  Search processes often involve multiple agents that collectively look for a
randomly located target. While increasing the number of agents usually
decreases the time at which the first agent finds the target, it also requires
resources to create and sustain more agents. In this letter, we consider a
collective search cost that not only accounts for the search time but also for
the cost associated to the creation and the maintenance of an agent. We first
present a general formalism for independent agents in terms of the survival
probability of the target for a single-agent search s(t), where we allow agents
to be introduced in the system one after the other. From this, we first derive
analytically the optimal number of searchers to launch initially in the system.
Then, we identify the optimal strategies for exponential and algebraic
single-agent survival probabilities by pointing out the ideal times at which
new searchers should be launched in the system. Our results show that all
searchers should be launched simultaneously in the exponential case, while some
should be launched at later times in the algebraic case. Finally, we compare
these results with numerical simulations of a strongly interacting collective
search, the true self-avoiding walk, and show how the optimal strategy differ
from the non-interacting case.

Statistical Mechanics;Soft Condensed Matter