  An approach is proposed to improve the efficiency of fourth-order algorithms
for numerical integration of the equations of motion in molecular dynamics
simulations. The approach is based on an extension of the decomposition scheme
by introducing extra evolution subpropagators. The extended set of parameters
of the integration is then determined by reducing the norm of truncation terms
to a minimum. In such a way, we derive new explicit symplectic Forest-Ruth- and
Suzuki-like integrators and present them in time-reversible velocity and
position forms. It is proven that these optimized integrators lead to the best
accuracy in the calculations at the same computational cost among all possible
algorithms of the fourth order from a given decomposition class. It is shown
also that the Forest-Ruth-like algorithms, which are based on direct
decomposition of exponential propagators, provide better optimization than
their Suzuki-like counterparts which represent compositions of second-order
schemes. In particular, using our optimized Forest-Ruth-like algorithms allows
us to increase the efficiency of the computations more than in ten times with
respect to that of the original integrator by Forest and Ruth, and
approximately in five times with respect to Suzuki's approach. The theoretical
predictions are confirmed in molecular dynamics simulations of a Lennard-Jones
fluid. A special case of the optimization of the proposed Forest-Ruth-like
algorithms to celestial mechanics simulations is considered as well.
