  The secretary problem has been a focus of extensive study with a variety of
extensions that offer useful insights into the theory of optimal stopping. The
original solution is to set one stopping threshold that gives rise to an
immediately rejected sample $r$ out of the candidate pool of size $n$ and to
accept the first candidate that is subsequently interviewed and bests the prior
$r$ rejected. In reality, it is not uncommon to draw a line between job
candidates to distinguish those above the line vs those below the line. Here we
consider such satisficing sectary problem that views suboptimal choices
(finding any of the top $d$ candidates) also as hiring success. We use a
multiple stopping criteria $(r_1, r_2, \cdots, r_d)$ that sequentially lowers
the expectation when the prior selection criteria yields no choice. We
calculate the probability of securing the top $d$ candidate in closed form
solutions which are in excellent agreement with computer simulations. The
exhaustive search for optimal stopping has to deal with large parameter space
and thus can quickly incur astronomically large computational times. In light
of this, we apply the effective computational method of simulated annealing to
find optimal $r_i$ values which performs reasonably well as compared with the
exhaustive search despite having significantly less computing time. Our work
sheds light on maximizing the likelihood of securing satisficing (suboptimal)
outcomes using adaptive search strategy in combination with computation
methods.
