A multi-objective optimization scheme based on stochastic global search is developed and used to examine the performance of an HCCI model containing a reduced chemical kinetic mechanism, and to study interrelations among different model responses. A stochastic reactor model of an HCCI engine is used in this study, and dedicated HCCI engine experiments are performed to provide reference for the optimization. The results revealed conflicting trends among objectives normally used in mechanism optimization, such as ignition delay and engine cylinder pressure history, indicating that a single best combination of optimization variables for these objectives did not exist. This implies that optimizing chemical mechanisms to maintain universal predictivity across such conflicting responses will only yield a predictivity tradeoff. It also implies that careful selection of optimization objectives increases the likelihood of better predictivity for these objectives. This may have a particular importance in those practical applications where high degree of predictivity for a limited number of responses is needed, but only a reasonable computational expense can be afforded. These insights are utilized here to develop a highly predictive HCCI model of engine cylinder pressure history, and to evaluate the model ability to predict exhaust emissions. The insight provided by multi-objective optimization on the interplay among different model responses could be of great help for guiding mechanism reduction process and for customizing models based on specific needs.