Optimal Distributed Market-Based Planning for Multi-Agent Systems with Shared Resources

Market-based algorithms have become popular in collaborative multi-agent planning due to their simplicity, distributedness, low communication requirements, and proven success in domains such as task allocation and robotic exploration. Most existing marketbased algorithms, however, suffer from two main drawbacks: resource prices must be carefully handcrafted for each problem domain, and there is no guarantee on final solution quality. We present an optimal marketbased algorithm, derived from a mixed integer program formulation of planning problems. Our method is based on two wellknown techniques for optimization: DantzigWolfe decomposition and Gomory cuts. The former prices resources optimally for a relaxed version of the problem, while the latter introduces new derivative resources to correct pricing imbalances that arise from the relaxation. Our algorithm is applicable to a wide variety of multi-agent planning domains. We provide optimality guarantees and demonstrate the effectiveness of our algorithm in both centralized and distributed settings on synthetic planning problems.