  Neighbor discovery (ND) protocols are used for establishing a first contact
between multiple wireless devices. The energy consumption and discovery latency
of this procedure are determined by the parametrization of the protocol. In
most existing protocols, reception and transmission are temporally coupled.
Such schemes are referred to as \textit{slotted}, for which the problem of
finding optimized parametrizations has been studied thoroughly in the
literature. However, slotted approaches are not efficient in applications in
which new devices join the network gradually and only the joining devices and a
master node need to run the ND protocol simultaneously. For example, this is
typically the case in IoT scenarios or Bluetooth Low Energy (BLE) piconets.
Here, protocols in which packets are transmitted with periodic intervals (PI)
can achieve significantly lower worst-case latencies than slotted ones. For
this class of protocols, optimal parameter values remain unknown. To address
this, we propose an optimization framework for PI-based BLE-like protocols,
which translates any specified duty-cycle (and therefore energy budget) into a
set of optimized parameter values. We show that the parametrizations resulting
from one variant of our proposed scheme are optimal when one receiver discovers
one transmitter, and no other parametrization or ND protocol - neither slotted
nor slotless - can guarantee lower discovery latencies for a given duty-cycle
in this scenario. Since the resulting protocol utilizes the channel more
aggressively than other ND protocols, beacons will collide more frequently.
Hence, due to collisions, the rate of successful discoveries gracefully
decreases for larger numbers of devices discovering each other simultaneously.
We also propose a scheme for configuring the BLE protocol (and not just
BLE-\textit{like} protocols).
