This paper establishes an irreversible Dual-Miller cycle (DMC) model with the heat transfer (HT) loss, friction loss (FL) and other internal irreversible losses. To analyze the effects of the cut-off ratio ( ) and Miller cycle ratio ( ) on the power output ( ), thermal efficiency ( ) and ecological function ( ), obtain the optimal and optimal , and compare the performance characteristics of DMC with its simplified cycles and with different optimization objective functions, the , and of irreversible DMC are analyzed and optimized by applying the finite time thermodynamic (FTT) theory. Expressions of , and are derived. The relationships among , , and compression ratio ( ) are obtained by numerical examples. The effects of and on , , , maximum power output ( ), maximum efficiency ( ) and maximum ecological function ( ) are analyzed. Performance differences among the DMC, the Otto cycle (OC), the Dual cycle (DDC), and the Otto-Miller cycle (OMC) are compared for fixed design parameters. Performance characteristics of irreversible DMC with the choice of , and as optimization objective functions are analyzed and compared. The results show that the irreversible DMC engine can reach a twice-maximum power, a twice-maximum efficiency, and a twice-maximum ecological function, respectively. Moreover, when choosing as the optimization objective, there is a 5.2% of improvement in while there is a drop of only 2.7% in compared to choosing as the optimization objective. However, there is a 5.6% of improvement in while there is a drop of only 1.3% in compared to choosing as the optimization objective.