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The secretary problem has been a focus of extensive study with a variety ofextensions that offer useful insights into the theory of optimal stopping. Theoriginal solution is to set one stopping threshold that gives rise to animmediately rejected sample $r$ out of the candidate pool of size $n$ and toaccept the first candidate that is subsequently interviewed and bests the prior$r$ rejected. In reality, it is not uncommon to draw a line between jobcandidates to distinguish those above the line vs those below the line. Here weconsider such satisficing sectary problem that views suboptimal choices(finding any of the top $d$ candidates) also as hiring success. We use amultiple stopping criteria $(r_1, r_2, \cdots, r_d)$ that sequentially lowersthe expectation when the prior selection criteria yields no choice. Wecalculate the probability of securing the top $d$ candidate in closed formsolutions which are in excellent agreement with computer simulations. Theexhaustive search for optimal stopping has to deal with large parameter spaceand thus can quickly incur astronomically large computational times. In lightof this, we apply the effective computational method of simulated annealing tofind optimal $r_i$ values which performs reasonably well as compared with theexhaustive search despite having significantly less computing time. Our worksheds light on maximizing the likelihood of securing satisficing (suboptimal)outcomes using adaptive search strategy in combination with computationmethods.

The satisficing secretary problem: when closed-form solutions meet simulated annealing