Local Search-Based Anytime Algorithms for Continuous Distributed Constraint Optimization Problems

Dear Editor, The distributed constraint optimization problems (DCOPs) [1]–[3] provide an efficient model for solving the cooperative problems of multiagent systems, which has been successfully applied to model the real-world problems like the distributed scheduling [4], sensor network management [5], [6], multi-robot coordination [7], and smart grid [8]. However, DCOPs were not well suited to solve the problems with continuous variables and constraint cost in functional form, such as the target tracking sensor orientation [9], the air and ground cooperative surveillance [10], and the sensor network coverage [11]. Therefore, the continuous DCOPs (C-DCOPs) [12] have been proposed to model such problems with continuous variables, whose goal is that all agents coordinate with each other to find the assignment to all variables such that it minimizes the sum of all constraints. Correspondingly, researchers propose various C-DCOP algorithms to deal with the modification of the C-DCOP formulation. Note that the anytime property is crucial for a C-DCOP algorithm since it guarantees to obtain the monotonic solutions in real-time. Specifically, an anytime algorithm should fulfill two conditions: 1) It can return a valid solution even if the agents are interrupted at any time before the algorithm terminates [1]; 2) The solution quality can only remain the same or increase if more steps are performed [13]. Existing C-DCOP algorithms either cannot guarantee the anytime property or utilize breadth first search (BFS) pseudo-trees, which results in privacy violations [14].