An endoreversible isothermal-heating modified (IHM) Miller-cycle model is established firstly herein. Expressions for thermal efficiency, power, power density ( \(P_{{\text{d}}}\) ) and ecological function ( \(E\) ) are derived. Influences of pre-expansion ratio, maximum temperature-ratio and modified Miller-cycle ratio ( \(\gamma_{{\text{M}}}\) ) on cycle performance are analyzed. Secondly, performances of IHM Miller-cycle and traditional Miller-cycle are compared. Compared with traditional Miller-cycle, \(P_{{\text{d}}}\) , \(E\) , thermal efficiency and power of IHM Miller-cycle increase by 12.94%, 3.52%, 19.37% and 14.18%, respectively under the same parameters. The IHM for Miller-cycle is meaningful. Thirdly, multi-objective optimizations (MOOs) are conducted. Compression-ratio is taken as optimization variable, and \(P_{{\text{d}}}\) , \(E\) , power and efficiency are taken as optimization objectives, NSGA-II algorithm is applied to optimize different combinations of multi-objective and single-objective, and deviation index is used to compare optimization results of three decision-making methods to find the best solution. Totally fifteen combinations, including one four-objective, four tri-objective, six bi-objective and four single-objective optimizations, are performed. Results show that, when pre-expansion ratio, maximum temperature-ratio and \(\gamma_{{\text{M}}}\) increase, \(P_{{\text{d}}}\) and \(E\) are improved. Optimal compression-ratio of MOO is between 8.9 and 20.4, mainly between 8.9 and 13.5. The most important innovation herein is establishing IHM Miller-cycle model and completing performance analyses and MOOs. The results can provide guidelines for designing actual engines.
