Mathematics: A Discrete Introduction
Mathematics: A Discrete Introduction
Ideal Evaluation from Coevolution
Evolutionary Computation
An overview of evolutionary algorithms in multiobjective optimization
Evolutionary Computation
Intransitivity revisited coevolutionary dynamics of numbers games
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
On identifying global optima in cooperative coevolution
GECCO '05 Proceedings of the 7th annual conference on Genetic and evolutionary computation
Ideal Evaluation from Coevolution
Evolutionary Computation
IEEE Intelligent Systems
A Monotonic Archive for Pareto-Coevolution
Evolutionary Computation
A coevolution archive based on problem dimension
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Coevolution in a large search space using resource-limited nash memory
Proceedings of the 12th annual conference on Genetic and evolutionary computation
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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.