  The figure of merit for refrigerators performing finite-time Carnot-like
cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is
optimized. It is found that the coefficient of performance at maximum figure of
merit is bounded between 0 and $(\sqrt{9+8\varepsilon_c}-3)/2$ for the
low-dissipation refrigerators, where $\varepsilon_c =T_c/(T_h-T_c)$ is the
Carnot coefficient of performance for reversible refrigerators. These bounds
can be reached for extremely asymmetric low-dissipation cases when the ratio
between the dissipation constants of the processes in contact with the cold and
hot reservoirs approaches to zero or infinity, respectively. The observed
coefficients of performance for real refrigerators are located in the region
between the lower and upper bounds, which is in good agreement with our
theoretical estimation.
