A Hybrid Continuous Max-Sum Algorithm for Decentralised Coordination

Recent advances in decentralised coordination of multiple agents have led to the proposal of the max-sum algorithm for solving distributed constraint optimisation problems (DCOPs). The max-sum algorithm is fully decentralised, converges to optimality for problems with acyclic constraint graphs and otherwise performs well in empirical studies. However, it requires agents to have discrete state spaces, which are of practical size to conduct repeated searches over. In contrast, there are decentralised non-linear optimisation methods that are capable of accurately finding local optima over multi-dimensional continuous state spaces, however these methods are not designed to navigate complex interactions between local constraints in order to find globally optimal solutions. Given this background, in this paper we tackle the problem of coordinating multiple decentralised agents with continuous state variables. Specifically we propose a hybrid approach, which combines the max-sum algorithm with continuous non-linear optimisation methods. We show that, for problems with acyclic factor graph representations, for suitable parameter choices, our proposed algorithm converges to a state with utility close to the global optimum. We empirically evaluate our approach for cyclic constraint graphs in a multi-sensor target classification problem, and compare its performance to the discrete max-sum algorithm, as well as a non-coordinated approach and the distributed stochastic algorithm (DSA). We show that our hybrid max-sum algorithm outperforms the non-coordinated algorithm, DSA and discrete max-sum considerably. Furthermore, the improvements in outcome over discrete max-sum come without significant increases in running time nor communication cost