What sense of of the word "random" does ID object to?
In the usual formulation of evolution, mutation is stochastic, or at least not "aware" of its consequenses.
In ID objections, and that of a growing number of non-ID investigators, the evidence speaks to an organization of functional complexity in fits and starts which would require more than a fair toss of a single coin - a single, random mutation.
Some are inclined to self-organizing complexity, some to metatransition. But the evidence speaks to a direction such as in eyeness developing concurrently across phyla - rather than a randomness in the mutation, i.e. because of the master control genes it could not have gone just any old random direction.
Swarm intelligence investigations may also help find a cause for the whole being more the sum of the parts. And then there's Wolfram's approach...