Coevolution provides a framework to implement search heuristics that are more elaborate than those driving the exploration of the state space in canonical evolutionary systems. However, some drawbacks have also to be overcome in order to ensure continuous progress on the long term. This paper presents the concept of coevolutionary learning and introduces a search procedure which successfully addresses the underlying impediments in coevolutionary search. The application of this algorithm to the discovery of cellular automata rules for a classification task is described. This work resulted in a significant improvement over previously known best rules for this task. 1 Introduction Some problems are difficult because solutions have to be evaluated against a very large number of test cases in order to determine their score accurately. The discovery of game strategies and learning control procedures for autonomous agents are a few examples of such problems. To make learning tractable, solu...

www.demo.cs.brandeis.edu Abstract. We develop a novel coevolutionary algorithm based upon the concept of Pareto optimality. The Pareto criterion is core to conventional multi-objective optimization (MOO) algorithms. We can think of agents in a coevolutionary system as performing MOO, as well: An agent interacts with many other agents, each of which can be regarded as an objective for optimization. We adapt the Pareto concept to allow agents to follow gradient and create gradient for others to follow, such that coevolutionary learning succeeds. We demonstrate our Pareto coevolution methodology with the majority function, a density classification task for cellular automata. 1

We review recent work done by our group on applying genetic algorithms (GAs) to the design of cellular automata (CAs) that can perform computations requiring global coordination. A GA was used to evolve CAs for two computational tasks: density classification and synchronization. In both cases, the GA discovered rules that gave rise to sophisticated emergent computational strategies. These strategies can be analyzed using a “computational mechanics ” framework in which “particles ” carry information and interactions between particles effects information processing. This framework can also be used to explain the process by which the strategies were designed by the GA. The work described here is a first step in employing GAs to engineer useful emergent computation in decentralized multi-processor systems. It is also a first step in understanding how an evolutionary process can produce complex systems with sophisticated collective computational abilities.

We present a comparative study of an evolutionary and a coevolutionary search model. In the latter, strategies for solving a problem coevolve with training cases. We find that the coevolutionary model has a relatively large efficacy: 41 out of 50 (82%) of the simulations produce high quality strategies. In contrast, the evolutionary model has a very low efficacy: 1 out of 50 runs (2%) produce high quality strategies. We show that the increased efficacy in the coevolutionary model results from the direct exploitation of lowquality 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.

Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of efficiency and robustness, as well as to model the behavior of complex systems in nature. For these reasons CAs and related architectures have

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Evolutionary algorithms apply the process of variation, reproduction and selection to look for an individual capable of solving the task at hand. In order to improve the evolvability of a population we propose to copy important characteristics of nature's search space. Desired characteristics for a genotype-phenotype mapping are described and several highly redundant genotype-phenotype mappings are analyzed in the context of a population based search. We show that evolvability, de ned as the ability of random variations to sometimes produce improvement, is inuenced by the existence of neutral networks in genotype space. Redundant mappings allow the population to spread along the network of neutral mutations and the population is quickly able to recover after a change has occurred. The extent of the neutral networks aects the interconnectivity of the search space and thereby aects evolvability.

Abstract. We investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which “particles ” embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how machine-learning processes can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation. 1.

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While standard evolutionary algorithms employ a static, absolute fitness metric, coevolutionary algorithms assess individuals by their performance relative to populations of opponents that are themselves evolving. Although this arrangement offers the possibility of avoiding long-standing difficulties such as premature convergence, it suffers from its own unique problems, cycling, over-focusing and disengagement. Here, we introduce a novel technique for dealing with the third and least explored of these problems. Inspired by studies of natural host-parasite systems, we show that disengagement can be avoided by selecting for individuals that exhibit reduced levels of “virulence”, rather than maximum ability to defeat coevolutionary adversaries. Experiments in both simple and complex domains are used to explain how this counterintuitive approach may be used to improve the success of coevolutionary algorithms.