Evolution strategies in optimization problems

Evolution strategies are inspired in biology and form part of a larger research field known as evolutionary algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting one to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.CEOCFCTFEDER/POCI 201

Evolution Strategies in Optimization Problems

Evolution Strategies are inspired in biology and part of a larger research field known as Evolutionary Algorithms. Those strategies perform a random search in the space of admissible functions, aiming to optimize some given objective function. We show that simple evolution strategies are a useful tool in optimal control, permitting to obtain, in an efficient way, good approximations to the solutions of some recent and challenging optimal control problems.Comment: Partially presented at the 5th Junior European Meeting on "Control and Information Technology" (JEM'06), Sept 20-22, 2006, Tallinn, Estonia. To appear in "Proceedings of the Estonian Academy of Sciences -- Physics Mathematics

Strategies for the evolution of sex

We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not necessary for the successful evolution of a steady state population of sexual individuals within a finite population. Simply allowing for a finite probability for conversion to sex in each generation also gives rise to a stable sexual population, in the presence of an upper limit on the number of deleterious mutations per individual. For large values of this probability, we find a phase transition to an intermittent, multi-stable regime. On the other hand, in the limit of extremely slow drive, another transition takes place to a different steady state distribution, with fewer deleterious mutations within the asexual population.Comment: RevTeX, 11 pages, multicolumn, including 12 figure

Evolution of Philosophical Strategies for Interacting with Chaos

After the discoveries of such scholars as J. H. Poincaré, E. N. Lorenz, I. Prigogine, etc. the term ‘chaos’ is used actively by representatives of various scientific fields; however, one important aspect remains uninvestigated: which attitude one should have toward chaotic phenomena. This is a philosophical question and my dissertation aims to find the answer in the history of philosophy, where chaos theme has had its investigators from ancient philosophy to the philosophical theories of the 21st century. My dissertation is based on the idea that sciences and philosophy can achieve significant success in exploring chaos theme when their efforts are combined. This dissertation research is designed to help in the planning of conscious, rational actions towards chaotic phenomena, since it is aimed at exploration and systematic presentation, as well as comprehension of possible systems of such actions – philosophical strategies for interacting with chaos. Results of the dissertation are the following. I reveal, reconstruct, and explain the content of six possible strategies for interacting with chaos that were worked out in history of philosophical thought: ordering, avoiding, transfiguring, preventing, controlling, and integrating. I argue that the first philosophical strategies for interacting with chaos were worked out in the 19th century by German philosophers K. W. F. Schlegel and F. W. Nietzsche on the basis of their rethinking the ideas which were expressed by different thinkers during classical antiquity, the Middle Ages, and the modern period. I show that ideas of strategic views towards chaos were also elaborated by such 20th-century thinkers as H. Rickert, N. Berdyaev, I. Prigogine, H. Haken, G. Deleuze, Q. Meillassoux, and others. I outline the main stages of the evolution of philosophical strategies for interacting with chaos as well as its regularities. The dissertation shows perspectives of further development of each one of the six strategies for interacting with chaos. In contemporary scientific and philosophical research on chaos, my exploration contributes to the new approach to improving the understanding of aims of acts towards chaotic phenomena. I think that knowing a range of different strategic views of chaos help researchers of chaotic phenomena to choose the most appropriate and rational reactions. In the area of history of philosophy, my research contributes detailed data about development and conceptual transformations of the notion of ‘chaos’ through all periods of Western philosophy. The dissertation consists of five chapters: 1) Literature Review, Methodology and Key Research Terms, 2) Ancient and Medieval Philosophical Ideas about Chaos, 3) Genesis of the First Strategies for Interacting with Chaos, 4) Strategies for Interacting with Chaos in the 20th and 21st Centuries, 5) Regularities and Prospects of the Development of Philosophical Strategies for Interacting with Chaos. In the first chapter I analyze more than five hundred books, articles, and other philosophical and scientific sources in which the chaos theme is raised. I also argue the necessity of applying methods such as analysis, the structural method, the hermeneutic method of interpretation, and the comparative method in my dissertation research. Moreover, in this chapter, I define key terms for my dissertation – ‘chaos’ and ‘philosophical strategies for interacting with chaos.’ Then, in the next chapter, I analyze the appearance and development of Ancient and Medieval philosophical ideas about chaotic phenomena and order. Particularly, I explore thoughts of philosophers such as Anaxagoras, Anaximander, Heraclitus, Empedocles, Plato, Aristotle, Augustine of Hippo, Bernard Silvestris, Ramon Llull, etc. In this chapter I also compare the first Western ideas about chaos with similar thoughts from Eastern philosophy, analyzing Indian and Chinese philosophical ideas about disorder. In the third chapter I explore transformations in understanding the meaning of the term ‘chaos’ in philosophy from the 15th to the end of the 19th century. I analyze ideas about chaos and order from thinkers such as M. Ficino, Paracelsus, F. Bacon, P. Bayle, Voltaire, J. G. Herder, I. Kant, F. W. J. Schelling and other philosophers from the Renaissance, the Age of Enlightenment, and the German idealist period, showing that these thinkers’ new approaches to interpreting the notion of ‘chaos’ were the background for K. W. F. Schlegel’s and F. W. Nietzsche’s creations of the first strategies for interacting with chaos in the 19th century. I finish the chapter with detailed analysis of K. W. F. Schlegel’s strategy for transfiguring chaos and F. W. Nietzsche’s strategy for ordering chaos. The development of philosophical strategies for interacting with chaos in the 20th and the beginning of the 21st century is the topic of the fourth chapter. I research new ideas about ordering chaos (H. Rickert) and transfiguring chaos (N. Berdyaev). Also, I reveal thoughts about avoiding chaos (A. Camus), preventing chaos (J. Ortega y Gasset), integrating chaos (G. Deleuze, Q. Meillassoux). Moreover, I analyze a philosophical component of the strategy for chaos control (I. Prigogine, H. Haken). In the final fifth chapter of the dissertation I trace the major features of philosophical strategies for interacting with chaos and find out the main conditions and periods of their development. Then I outline the prospects for the development of the philosophical strategies for interacting with chaos and show the most productive ways of their progress

Neural networks robot controller trained with evolution strategies

Congress on Evolutionary Computation. Washington, DC, 6-9 July 1999.Neural networks (NN) can be used as controllers in autonomous robots. The specific features of the navigation problem in robotics make generation of good training sets for the NN difficult. An evolution strategy (ES) is introduced to learn the weights of the NN instead of the learning method of the network. The ES is used to learn high performance reactive behavior for navigation and collision avoidance. No subjective information about “how to accomplish the task” has been included in the fitness function. The learned behaviors are able to solve the problem in different environments; therefore, the learning process has the proven ability to obtain a specialized behavior. All the behaviors obtained have been tested in a set of environments and the capability of generalization is shown for each learned behavior. A simulator based on the mini-robot, Khepera, has been used to learn each behavior

The Evolution of Extortion in Iterated Prisoner's Dilemma Games

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the possibility to use conditional strategies that depend on the outcome of previous interactions. In the context of evolution of cooperation, repeated games represent the mechanism of reciprocation. Recently a new class of strategies has been proposed, so called 'zero determinant strategies'. These strategies enforce a fixed linear relationship between one's own payoff and that of the other player. A subset of those strategies are 'extortioners' which ensure that any increase in the own payoff exceeds that of the other player by a fixed percentage. Here we analyze the evolutionary performance of this new class of strategies. We show that in reasonably large populations they can act as catalysts for the evolution of cooperation, similar to tit-for-tat, but they are not the stable outcome of natural selection. In very small populations, however, relative payoff differences between two players in a contest matter, and extortioners hold their ground. Extortion strategies do particularly well in co-evolutionary arms races between two distinct populations: significantly, they benefit the population which evolves at the slower rate - an instance of the so-called Red King effect. This may affect the evolution of interactions between host species and their endosymbionts.Comment: contains 4 figure