  Dusty high-z galaxies are extreme objects with high star formation rates
(SFRs) and luminosities. Characterising the properties of this population and
analysing their evolution over cosmic time is key to understanding galaxy
evolution in the early Universe. We select a sample of high-z dusty
star-forming galaxies (DSFGs) and evaluate their position on the main sequence
(MS) of star-forming galaxies, the well-known correlation between stellar mass
and SFR. We aim to understand the causes of their high star formation and
quantify the percentage of DSFGs that lie above the MS. We adopted a
multi-wavelength approach with data from optical to submillimetre wavelengths
from surveys at the North Ecliptic Pole (NEP) to study a submillimetre sample
of high-redshift galaxies. Two submillimetre selection methods were used,
including: sources selected at 850$\mathrm{\, \mu m}$ with the Sub-millimetre
Common-User Bolometer Array 2) SCUBA-2 instrument and {\it Herschel}-Spectral
and Photometric Imaging Receiver (SPIRE) selected sources (colour-colour
diagrams and 500$\mathrm{\, \mu m}$ risers), finding that 185 have good
multi-wavelength coverage. The resulting sample of 185 high-z candidates was
further studied by spectral energy distribution (SED) fitting with the CIGALE
fitting code. We derived photometric redshifts, stellar masses, SFRs, and
additional physical parameters, such as the infrared luminosity and active
galactic nuclei (AGN) contribution. We find that the different results in the
literature are, only in part, due to selection effects. The difference in
measured SFRs affects the position of DSFGs on the MS of galaxies; most of the
DSFGs lie on the MS (60\%). Finally, we find that the star formation efficiency
(SFE) depends on the epoch and intensity of the star formation burst in the
galaxy; the later the burst, the more intense the star formation.
