  Current wisdom accounts to the diversity of neutron star observational
manifestations to their birth scenarios, influencing their thermal and magnetic
field evolution. Among the kind of observed neutron stars, radio pulsars
represent by far the largest population of neutron stars. In this paper, we aim
at constraining the observed population of the canonical neutron star period,
magnetic field and spatial distribution at birth in order to understand the
radio and high-energy emission processes in a pulsar magnetosphere. For this
purpose we design a population synthesis method self-consistently taking into
account the secular evolution of a force-free magnetosphere and the magnetic
field decay. We generate a population of pulsars and evolve them from their
birth to the present time, working in the force-free approximation. We assume a
given initial distribution for the spin period, surface magnetic field and
spatial galactic location. Radio emission properties are accounted by the polar
cap geometry, whereas the gamma-ray emission is assumed to be produced within
the striped wind model. We found that a decaying magnetic field gave better
agreement with observations compared to a constant magnetic field model.
Starting from an initial mean magnetic field strength of $B=2.5\times 10^8$~T
with a characteristic decay timescale of $4.6 \times 10^5~$yr, a neutron star
birth rate of $1/70~$yr and a mean initial spin period of 60~ms, we found that
the force-free model satisfactorily reproduces the distribution of pulsars in
the $P-\dot{P}$ diagram with simulated populations of radio-loud, radio-only
and radio quiet gamma-ray pulsars similar to the observed populations.
