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When applied to optimization problems, Cooperative Coevolutionary Algorithms (CCEA) have been observed to exhibit a behavior called relative overgeneralization. Roughly, they tend to identify local optima with large basins of attraction which may or may not correspond to global optima. A question which arises is whether one can modify the algorithm to promote the discovery of global optima. We argue that a mechanism from Pareto coevolution can achieve this end. We observe that in CCEAs candidate individuals from one population are used as tests or measurements of individuals in other populations; by treating individuals as tests in this way, a finer-grained comparison can be made among candidate individuals. This finer-grained view permits an algorithm to see when two candidates are differently capable, even when one's evident value is higher than the other's. By modifying an existing CCEA to compare individuals using Pareto dominance we have produced an algorithm which reliably finds global optima. We demonstrate the algorithm on two Maximum of Two Quadratics problems and discuss why it works.

Abstract. Most problems studied in artificial intelligence possess some form of structure, but a precise way to define such structure is so far lacking. We investigate how the notion of problem structure can be made precise, and propose a formal definition of problem structure. The definition is applicable to problems in which the quality of candidate solutions is evaluated by means of a series of tests. This specifies a wide range of problems: tests can be examples in classification, test sequences for a sorting network, or opponents for board games. Based on our definition of problem structure, we provide an automatic procedure for problem structure extraction, and results of proof-of-concept experiments. The definition of problem structure assigns a precise meaning to the notion of the underlying objectives of a problem, a concept which has been used to explain how one can evaluate individuals in a coevolutionary setting. The ability to analyze and represent problem structure may yield new insight into existing problems, and benefit the design of algorithms for learning and search.

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Abstract. Recently, a minimal domain dubbed the numbers game has been proposed to illustrate well-known issues in co-evolutionary dynamics. The domain permits controlled introduction of features like intransitivity, allowing researchers to understand failings of a co-evolutionary algorithm in terms of the domain. In this paper, we show theoretically that a large class of co-evolution problems closely resemble this minimal domain. In particular, all the problems in this class can be embedded into an ordered, n-dimensional Euclidean space, and so can be construed as greater-than games. Thus, conclusions derived using the numbers game are more widely applicable than might be presumed. In light of this observation, we present a simple algorithm aimed at remedying focusing problems and relativism in the numbers game. With it we show empirically that, contrary to expectations, focusing in transitive games can be more troublesome for co-evolutionary algorithms than intransitivity. Practitioners should therefore be just as wary of focusing issues in application domains.