Abstract. Coevolution often gives rise to counter-intuitive dynamics that defy our expectations. Here we suggest that much of the confusion surrounding coevolution results from imprecise notions of superiority and progress. In particular, we note that in the literature, three distinct notions of progress are implicitly lumped together: local progress (superior performance against current opponents), historical progress (superior performance against previous opponents) and global progress (superior performance against the entire opponent space). As a result, valid conditions for one type of progress are unduly assumed to lead to another. In particular, the confusion between historical and global progress is a case of a common error, namely using the training set as a test set. This error is prevalent among standard methods for coevolutionary analysis (CIAO, Master Tournament, Dominance Tournament, etc.) By clearly defining and distinguishing between different types of progress, we identify limitations with existing techniques and algorithms, address them, and generally facilitate discussion and understanding of coevolution. We conclude that the concepts proposed in this paper correspond to important aspects of the coevolutionary process. 1

We mowen nat, although we hadden it sworn, It overtake, it slit awey so faste. It wole us maken beggers atte laste! Evolution is notorious for its creative power, but also for giving rise to complex, unpredictable dynamics. As a result, practitioners of artificial evolution have encountered difficulties in predicting, analysing, or even understanding the outcome of their experiments. In particular, the concept of evolutionary “progress ” (whether in the sense of performance increase or complexity growth) has given rise to much debate and confusion. After a careful description of the mechanisms of evolution and natural selection, we provide usable concepts of performance and progress in coevolution. In particular, we introduce a distinction between three types of progress: local, historical, and global, which we suggest underlies much of the confusion that surrounds coevolutionary dynamics. Similarly, we provide a comprehensive answer to the question of whether an “arrow of complexity ” exists in evolution. We introduce several methods to detect and analyse performance and progress in coevolutionary experiments. We propose a statistical

Abstract—Problems in which some entities interact with each other are common in computational intelligence. This scenario, typical for co-evolving artificial-life agents, learning strategies for games, and machine learning from examples, can be formalized as test-based problem. In test-based problems, candidate solutions are evaluated on a number of test cases (agents, opponents, examples). It has been recently shown that at least some of such problems posses underlying problem structure, which can be formalized in a notion of coordinate system, which spatially arranges candidate solutions and tests in a multidimensional space. Such a coordinate system can be extracted to reveal underlying objectives of the problem, which can be then further exploited to help coevolutionary algorithm make progress. In this study, we propose a novel coevolutionary archive method, called Coordinate System Archive (COSA) that is based on these concepts. In the experimental part, we compare COSA to two state-of-the-art archive methods, IPCA and LAPCA. Using two different objective performance measures, we find out that COSA is superior to these methods on a class of artificial problems (COMPARE-ON-ONE). I.