The task of searching for and tracking of multiple targets is a challenging one. However, most works in this area do not consider evasive targets that move faster than the agents comprising the multi-robot system. This is due to the assumption that the movement patterns of such targets, combined with their excessive speed, would make the task nearly impossible to accomplish. In this work, we show that this is not the case and we propose a decentralized search and tracking strategy in which the level of exploration and exploitation carried out by the swarm is adjustable. By tuning a swarm's exploration and exploitation dynamics, we demonstrate that there exists an optimal balance between the level of exploration and exploitation performed. This optimum maximizes its tracking performance and changes depending on the number of targets and the targets’ movement profiles. We also show that the use of agent-based memory is critical in enabling the tracking of an evasive target. The obtained simulation results are validated through experimental tests with a decentralized swarm of six robots tracking a virtual fast-moving target.