Group Multirole Assignment With General Conflict

Role-based collaboration (RBC) is a novel problem-solving paradigm to facilitate collaboration. Group multirole assignment (GMRA), an extension of group role assignment (GRA), is a critical step in the RBC process, enabling the formation of efficient collaborative teams by reasonably assigning roles to agents. Recognized as a significant determinant impacting assignment and collaboration, conflict has been delineated and incorporated into GMRA. Nevertheless, the specified conflict is characterized as an oppositional conflict (OC), signifying that conflicting agents are engaged in conflict across the entirety of the role set. Rather than completely OC, which is highly specific, a more prevalent relationship involves conflict in certain aspects while remaining conflict-free in others. Therefore, we propose the concept of general conflict (GC) to describe the more common and realistic conflict relationship, offering a broader and novel perspective to depict conflict relationships. Then, we formalize these two problems by considering GC avoidance in GRA and GMRA, called GRA with GC (GRAGC) and GMRA with GC (GMRAGC), respectively. Furthermore, we establish the necessary conditions for the GRAGC and GMRAGC problems through a graph-theoretical lens, accompanied by a thorough analysis of their mathematical nature. Additionally, we propose practical solutions and refine methodologies to address both problems. The effectiveness of the improved algorithms utilizing necessary conditions is verified by simulations, which also provides evidence supporting the advantages of conflict avoidance.