Large-scale, Dynamic and Distributed Coalition Formation with Spatial and Temporal Constraints

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task allocation problem in which few agents have to perform many tasks, each with its deadline and workload. To maximize the number of completed tasks, the agents need to cooperate by forming, disbanding and reforming coalitions. The original mathematical programming formulation of the CFSTP is difficult to implement, since it is lengthy and based on the problematic Big-M method. In this paper, we propose a compact and easy-to-implement formulation. Moreover, we design D-CTS, a distributed version of the state-of-the-art CFSTP algorithm. Using public London Fire Brigade records, we create a dataset with $347588$ tasks and a test framework that simulates the mobilization of firefighters in dynamic environments. In problems with up to $150$ agents and $3000$ tasks, compared to DSA-SDP, a state-of-the-art distributed algorithm, D-CTS completes $3.79\% \pm [42.22\%, 1.96\%]$ more tasks, and is one order of magnitude more efficient in terms of communication overhead and time complexity. D-CTS sets the first large-scale, dynamic and distributed CFSTP benchmark.

Multi-Agent Routing and Scheduling Through Coalition Formation

In task allocation for real-time domains, such as disaster response, a limited number of agents is deployed across a large area to carry out numerous tasks, each with its prerequisites, profit, time window and workload. To maximize profits while minimizing time penalties, agents need to cooperate by forming, disbanding and reforming coalitions. In this paper, we name this problem Multi-Agent Routing and Scheduling through Coalition formation (MARSC) and show that it generalizes the important Team Orienteering Problem with Time Windows. We propose a binary integer program and an anytime and scalable heuristic to solve it. Using public London Fire Brigade records, we create a dataset with 347588 tasks and a test framework that simulates the mobilization of firefighters. In problems with up to 150 agents and 3000 tasks, our heuristic finds solutions up to 3.25 times better than the Earliest Deadline First approach commonly used in real-time systems. Our results constitute the first large-scale benchmark for the MARSC problem.

Anytime and Efficient Coalition Formation with Spatial and Temporal Constraints

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task allocation problem where the agents are cooperative and few, the tasks are many, spatially distributed, with deadlines and workloads, and the objective is to find a schedule that maximises the number of completed tasks. The current state-of-the-art CFSTP solver, the Coalition Formation with Look-Ahead (CFLA) algorithm, has two main limitations. First, its time complexity is quadratic with the number of tasks and exponential with the number of agents, which makes it not efficient. Second, its look-ahead technique is not effective in real-world scenarios, such as open multi-agent systems, where new tasks can appear at any time. Motivated by this, we propose an extension of CFLA, which we call Coalition Formation with Improved Look-Ahead (CFLA+). Since CFLA+ inherits the limitations of CFLA, we also develop a novel algorithm to solve the CFSTP, the first to be both anytime and efficient, which we call Cluster-based Coalition Formation (CCF). We empirically show that, in settings where the look-ahead technique is highly effective, CCF completes up to 20% (resp. 10%) more tasks than CFLA (resp. CFLA+) while being up to four orders of magnitude faster. Our results affirm CCF as the new state-of-the-art CFSTP solver.