Thermal optimization is very important for improving the performances of thermal systems.In engineering,the entropy generation minimization (EGM) has been widely used to optimize and evaluate the performances of thermal systems.However,the consistency between the EGM and the optimization objective should be specified when the EGM is used.In this paper,we discuss the view angle of irreversibility of entropy generation,and show that entropy generation directly reflects the exergy destruction or the ability loss of doing work.As the design objective in a thermal system is not often consistent with the view angle of irreversibility of entropy generation,the EGM may not lead to the optimal value of the design objective.In heat transfer and heat-work conversion,the inconsistence between the design objectives and the EGM is shown with some examples,and the applicability of the EGM is found to be conditional.The "entropy generation paradox" in heat exchanger analyses is also discussed,and it is shown that there is no direct monotonic relation between the minimum entropy generation rate and the best heat transfer performance of heat exchangers.