  We investigate quantum Otto engine and refrigeration cycles of a
time-dependent harmonic oscillator operating under the conditions of maximum
$\Omega$-function, a trade-off objective function which represents a compromise
between energy benefits and losses for a specific job, for both adiabatic and
nonadiabatic (sudden) frequency modulations. We derive analytical expressions
for the efficiency and coefficient of performance of the Otto cycle. For the
case of adiabatic driving, we point out that in the low-temperature regime, the
harmonic Otto engine (refrigerator) can be mapped to Feynman's ratchet and pawl
model which is a steady state classical heat engine. For the sudden switch of
frequencies, we obtain loop-like behavior of the efficiency-work curve, which
is characteristic of irreversible heat engines. Finally, we discuss the
behavior of cooling power at maximum $\Omega$-function and indicate the optimal
operational point of the refrigerator.
