Group Role Assignment With Minimized Agent Conflicts

In role-based collaboration (RBC) methodology, eliminating agent conflicts during the role assignment process is crucial for establishing a sustainable cooperative system. However, when agent resources are scarce, assignment strategies aimed at eliminating agent conflicts become infeasible. Consequently, there is a need to select the optimal assignment with a minimal number of agent conflicts, which is essentially a nonlinear bilevel optimization problem. To tackle this issue, we first design the group role assignment with minimized agent conflicts (GRAMAC) model to formalize this problem. It converts this problem into an extended integer linear programming (x-ILP) one and finds the optimal solution. Then, we prove that solving the GRAMAC model is an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathscr {NP} - \mathrm {complete}$ </tex-math></inline-formula> task. Moreover, we identify the sufficient and necessary condition under which the GRAMAC model has the optimal conflict-free solution. Finally, extensive experiments demonstrate that, compared to existing strategies, our proposed method reduces the number of agent conflicts by an average of approximately 30% while ensuring the group performance of the collaborative system.