Universality of efficiency at unified trade-off optimization

We calculate the efficiency at the unified trade-off optimization criterion (the so-called maximum Omega criterion) representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials, and demonstrate that the linear coefficient 3/4 and quadratic coefficient 1/32 of the efficiency at maximum Omega are universal for heat engines under strong coupling and symmetry conditions. It is further proved that the conclusions obtained here also apply to the ecological optimization criterion.