  In this study we present an optimization method based on the quantum Monte
Carlo diagonalization for many-fermion systems. Using the Hubbard-Stratonovich
transformation, employed to decompose the interactions in terms of auxiliary
fields, we expand the true ground-state wave function. The ground-state wave
function is written as a linear combination of the basis wave functions. The
Hamiltonian is diagonalized to obtain the lowest energy state, using the
variational principle within the selected subspace of the basis functions. This
method is free from the difficulty known as the negative sign problem. We can
optimize a wave function using two procedures. The first procedure is to
increase the number of basis functions. The second improves each basis function
through the operators, $e^{-\Delta\tau H}$, using the Hubbard-Stratonovich
decomposition. We present an algorithm for the Quantum Monte Carlo
diagonalization method using a genetic algorithm and the renormalization
method. We compute the ground-state energy and correlation functions of small
clusters to compare with available data.
