  We propose the Particle Swarm Optimization (PSO) as an alternative method for
locating periodic orbits in a three--dimensional (3D) model of barred galaxies.
We develop an appropriate scheme that transforms the problem of finding
periodic orbits into the problem of detecting global minimizers of a function,
which is defined on the Poincar\'{e} Surface of Section (PSS) of the
Hamiltonian system. By combining the PSO method with deflection techniques, we
succeeded in tracing systematically several periodic orbits of the system. The
method succeeded in tracing the initial conditions of periodic orbits in cases
where Newton iterative techniques had difficulties. In particular, we found
families of 2D and 3D periodic orbits associated with the inner 8:1 to 12:1
resonances, between the radial 4:1 and corotation resonances of our 3D Ferrers
bar model. The main advantages of the proposed algorithm is its simplicity, its
ability to work using function values solely, as well as its ability to locate
many periodic orbits per run at a given Jacobian constant.
