Quantifying the Search Space for Multi-Agent System (MAS) Decision-Making Organizations

. Suzanne Barber and Matthew T. MacMahon

When a group comes together to pursue a goal, how should the group interact? Both theory and practice show no single organization always performs best; the best organization depends on context. Therefore, a group should adapt how it interacts to fit the situation. In a Multi-Agent System (MAS), a Decision-Making Framework (DMF) specifies the allocation of decision-making and action-execution responsibilities for a set of goals among agents within the MAS. Adaptive Decision-Making Frameworks (ADMF) is the ability to change the DMF, changing which agents are responsible for decision-making and action-execution for a set of goals. Prior research embedded ADMF capabilities within an agent to search, evaluate, select, and establish a DMF for a given situation and given goal(s) the agent sought to achieve. Using the ADMF capability, the Multi-Agent System improved system performance compared to using the same, static Decision-Making Framework (DMF) in all situations. While the motivation for an agent possessing ADMF has been proven and an example MAS system with agents employing ADMF has been built, interesting questions arise as one investigates the ability of an agent to find the best, or near optimal or sufficient DMF among all the possible DMFs. This paper presents initial exploration of this investigation by asking, How large is the DMF search space for an agent? This paper presents tight computational bounds on the size of the search space for Decision-Making Frameworks by applying combinatorial mathematics. The DMF representation is also shown to be a factor in the size of this search space.

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