Market-Based Algorithms for Allocating Complex Tasks

Introduction It is often important to coordinate teams of cooperative agents in a distributed manner. We study how to assign tasks to cooperative agents so that the resulting team cost is small (that is, team performance is high). Market-based mechanisms are promising distributed task-allocation methods. Robotics researchers have recently studied how to use sequential single-item (SSI) auctions to allocate simple tasks to agents (Tovey et al. 2005), where simple tasks need to be performed by exactly one agent. In this paper, we study how to allocate complex tasks to agents, where complex tasks (different from (Zlot 2006)) need to be performed by several agents simultaneously. Our motivating example is multi-agent routing, where the tasks are to visit targets in the plane. Each target needs to be visited by a given number of agents that depends on the target. Simple targets need to be visited by only one agent, while complex targets need to be visited by several agents simultaneously. For example, large fires can be extinguished only with several fire engines, and heavy objects can be moved only with several robots. The agent cost is the smallest sum of travel and wait times needed by an agent to visit all targets assigned to it. The team cost is the largest agent cost of any agent (that is, the task-completion time). Our objective is to determine which targets each agent should visit and when it should visit them so that the team cost is minimal. Most existing research treats task allocation as a complete set partitioning or set covering problem where the cost of performing a complex task with a given set of agents is either pre-defined (Abdallah and Lesser 2004) or easy to calculate (Shehory and Kraus 1998). In the context of multi-agent routing, however, the agent cost of visiting an additional complex target depends not only on the target and the agent that visits it but also on the visit time. The most closely related research to our work is some of our own previous research for the special case where each agent can visit at most one complex target (Zheng and Koenig 2008).