  The fitness level method is a popular tool for analyzing the hitting time of
elitist evolutionary algorithms. Its idea is to divide the search space into
multiple fitness levels and estimate lower and upper bounds on the hitting time
using transition probabilities between fitness levels. However, the lower bound
generated by this method is often loose. An open question regarding the fitness
level method is what are the tightest lower and upper time bounds that can be
constructed based on transition probabilities between fitness levels. To answer
this question, {\color{red} we combine drift analysis with fitness levels and
define the tightest bound problem as a constrained multi-objective optimization
problem subject to fitness levels.} The tightest metric bounds from fitness
levels are constructed and proven for the first time. Then linear bounds are
derived from metric bounds and a framework is established that can be used to
develop different fitness level methods for different types of linear bounds.
The framework is generic and promising, as it can be used to draw tight time
bounds on both fitness landscapes without and with shortcuts. This is
demonstrated in the example of the (1+1) EA maximizing the TwoMax1 function
