We present a novel anytime heuristic (ALMA), inspired by the human principle of altruism, for solving the assignment problem. ALMA is decentralized, completely uncoupled, and requires no communication between the participants. We prove an upper bound on the convergence speed that is polynomial in the desired number of resources and competing agents per resource; crucially, in the realistic case where the aforementioned quantities are bounded independently of the total number of agents resources, the convergence time remains constant as the total problem size increases. We have evaluated ALMA under three test cases: (i) an anti-coordination scenario where agents with similar preferences compete over the same set of actions, (ii) a resource allocation scenario in an urban environment, under a constant-time constraint, and finally, (iii) an on-line matching scenario using real passenger-taxi data. In all of the cases, ALMA was able to reach high social welfare, while being orders of magnitude faster than the centralized, optimal algorithm. The latter allows our algorithm to scale to realistic scenarios with hundreds of thousands of agents, e.g., vehicle coordination in urban environments.
In reality, a centralized coordinator is not always available, and if so, it has to know the utilities of all the participants, which is often not feasible. In the literature of the assignment problem, there also exist several decentralized algorithms (e.g., @cite_18 @cite_33 @cite_3 @cite_13 which are the decentralized versions of the aforementioned well-known centralized algorithms). However, these algorithms require polynomial computational time and polynomial number of messages (such as cost matrices @cite_33 , pricing information @cite_3 , or a basis of the LP @cite_13 , etc.). Yet, agent interactions often repeat no more than a few hundreds of times. To the best of our knowledge, a decentralized algorithm that requires no message exchange (i.e., no communication network) between the participants, and achieves high efficiency, like ALMA does, has not appeared in the literature before. Let us stress the importance of such a heuristic: as autonomous agents proliferate, and their number and diversity continue to rise, differences between the agents in terms of origin, communication protocols, or the existence of sub-optimal, legacy agents will bring forth the need to collaborate without any form of explicit communication @cite_21 . Finally, inter-agent communication creates high overhead as well.
@cite_18 @cite_33 @cite_21 @cite_3 @cite_13
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In this work we address the Multi-Robot Task Allocation Problem (MRTA). We assume that the decision making environment is decentralized with as many decision makers (agents) as the robots in the system. To solve this problem, we developed a distributed version of the Hungarian Method for the assignment problem. The robots autonomously perform different substeps of the Hungarian algorithm on the base of the individual and the information received through the messages from the other robots in the system. It is assumed that each robot agent has an information regarding its distance from the targets in the environment. The inter-robot communication is performed over a connected dynamic communication network and the solution to the assignment problem is reached without any common coordinator or a shared memory of the system. The algorithm comes up with a global optimum solution in O(n3) cumulative time (O(n2) for each robot), with O(n3) number of messages exchanged among the n robots. In this paper, a novel decentralized task allocation algorithm based on the Hungarian approach is proposed. The proposed algorithm guarantees an optimal solution as long as the agent network is connected, i.e., the second smallest eigenvalue of the Laplacian matrix of the agent graph is greater than zero. In order to show the motivation of the proposed algorithm, the original centralized auction and Hungarian algorithms are compared in terms of the converging speed versus the number of agents. The result shows the superiority of the Hungarian algorithm in scalability over the auction algorithm. Then, the performance of the proposed decentralized Hungarian-Based algorithm (DHBA) is compared with the consensus-based auction algorithm (CBAA) under different situations, including different number of agents and different network topologies. The simulation results show that DHBA outperforms CBAA in all cases on the basis of the converging speed, the optimality of assignments, and the computational time. As autonomous agents proliferate in the real world, both in software and robotic settings, they will increasingly need to band together for cooperative activities with previously unfamiliar teammates. In such ad hoc team settings, team strategies cannot be developed a priori. Rather, an agent must be prepared to cooperate with many types of teammates: it must collaborate without pre-coordination. This paper challenges the AI community to develop theory and to implement prototypes of ad hoc team agents. It defines the concept of ad hoc team agents, specifies an evaluation paradigm, and provides examples of possible theoretical and empirical approaches to challenge. The goal is to encourage progress towards this ambitious, newly realistic, and increasingly important research goal. The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems? size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multi-hop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one. In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is not unique, or will determine infeasibility or unboundedness of the problem. We establish how the multi-agent assignment problem can be efficiently solved by means of our distributed simplex algorithm. We provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph.