  The fitness level method is an easy-to-use tool for estimating the hitting
time of elitist evolutionary algorithms. Recently, linear lower and upper
bounds by fitness levels have been constructed. But these bounds require
recursive computation, which makes them difficult to use in practice. We
address this shortcoming with a new directed graph (digraph) method that does
not require recursive computation and significantly simplifies the calculation
of coefficients in the lower bound. In the method, we select a sub-digraph and
divide it into fitness levels, then construct an explicit formula for computing
the linear lower bound coefficients using transition probabilities restricted
to the subdigraph. A major advantage of the new method is the derivation of
tight lower bounds on fitness functions with shortcuts, which are difficult to
achieve using previous fitness methods. We use three examples (FullyDeceptive,
TwoMax1 and Deceptive) to demonstrate that each new lower bound is tight, but
previous lower bounds are not. Our work significantly extends the fitness level
method from addressing simple fitness functions without shortcuts to more
complex functions with shortcuts.
