Melanie Mitchell

Evolving cellular automata to perform computations: mechanisms and impediments

Abstract We present results from experiments in which a genetic algorithm (GA) was used to evolve cellular automata (CAs) to perform a particular computational task - one-dimensional density classification. We look in detail at the evolutionary mechanisms producing the GAs behavior on this task and the impediments faced by the GA. In particular, we identify four “epochs of innovation” in which new CA strategies for solving the problem are discovered by the GA, describe how these strategies are implemented in CA rule tables, and identify the GA mechanisms underlying their discovery. The epochs are characterized by a breaking of the tasks symmetries on the part of the GA. The symmetry breaking results in a short-term fitness gain but ultimately prevents the discovery of the most highly fit strategies. We discuss the extent to which symmetry breaking and other impediments are general phenomena in any GA search.

What Makes a Problem Hard for a Genetic Algorithm? Some Anomalous Results and Their Explanation

What makes a problem easy or hard for a genetic algorithm (GA)? This question has become increasingly important as people have tried to apply the GA to ever more diverse types of problems. Much previous work on this question has studied the relationship between GA performance and the structure of a given fitness function when it is expressed as aWalsh polynomial. The work of Bethke, Goldberg, and others has produced certain theoretical results about this relationship. In this article we review these theoretical results, and then discuss a number of seemingly anomalous experimental results reported by Tanese concerning the performance of the GA on a subclass of Walsh polynomials, some members of which were expected to be easy for the GA to optimize. Tanese found that the GA was poor at optimizing all functions in this subclass, that a partitioning of a single large population into a number of smaller independent populations seemed to improve performance, and that hillelimbing outperformed both the original and partitioned forms of the GA on these functions. These results seemed to contradict several commonly held expectations about GAs.We begin by reviewingschema processing in GAs. We then given an informal description of how Walsh analysis and Bethkes Walsh-schema transform relate to GA performance, and we discuss the relevance of this analysis for GA applications in optimization and machine learning. We then describe Taneses surprising results, examine them experimentally and theoretically, and propose and evaluate some explanations. These explanations lead to a more fundamental question about GAs: what are the features of problems that determine the likelihood of successful GA performance?

Adaptive individuals in evolving populations: models and algorithms

* Introduction R.K. Belew and M. Mitchell Biology * Overview * Adaptive Computation in Ecology and Evolution: A Guide to Future Research J. Roughgarden, A. Bergman, S. Shafir, and C. Taylor Reprinted Classics * The Classics in Their Context, and in Ours J. Schull * Of the Influence of the Environment on the Activities and Habits of Animals, and the Influence of the Activities and Habits of These Living Bodies in Modifying Their Organization and Structure J.B. Lamarck * A New Factor in Evolution J.M. Baldwin * On Modification and Variation C. Lloyd Morgan * Canalization of Development and the Inheritance of Acquired Characters C.H. Waddington * The Baldwin Effect G.G. Simpson * The Role of Somatic Change in Evolution G. Bateson New Work * A Model of Individual Adaptive Behavior in a Fluctuating Environment L. A. Zhivotovsky, A. Bergman, and M. W. Feldman * The Baldwin Effect in the Immune System: Learning by Somatic Hypermutation R. Hightower, S. Forrest, and A. S. Perelson * The Effect of Memory Length on Individual Fitness in a Lizard S. Shafir and J. Roughgarden * Latent Energy Environments F. Menczer and R. K. Belew Psychology * Overview * The Causes and Effects of Evolutionary Simulation in the Behavioral Sciences P.M. Todd Reprinted Classics * Excerpts from Principles of Biology H. Spencer * Excerpts from Principles of Psychology H. Spencer * William James and the Broader Implications of a Multilevel Selectionism J. Schull * Excerpts from The Phylogeny and Ontogeny of Behavior B.F. Skinner * Excerpts from Adaptation and Intelligence: Organic Selection and Phenocopy J. Piaget * Selective Costs and Benefits of in the Evolution of Learning T. D. Johnston New Work * Sexual Selection and the Evolution of Learning P. M. Todd * Discontinuity in Evolution: How Different Levels of Organization Imply Preadaptation O. Miglino, S. Nolfi, and D. Parisi * The Influence of Learning on Evolution D. Parisi and S. Nolfi Computer Science * Overview * Computation and the Natural Sciences R. K. Belew, M. Mitchell, and D. H. Ackley Reprinted Classics * How Learning Can Guide Evolution G. E. Hinton and S. J. Nowlan * Natural Selection: When Learning Guides Evolution J. Maynard Smith New Work * Simulations Combining Evolution and Learning M. L. Littman * Optimization with Genetic Algorithm Hybrids that Use Local Searches W. E. Hart and R. K. Belew

A Genetic Algorithm Discovers Particle-Based Computation in Cellular Automata

How does evolution produce sophisticated emergent computation in systems composed of simple components limited to local interactions? To model such a process, we used a genetic algorithm (GA) to evolve cellular automata to perform a computational task requiring globally-coordinated information processing. On most runs a class of relatively unsophisticated strategies was evolved, but on a subset of runs a number of quite sophisticated strategies was discovered. We analyze the emergent logic underlying these strategies in terms of information processing performed by “particles” in space-time, and we describe in detail the generational progression of the GA evolution of these strategies. Our analysis is a preliminary step in understanding the general mechanisms by which sophisticated emergent computational capabilities can be automatically produced in decentralized multiprocessor systems.

Statistical dynamics of the Royal Road genetic algorithm

Abstract Metastability is a common phenomenon. Many evolutionary processes, both natural and artificial, alternate between periods of stasis and brief periods of rapid change in their behavior. In this paper an analytical model for the dynamics of a mutation-only genetic algorithm (GA) is introduced that identifies a new and general mechanism causing metastability in evolutionary dynamics. The GAs population dynamics is described in terms of flows in the space of fitness distributions. The trajectories through fitness distribution space are derived in closed form in the limit of infinite populations. We then show how finite populations induce metastability, even in regions where fitness does not exhibit a local optimum. In particular, the model predicts the occurrence of “fitness epochs” — periods of stasis in population fitness distributions — at finite population size and identifies the locations of these fitness epochs with the flows hyperbolic fixed points. This enables exact predictions of the metastable fitness distributions during the fitness epochs, as well as giving insight into the nature of the periods of stasis and the innovations between them. All these results are obtained as closed-form expressions in terms of the GAs parameters. An analysis of the Jacobian matrices in the neighborhood of an epochs metastable fitness distribution allows for the calculation of its stable and unstable manifold dimensions and so reveals the state spaces topological structure. More general quantitative features of the dynamics — fitness fluctuation amplitudes, epoch stability, and speed of the innovations — are also determined from the Jacobian eigenvalues. The analysis shows how quantitative predictions for a range of dynamical behaviors, that are specific to the finite population dynamics, can be derived from the solution of the infinite population dynamics. The theoretical predictions are shown to agree very well with statistics from GA simulations. We also discuss the connections of our results with those from population genetics and molecular evolution theory.

Genetic algorithms: An overview

Genetic algorithms (GAs) are computer programs that mimic the processes of biological evolution in order to solve problems and to model evolutionary systems. In this paper I describe the appeal of using ideas from evolution to solve computational problems, give the elements of simple GAs, survey some application areas of GAs, and give a detailed example of how a GA was used on one particularly interesting problem—automatically discovering good strategies for playing the Prisoner’s Dilemma. The paper concludes with a short introduction to the theory of GAs.

A Comparison of Evolutionary and Coevolutionary Search

Previous work on coevolutionary search has demonstrated both successful and unsuccessful applications. As a step in explaining what factors lead to success or failure, we present a comparative study of an evolutionary and a coevolutionary search model. In the latter model, strategies for solving a problem coevolve with training cases. We find that the coevolutionary model has a relatively large efficacy: 86 out of 100 (86%) of the simulations produce high quality strategies. In contrast, the evolutionary model has a very low efficacy: a high quality strategy is found in only two out of 100 runs (2%). We show that the increased efficacy in the coevolutionary model results from the direct exploitation of low quality strategies by the population of training cases. We also present evidence that the generality of the high-quality strategies can suffer as a result of this same exploitation.

Mechanisms of Emergent Computation in Cellular Automata

We introduce a class of embedded-particle models for describing the emergent computational strategies observed in cellular automata (CAs) that were evolved for performing certain computational tasks. The models are evaluated by comparing their estimated performances with the actual performances of the CAs they model. The results show, via a close quantitative agreement, that the embedded-particle framework captures the main information processing mechanisms of the emergent computation that arise in these evolved CAs.

The emergence of understanding in a computer model of concepts and analogy-making

Abstract This paper describes Copycat, a computer model of the mental mechanisms underlying the fluidity and adaptability of the human conceptual system in the context of analogy-making. Copycat creates analogies between idealized situations in a microworld that has been designed to capture and isolate many of the central issues of analogy-making. In Copycat, an understanding of the essence of a situation and the recognition of deep similarity between two superficially different situations emerge from the interaction of a large number of perceptual agents with an associative, overlapping, and context-sensitive network of concepts. Central features of the model are: a high degree of parallelism; competition and cooperation among a large number of small, locally acting agents that together create a global understanding of the situation at hand; and a computational temperature that measures the amount of perceptual organization as processing proceeds and that in turn controls the degree of randomness with which decisions are made in the system.

X-ray Survey of the Small Magellanic Cloud

A region of over 40 square degrees centered on the Small Magellanic Cloud (SMC) has been surveyed with the imaging instruments of the Einstein Observatory. The survey is approximately complete to a luminosity of 10 to the 36th ergs/sec, and the faintest source detected, if in the SMC, has a luminosity of approximately 3 x 10 to the 35th ergs/sec. Twenty-six sources were clearly seen. Five are identified with objects not associated with the SMC. The only previously known source detected was SMC X-1 which, when in a high state, is the brightest source in the SMC. The second brightest source observed, a previously unknown supernova remnant (SNR), is located in the central part of the SMC. Four other weaker sources are probably also SNRs in the SMC. The remaining 15 sources are not yet identified and, since some are far from the center of the cloud, are probably not all members of the SMC.