A QUBO Framework for Team Formation
Karan Vombatkere, Evimaria Terzi, Theodoros Lappas
TL;DR
This work proposes a unified QUBO framework for the TeamFormation problem, aiming to maximize task coverage while minimizing expert costs across three cost definitions. It formulates the problem as a QUBO using an augmented solution vector $\mathbf{y} = (\mathbf{s} \;||\; \mathbf{x})$ and derives specific QUBO encodings, including a detailed Max-k-Cover formulation. Two general-purpose solvers are evaluated: a classical QUBO solver ($Qsolver$) and a GNN-based approach ($QUBO-GNN$) that learns transferable embeddings to solve related instances, achieving competitive performance and enabling transfer learning. Experiments on real-world datasets show that QUBO-based methods often outperform baselines, with Q solver typically delivering the best objective values and QUBO-GNN enabling effective cross-instance transfer via learned skill–expert representations. The work highlights the potential for scalable, transferable, and hardware-accelerated solutions to complex team-formation problems, bridging submodular coverage, cost balancing, and graph-structured coordination.
Abstract
The team formation problem assumes a set of experts and a task, where each expert has a set of skills and the task requires some skills. The objective is to find a set of experts that maximizes coverage of the required skills while simultaneously minimizing the costs associated with the experts. Different definitions of cost have traditionally led to distinct problem formulations and algorithmic solutions. We introduce the unified TeamFormation formulation that captures all cost definitions for team formation problems that balance task coverage and expert cost. Specifically, we formulate three TeamFormation variants with different cost functions using quadratic unconstrained binary optimization (QUBO), and we evaluate two distinct general-purpose solution methods. We show that solutions based on the QUBO formulations of TeamFormation problems are at least as good as those produced by established baselines. Furthermore, we show that QUBO-based solutions leveraging graph neural networks can effectively learn representations of experts and skills to enable transfer learning, allowing node embeddings from one problem instance to be efficiently applied to another.