A Quantum Annealing Approach for Solving Optimal Feature Selection and Next Release Problems

Search-based software engineering (SBSE) tackles critical optimization problems in software engineering, including the next release problem (NRP) and feature selection problem (FSP). Traditional heuristic approaches and integer linear programming (ILP) methods work well for small- to medium-scale problems but face growing computational cost as instances scale up. We investigate quantum annealing (QA) as an optimization subroutine for multi-objective SBSE problems. We propose two QA-based algorithms tailored to different problem scales. For small-scale problems, we reformulate multi-objective optimization (MOO) as single-objective optimization (SOO) using penalty-based mappings for quantum processing. For large-scale problems that exceed current hardware capacity, we employ a decomposition strategy guided by maximum energy impact (MEI) that partitions the problem into smaller sub-QUBOs, integrating QA with a steepest-descent method for local search. Applied to NRP and FSP, our approaches are benchmarked against the heuristic NSGA-II, IBEA, and MOEA/D, as well as the ILP-based ϵ-constraint method. The experimental results reveal that while our methods produce fewer non-dominated solutions than ϵ-constraint, they achieve substantial reductions in execution time. Compared to the evolutionary baselines, our methods achieve competitive solution quality with lower runtime on the instances that they can encode. The penalty-based QUBO formulation fails to reach feasible regions on constraint-dense FSP instances, limiting the current applicability of the approach. QA is a promising but still hardware-limited component for multi-objective SBSE workflows, rather than a wholesale replacement for classical solvers.