An Anytime Algorithm for Large-scale Heterogeneous Task Allocation

In this paper, we study a large-scale heterogeneous task allocation problem in complex systems. Existing work on task allocation mainly tackles this well-known NP-hard problem from an optimisation perspective, where an exact or approximate solutions can be found after intensive computation. They have not been able to cater for the extra needs of scalability and robustness in large scale complex systems. In this work, we employ a game-theoretic framework to model the studied task allocation problem, and align the objective in task allocation (i.e., system optimality) with the concept of Nash equilibrium in game theory. Our formulation enables the expression of heterogeneity in both agents and tasks, and allows multiple agents to form teams or coalitions to cooperatively perform a task. Based on this formulation, we propose a novel GreedyNE algorithm to efficiently search for a Nash equilibrium solution. The proposed GreedyNE algorithm is a scalable, anytime, and monotonic algorithm, which in turn, makes it robust for the deployment in complex systems. GreedyNE is simple, easy to implement and flexible enough, so that it can also be used as a local search algorithm for improving the quality of any existing allocation solution. By conducting comprehensive experiments, we show that GreedyNE achieves a solution quality as good as the state-of-the-art approximation algorithms, yet with significantly lower computation time.