Order-theoretic Analysis of Coevolution Problems: Coevolutionary Statics

We present an order-theoretic framework for analyzing coevolution problems. The framework focuses attention on the underlying problem definition, or statics of coevolution, as opposed to the dynamics of search algorithms. We define a notion of solution for coevolution which generalizes similar solution concepts in GA function optimization and MOO. We then define the ideal test set, a potentially small set of tests which allow us to find the solution set of a problem. One feature of the ideal test set is that we are able to categorize problems by considering its cardinality. We conclude by discussing three issues which commonly arise in coevolution from the point of view of coevolutionary statics, pointing out analytical attacks on these issues.