Resolving multiple supermassive black hole binaries with pulsar timing
  arrays II: genetic algorithm implementation
  Pulsar timing arrays (PTAs) might detect gravitational waves (GWs) from
massive black hole (MBH) binaries within this decade. The signal is expected to
be an incoherent superposition of several nearly-monochromatic waves of
different strength. The brightest sources might be individually resolved, and
the overall deconvolved, at least partially, in its individual components. In
this paper we extend the maximum-likelihood based method developed in Babak &
Sesana 2012, to search for individual MBH binaries in PTA data. We model the
signal as a collection of circular monochromatic binaries, each characterized
by three free parameters: two angles defining the sky location, and the
frequency. We marginalize over all other source parameters and we apply an
efficient multi-search genetic algorithm to maximize the likelihood function
and look for sources in synthetic datasets. On datasets characterized by white
Gaussian noise plus few injected sources with signal-to-noise ratio (SNR) in
the range 10-60, our search algorithm performs well, recovering all the
injections with no false positives. Individual source SNRs are estimated within
few % of the injected values, sky locations are recovered within few degrees,
and frequencies are determined with sub-Fourier bin precision.
