An efficient algorithm for task allocation with multi-agent collaboration constraints

In this paper, we study a heterogeneous task assignment problem with a constraint on the number of collaborators. Existing work on task allocation pays little attention to the task's requirement on the number of collaborators, so most algorithms may not work at all when this constraint is taken into account. First, this paper proposes a new task utility function that makes the traditional task allocation algorithm work properly. Then, this task allocation problem is modeled based on a game and an algorithm named IGreedyNE is proposed to solve this problem. IGreedyNE is a greedy strategy-based algorithm that allows multiple agents to change their game strategy simultaneously in each iteration, so it takes fewer iterations and less time to solve. Finally, we also show that the IGreedyNE algorithm converges in a finite number of iterations and returns a Nash equilibrium solution. We have performed numerous simulations, and the statistical results show that our proposed utility function can effectively handle the constraint on the number of cooperators, and our proposed IGreedyNE algorithm has a significant advantage in the speed of solving.