Precise Runtime Analysis for Plateau Functions

To gain a better theoretical understanding of how evolutionary algorithms (EAs) cope with plateaus of constant fitness, we propose the n -dimensional \textsc {Plateau} _k function as natural benchmark and analyze how different variants of the (1 + 1) EA optimize it. The \textsc {Plateau} _k function has a plateau of second-best fitness in a ball of radius k around the optimum. As evolutionary algorithm, we regard the (1 + 1) EA using an arbitrary unbiased mutation operator. Denoting by \alpha the random number of bits flipped in an application of this operator and assuming that \Pr [\alpha = 1] has at least some small sub-constant value, we show the surprising result that for all constant k \ge 2 , the runtime T follows a distribution close to the geometric one with success probability equal to the probability to flip between 1 and k bits divided by the size of the plateau. Consequently, the expected runtime is the inverse of this number, and thus only depends on the probability to flip between 1 and k bits, but not on other characteristics of the mutation operator. Our result also implies that the optimal mutation rate for standard bit mutation here is approximately k/(en) . Our main analysis tool is a combined analysis of the Markov chains on the search point space and on the Hamming level space, an approach that promises to be useful also for other plateau problems.

Motion Estimation for Gray Level Videos Using Different Block Matching Algorithms

Motion Estimation (ME) is a very important operation in video coding. In order to reduce complexity of computations involved in ME and to increase quality of this process, many Block Matching Motion Estimation (BMME) Algorithms are proposed. The aim of this paper is to compare between these algorithms and find the best one. Seven BMME algorithms are used in this paper. The performance of each algorithm is evaluated for different types of motion to determine the best one of these algorithms. The evaluation is based on search points, and Peak Signal to Noise Ratio (PSNR). The simulation shows that Hexagonal Search is faster than all other Block Matching (BM) algorithms used in this paper regardless the type of video because it requires less number of search points to evaluate motion vectors for the video sequence. It requires 11.2424 average search point (SP) for small motions and 13.9708 for fast motions. It also gives a good quality that is close enough to the quality given by Full Search

Drift Analysis and Evolutionary Algorithms Revisited

One of the easiest randomized greedy optimization algorithms is the following evolutionary algorithm which aims at maximizing a function f: {0,1}n → ℝ. The algorithm starts with a random search point ξ ∈ {0,1}n, and in each round it flips each bit of ξ with probability c/n independently at random, where c > 0 is a fixed constant. The thus created offspring ξ' replaces ξ if and only if f(ξ') ≥ f(ξ). The analysis of the runtime of this simple algorithm for monotone and for linear functions turned out to be highly non-trivial. In this paper we review known results and provide new and self-contained proofs of partly stronger results.

Epistemologias não-cartesianas na interface artes-humanidades [Denise Coutinho, Eleonora C. da Motta Santos]

O objetivo deste artigo é apresentar resultados de três anos de trabalho sobre o desenvolvimento de modelos epistemo-metodológicos não-cartesianos para pesquisas em artes e humanidades na universidade. Uma questão norteou esta investigação: A pesquisa acadêmica necessitaria ter como referenciais modos consagrados pela cientificidade para apresentar- se rigorosa em seus objetos, métodos, questões, objetivos e finalidades? Nosso trajeto busca apontar, na história do pensamento ocidental, as bases para o que viria a vingar, no século 17, como modelo da constituição das ciências modernas com a cisão artes x ciências, não existente até então. Em seguida, apresentamos alguns pensadores que, entre o final do século 19 e todo o século 20, produziram importantes quebras no edifício cartesiano, com destaque para Sigmund Freud e alguns conceitos psicanalíticos. Por fim, apostamos que a presença da cultura artística na universidade é tão irreversível quanto a presença, já bastante estabelecida, das ciências, das humanidades, da tecnologia. A singularidade do fazer artístico, refletida em seus processos e objetos, impõe estudos e desenvolvimento de métodos coerentes com tais investigações.<br />The aim of this paper is to present the result of over three years working on the development of models epistemo-methodological non-Cartesian for research in the arts and humanities in the university environment. One question guided this endeavor: should academic research have as reference methods laid down by science in order to be rigorous regarding objects, methods, issues, goals and purposes? Our path search point to the history of Western thought, the basis for what came to succeed in the 17th century as a model of the constitution of modern sciences, with the arts versus sciences divide, which did not exist until then. Next, we introduce some thinkers that since late 19th century and throughout the 20th century produced major breaks in the Cartesian building, especially Sigmund Freud and some of psychoanalytical concepts. Finally, we bet that the presence of the arts at the University is as irreversible as the presence, already well established, of sciences, humanities and technology. The uniqueness of artistic making, reflected in its processes and objects, requires study and development of methods consistent with such investigations.