  The construction of efficient thermal engines operating at finite times
constitutes a fundamental and timely topic in nonequilibrium thermodynamics. We
introduce a strategy for optimizing the performance of Brownian engines, based
on a collisional approach for unequal interaction times between the system and
thermal reservoirs. General (and exact) expressions for thermodynamic
properties and their optimized values are obtained, irrespective of the driving
forces, asymmetry, the temperatures of reservoirs and protocol to be maximized.
Distinct routes for the engine optimization, including maximizations of output
power and efficiency with respect to the asymmetry, force and both of them are
investigated. For the isothermal work-to-work converter and/or small difference
of temperature between reservoirs, they are solely expressed in terms of
Onsager coefficients. Although the symmetric engine can operate very
inefficiently depending on the control parameters, the usage of distinct
contact times between the system and each reservoir not only can enhance the
machine performance (signed by an optimal tuning ensuring the largest gain) but
also enlarges substantially the machine regime operation. The present approach
can pave the way for the construction of efficient Brownian engines operating
at finite times.
