A \textit{test instance generator} (an \textit{instance generator} for short)
for MAX2SAT is a procedure that produces,
given a number $n$ of variables,
a 2-CNF formula $F$ of $n$ variables
(randomly chosen from some reasonably large domain),
and simultaneously provides one of the optimal solutions for $F$.
We propose an outline to design an instance generator
using an expanding graph of a certain type,
called here an ``exact $1/2$-enlarger''.
We first show a simple algorithm for constructing an exact $1/2$-enlarger,
thereby deriving one concrete polynomial-time instance generator \texttt{GEN}.
We also show that an exact $1/2$-enlarger can be obtained with high probability
from graphs \textit{randomly} constructed.
From this fact, we propose another type of instance generator \texttt{RGEN};
it produces a 2-CNF formula with a solution
which is optimal for the formula with high probability.
However, \texttt{RGEN} produces less structured formulas and much larger class of 
formulas than \texttt{GEN}'s.
In fact, we prove the NP-hardness of MAX2SAT over the set of 2-CNF formulas
produced by \texttt{RGEN}.