1 research outputs found
An efficient branch-and-bound algorithm for submodular function maximization
The submodular function maximization is an attractive optimization model that
appears in many real applications. Although a variety of greedy algorithms
quickly find good feasible solutions for many instances while guaranteeing
(1-1/e)-approximation ratio, we still encounter many real applications that ask
optimal or better feasible solutions within reasonable computation time. In
this paper, we present an efficient branch-and-bound algorithm for the
non-decreasing submodular function maximization problem based on its binary
integer programming (BIP) formulation with a huge number of constraints.
Nemhauser and Wolsey developed an exact algorithm called the constraint
generation algorithm that starts from a reduced BIP problem with a small subset
of constraints taken from the constraints and repeats solving a reduced BIP
problem while adding a new constraint at each iteration. However, their
algorithm is still computationally expensive due to many reduced BIP problems
to be solved. To overcome this, we propose an improved constraint generation
algorithm to add a promising set of constraints at each iteration. We
incorporate it into a branch-and-bound algorithm to attain good upper bounds
while solving a smaller number of reduced BIP problems. According to
computational results for well-known benchmark instances, our algorithm
achieved better performance than the state-of-the-art exact algorithms