  [abridged] The ALESS survey has followed-up a sample of 122 sub-millimeter
sources in the Extended Chandra Deep Field South at 870um with ALMA, allowing
to pinpoint the positions of sub-millimeter galaxies (SMGs) to 0.3'' and to
find their precise counterparts at different wavelengths. This enabled the
first compilation of the multi-wavelength spectral energy distributions (SEDs)
of a statistically reliable survey of SMGs. In this paper, we present a new
calibration of the MAGPHYS modelling code that is optimized to fit these
UV-to-radio SEDs of z>1 star-forming galaxies using an energy balance technique
to connect the emission from stellar populations, dust attenuation and dust
emission in a physically consistent way. We derive statistically and physically
robust estimates of the photometric redshifts and physical parameters for the
ALESS SMGs. We find that they have a median stellar mass
$M_\ast=(8.9\pm0.1)\times10^{10} M_\odot$, SFR$=280\pm70 M_\odot$/yr, overall
V-band dust attenuation $A_V=1.9\pm0.2$ mag, dust mass
$M_\rm{dust}=(5.6\pm1.0)\times10^8 M_\odot$, and average dust temperature
Tdust~40 K. The average intrinsic SED of the ALESS SMGs resembles that of local
ULIRGs in the IR range, but the stellar emission of our average SMG is brighter
and bluer, indicating lower dust attenuation, possibly because they are more
extended. We explore how the average SEDs vary with different parameters, and
we provide a new set of SMG templates. To put the ALESS SMGs into context, we
compare their stellar masses and SFRs with those of less actively star-forming
galaxies at the same redshifts. At z~2, about half of the SMGs lie above the
star-forming main sequence, while half are at the high-mass end of the
sequence. At higher redshifts (z~3.5), the SMGs tend to have higher SFR and
Mstar, but the fraction of SMGs that lie significantly above the main sequence
decreases to less than a third.
