A search for supersymmetry involving the pair production of gluinos decaying via third-generation squarks to the lightest neutralino (${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$) is reported. It uses an LHC proton-proton data set at a center-of-mass energy $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ with an integrated luminosity of $3.2\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ collected with the ATLAS detector in 2015. The signal is searched for in events containing several energetic jets, of which at least three must be identified as $b$ jets, large missing transverse momentum, and, potentially, isolated electrons or muons. Large-radius jets with a high mass are also used to identify highly boosted top quarks. No excess is found above the predicted background. For ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$ masses below approximately 700 GeV, gluino masses of less than 1.78 TeV and 1.76 TeV are excluded at the 95% C.L. in simplified models of the pair production of gluinos decaying via sbottom and stop, respectively. These results significantly extend the exclusion limits obtained with the $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ data set.