Anytime and Efficient Coalition Formation with Spatial and Temporal Constraints

Abstract

The Coalition Formation with Spatial and Temporal constraints Problem (CFSTP) is a multi-agent task scheduling problem where the tasks are spatially distributed, with deadlines and workloads, and the number of agents is typically much smaller than the number of tasks. Thus, the agents have to form coalitions in order to maximise the number of completed tasks. The state-of-the-art CFSTP solver, the Coalition Formation with Look-Ahead (CFLA) algorithm, has two main limitations. First, its time complexity is exponential with the number of agents. Second, as we show, 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. In this work, we study its design and define an extension, called Coalition Formation with Improved Look-Ahead ($\text {CFLA}2$), which achieves better performance. Since we cannot eliminate the limitations of CFLA in $\text {CFLA}2$, we also develop a novel algorithm to solve the CFSTP, the first to be simultaneously anytime, efficient and with convergence guarantee, called Cluster-based Task Scheduling (CTS). In tests where the look-ahead technique is highly effective, CTS completes up to 30% (resp. 10%) more tasks than CFLA (resp. $\text {CFLA}2$) while being up to four orders of magnitude faster. Our results affirm CTS as the new state-of-the-art algorithm to solve the CFSTP.