A Stochastic Clustering Auction (SCA) for Centralized and Distributed Task Allocation in Multi-agent Teams

This paper considers the problem of optimal task allocation for heterogeneous teams, e.g., teams of heterogeneous robots or human-robot teams. It is well known that this problem is NP hard and hence computationally feasible approaches must develop an approximate solution. This paper proposes a solution via a Stochastic Clustering Auction (SCA) that uses a Markov chain search process along with simulated annealing. The original developments are for a centralized auction, which may be feasible at the beginning of a mission. The problem of developing a distributed auction is also considered. It can be shown that if the distributed auction is such that the auctioneer allocates tasks to optimize the regional cost, then the distributed auction will always decrease the global cost or have it remain constant, which provides the theoretical basis for distributed SCA. Both centralized SCA and distributed SCA are demonstrated via simulations. In addition, simulation results show that by appropriate choice of the parameter in SCA representing the rate of "temperature" decrease, the number of iterations (i.e., auction rounds) in SCA can be dramatically reduced while still achieving reasonable performance. It is also shown via simulation that in relatively few iterations (8 to 35), SCA can improve the performance of sequential or parallel auctions, which are relatively computationally inexpensive, by 6%-12%. Hence, it is complimentary to these existing auction approaches.