  New sets of parameter tunes for two of the colour reconnection models,
quantum chromodynamics-inspired and gluon-move, implemented in the PYTHIA 8
event generator, are obtained based on the default CMS PYTHIA 8
underlying-event tune, CP5. Measurements sensitive to the underlying event
performed by the CMS experiment at centre-of-mass energies $\sqrt{s}$ = 7 and
13 TeV, and by the CDF experiment at 1.96 TeV are used to constrain the
parameters of colour reconnection models and multiple-parton interactions
simultaneously. The new colour reconnection tunes are compared with various
measurements at 1.96, 7, 8, and 13 TeV including measurements of the
underlying-event, strange-particle multiplicities, jet substructure
observables, jet shapes, and colour flow in top quark pair
($\mathrm{t\bar{t}}$) events. The new tunes are also used to estimate the
uncertainty related to colour reconnection modelling in the top quark mass
measurement using the decay products of $\mathrm{t\bar{t}}$ events in the
semileptonic channel at 13 TeV.
