An exact solver for submodular knapsack problems
Year: 2026
Type: article
Abstract: We study the problem of maximizing a monotone increasing submodular function over a set of weighted elements subject to a knapsack constraint. Although this problem is NP-hard, many applications require exact solutions, as approximate solutions are often insufficient in practice. To address this need, we propose an exact branch-and-bound algorithm tailored for the submodular knapsack problem and introduce several acceleration techniques to enhance its efficiency. We evaluate these techniques on artificial instances of three benchmark problems as well as on instances derived from real-world data. We compare the proposed solver with two solvers by Sakaue and Ishihata(2018) as well as with a branch-and-cut algorithm implemented using Gurobi that solves a binary linear reformulation of the submodular knapsack problem, demonstrating that our methods are highly successful. • An exact branch-and-bound algorithm for the submodular knapsack problem. • We developed several acceleration techniques for this branch-and-bound algorithm. • Computational experiments show that the acceleration techniques are highly effective.
Source: Computers & Operations Research
Authors: Sabine Münch, Stephen Raach
Institution: Universität Trier
Language: English
Subfield: Industrial and Manufacturing Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,570
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7124907986