  This paper presents the formulation of a combinatorial optimization problem
with the following characteristics: i.the search space is the power set of a
finite set structured as a Boolean lattice; ii.the cost function forms a
U-shaped curve when applied to any lattice chain. This formulation applies for
feature selection in the context of pattern recognition. The known approaches
for this problem are branch-and-bound algorithms and heuristics, that explore
partially the search space. Branch-and-bound algorithms are equivalent to the
full search, while heuristics are not. This paper presents a branch-and-bound
algorithm that differs from the others known by exploring the lattice structure
and the U-shaped chain curves of the search space. The main contribution of
this paper is the architecture of this algorithm that is based on the
representation and exploration of the search space by new lattice properties
proven here. Several experiments, with well known public data, indicate the
superiority of the proposed method to SFFS, which is a popular heuristic that
gives good results in very short computational time. In all experiments, the
proposed method got better or equal results in similar or even smaller
computational time.
