improvements in convergence rates both locally within sub-problems and globally across sub-problems, yielding significant computational savings. A second fundamental aspect of this work is that these multiscale decompositions yield new transfer opportunities across different problems, where solutions of sub-tasks at different levels of the hierarchy may be amenable to transfer to new problems. Localized transfer of policies and potential operators at arbitrary scales is emphasized. Finally, we demonstrate compression and transfer in a collection of illustrative domains, including examples involving discrete and continuous statespaces.Comment: 86 pages, 15 figure