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Search processes often involve multiple agents that collectively look for arandomly located target. While increasing the number of agents usuallydecreases the time at which the first agent finds the target, it also requiresresources to create and sustain more agents. In this letter, we consider acollective search cost that not only accounts for the search time but also forthe cost associated to the creation and the maintenance of an agent. We firstpresent a general formalism for independent agents in terms of the survivalprobability of the target for a single-agent search s(t), where we allow agentsto be introduced in the system one after the other. From this, we first deriveanalytically the optimal number of searchers to launch initially in the system.Then, we identify the optimal strategies for exponential and algebraicsingle-agent survival probabilities by pointing out the ideal times at whichnew searchers should be launched in the system. Our results show that allsearchers should be launched simultaneously in the exponential case, while someshould be launched at later times in the algebraic case. Finally, we comparethese results with numerical simulations of a strongly interacting collectivesearch, the true self-avoiding walk, and show how the optimal strategy differfrom the non-interacting case.

Should you hire new searchers? Optimal number of agents in a collective search, and when to launch them