Solving Subset Sum Problems using Binary Optimization with Applications
in Auditing and Financial Data Analysis
Abstract
Many applications in automated auditing and the analysis and consistency
check of financial documents can be formulated in part as the subset sum
problem: Given a set of numbers and a target sum, find the subset of
numbers that sums up to the target. The problem is NP-hard and classical
solving algorithms are therefore not practical to use in real
applications. We tackle the problem as a QUBO (quadratic unconstrained
binary optimization) problem and show how gradient descent on Hopfield
Networks reliably finds solutions for both artificial and real data. We
give an outlook for the application of specialized hardware and quantum
algorithms.