A collection of one or more functions, called metrics, of the form p:X1×X2×⋯×Xn→R, where
- each i with 1≤i≤n is a domain role
- an element x∈Xi is an entity (playing the domain role i)
- a tuple (x1,…,xn)∈X1×⋯×Xn is an interaction
- the value p(x1,…,xn)∈R is an outcome (of the interaction)
- the ordered set R is the outcome set
These are really only interesting from the perspective of coevolutionary algorithms when n≥2. When n=1, you have one or more single-variable functions, meaning something that looks like an optimization problem or a multi-objective optimziation problem as opposed to a co-optimization problem.
It is important to recognize that an interactive domain does not specify a solution concept–in other words, what one might want to find–only the structure of its information. As an analogy, a function f:S→R does not specify enough information to be optimized; you'd also have to know whether you're trying to minimize or maximize, whether you're seeking one or all solutions, whether you're looking for an argument or a value, etc. The function is like an interactive domain; the arg max (for instance) is the solution concept.
References
- The book chapter titled Coevolutionary Principles in the Handbook of Natural Computing goes into depth about interactive domains and their role in coevolutionary algorithms