  We consider a class of combinatorial optimization problems that emerge in a
variety of domains among which: condensed matter physics, theory of financial
risks, error correcting codes in information transmissions, molecular and
protein conformation, image restoration. We show the performances of two
algorithms, the``greedy'' (quick decrease along the gradient) and
the``reluctant'' (slow decrease close to the level curves) as well as those of
a``stochastic convex interpolation''of the two. Concepts like the average
relaxation time and the wideness of the attraction basin are analyzed and their
system size dependence illustrated.
