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interactive domains

Anthony • Dec 14, 2021 • #coev #note #complexity #domains

A collection of one or more functions, called metrics, of the form p:X1×X2××XnR, where

  • each i with 1in is a domain role
  • an element xXi 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 n2. 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:SR 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.

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